Diether de La Motte-The Study of Harmony
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The
of Harmony
Study
An Historical Perspective By
de
Diether
la
Motte
Translated from the OriginalGerman
Jeffrey
L.
Prater
TABLE OF
About this Book, the Author, Author's
Preface
Author's
Preface
vii
Translator \342\200\242\342\226\240
xv
Foreword
CHAPTER
ONE: Harmony
ca. 1600 (Lasso-Palestrina-Lechner-Cavalieri)
CHAPTER
TWO:
between
Harmony
l.The
Fifth
Perfect
2.First Inversion
in
Relationship
4.Characteristic
1750(Bach-Handel-Vivaldi-Telemann) 28 Major Keys 42
Triads
51 58
Dissonances
6.TheMinor
75
Tones
5. Non-Harmonic
94 110
Mode
7. Augmented Triads and the 8. The 9-8 SuspensionsApplied
and Leading-Tone
9.
Secondary
10. Secondary
11.
Dominant-Seventh
115
DiminishedSeventh Chords
128
134
in Minor
in Major
and Seventh
16.Chords
from
Borrowed
and Minor
Keys
Secondary Chord as
the
in Minor
Subdominants
a Secondary
Dominant
1810
178
Form-Generating
3. The Leading-Tone 4. Modulation
7.
8. The CHAPTER
Role Seventh
of Harmonic Progressions Chord in Major
Harmony ofSlowIntroduction FOUR: Harmony
Transformation
Sections
189
196 200 210
between 1800and 1828(Beethoven-Schubert)
Triads Related by the Interval of 2. Leading-Tone Relationships 1.
3. Note-for-Note
185 186 187
to the SecondTheme within the DevelopmentSection
Chords
Altered
169
(Haydn-Mozart-Beethoven)
1. Introduction
5. Modulation 6. Modulation
165 176
Minor Mode
CHAPTER THREE:Harmony between1770and 2. The
147 154
Space
14. SecondaryDominants
15.TheDiminished
141
Keys
Sequences of Tonal
Expansion
to the
Triads in MajorKeys
12.Descending-Fifth
13.
Sixth
Neapolitan
Triads Triads
Secondary
1
1700 and
Sonorities
3. Six-Four
ix
xii
Fourth German Edition
to the
Translator's
and
CONTENTS
a Third
215
227 229
1.
between 1830and 1850(Schumann)
FIVE: Harmony
CHAPTER
233
Introduction
Dominant-SeventhChord Progressions Below Triads and Seventh Chords
2. Non-Functional
3.
Added
Thirds
4. Dominant
5. Abridged Dominant Ninth 6. Freedom from the Tonic SIX: Harmony
CHAPTER
1.
3. The
in Opera
(1600-1900) 255
and UnstableHarmony
4. Impending
and Scenes in Italian
in Arias
Leading-Tone
258 Music
6. Dramatic
268
of Conflict
269
Climax
7. Large-Form SEVEN:
Disposition of Tonality
274
between 1857 and 1882(Wagner)
Harmony
278
Introduction
2. Cadences in Atonal Space 3. Setting the Text to Music 4. Wagner's Functionally Free Four-Tone 5. The Tristan Chord
6. Expressive 7. A
1.
Suspension
Model for Analysis
CHAPTER
Figures
278 281 283
Sonorities
292
in Wagner's
Late
of Passagesin Wagner's
EIGHT: Harmony
Late
Works
Works
4. Two
307
309
of Tonal Harmony to Atonality Pathways
313
End
317
Topics in Harmony Harmony (Scriabin,Schonberg)
TEN: Selected
1. Atonal
2.
Sonority
and
Structure
(after
Discussion
of Selected
321
324 327 334
1912)
336 342
(Webern)
3. Classificationof Harmony (Hindemith) 4. Sonority as Theme (Messiaen)
5.
298
as Reminiscence
CHAPTER NINE: Harmony between1900 and 1918 (Debussy) 1. Slendro and Whole-ToneScales 2.Harmonic in the Music of Debussy Texture 3. Mixture-like Sonorities in the Music of Debussy 4. Harmony of Invention Structure as a Unity and Compositional CHAPTER
296
between 1839and 1885(Liszt)
Introduction
2. Tonality
3. The
261 264
Danger
5. Resolution
1.
251
Downward-Resolving
CHAPTER
244
Chords
Paintbrush
Wide
The
2. Stable
240 242
Chords
Ninth
237
346
351 Sonorities
Twentieth-Century
354
361
Table of Functional Symbols
363
Index
VI
About
(translated
and
edited
this Book from the Fourth
German Edition)
of different eras from music vocabulary chapters in this book coverthe harmonic first two chapters deal with the materials of broad musical periods, whereasthe with the exception of a single chapter devoted to harmonic in opera, later chapters, practices focuson the innovations of specific composers and their personalharmonic The historical styles. treatment of this topic avoids of the anonymous and artless rules which are many regularly of harmony to the study associated with \"strict\" (stronger Satz). The part-writing approaches is offered as an alternative to the many texts which :AnHistorical StudyofHarmony Perspective \"rules\" of harmony without reference to actual music. All of the rules and principles present found in this book were derived from an examination of numerous musical examples, and each under Instead of the specific periodor composer examplewaschosento be representative study. of a music theorytext, thisbookis a study of musicalpractice,where harmonic materials actually and musical contexts. and techniques are presented within their historical appropriate This text is primarily to Nevertheless, musical exercises included analysis-centered. extra drill and practice for those who wish to thoroughly assimilate the materials and provide to do the musical examples in order techniques presented in each chapter. It is not necessary to benefit from this text, however. Many readers will find this book to be an excellentsourcefor of harmonic materials or a tool for building a better understanding ofthe rolesharmony review in Western music overthe past four centuries. has played This book is not limited the only to compositions that employ functional harmony, although share of this book. It also coversa number of important approaches to such piecestakethe texts up to this point have neglected. topics from the twentieth century, which many The An Historical Perspectiveby Dietherdela Motte has been Study of Harmony: The German translated into Finnish, Italian, Portugese, Polish,Swedish,andnow English. Japanese, ten
The
history.
The
are
largest
edition is
also available
in braille.
About
the Author
with Diether dela Motte was born in 1928 in Bonn. He studiedcomposition Wilhelm Maler at the NordwestdeutscheMusikakademiein Detmold summer courses at Darmstadt and attended under Leibowitz, Fortner and Messiaen. He was appointedlecturerat the Evangelische Krenek, in Diisseldorf (1950).From 1955 he has also been active as a music Landeskirchenmusikschule critic. Between 1959 and 1962 he was a reader/reviewerfor the publishing house of Schott. In 1962 de la Motte was lecturer and then professor (1964)at the Hamburg appointed in Musikhochschule. He was then elected vice-president of the Free Academy of the Arts at the Hochschule fur Musik und 1972. In 1982 hewas appointedProfessor of Music Hamburgin Theater in Hannover, and in March of 1988 he took the post of Professorof Composition and Austria. He has written operas,orchestraworks, Theory at the Hochschulefur Musikin Vienna, and recorded compositions. In chamber, choral, piano and organ works and has many published addition to his Study written a number he has published a text on counterpoint, of Harmony, of important article s s on music and has several of journal theory, analyse maj or works. published Vll
About
Translator
the
he is where Jeffrey Prater is a member of the music faculty at Iowa State University, Associate Professor ofMusicandAssociateChair of the Music Theory and Composition Division. Bornin Endicott, from the University New of York, he received the Ph.D.in MusicComposition
Iowa, the Masterof
State University,and his baccalaureatedegree his Richard teachers are William University. Among Bergsma, Hervig, H. Owen he held faculty positions at the Reedand Gary White. Before coming to Iowa State University, of Wisconsin Center-Marinette and Northern MichiganUniversity. University Dr. Prater a strong interest in musical analysis,analysis for the performing pursues lectures and pedagogy of music theory. Hehasregularly and musician, and the history presented an acclaimed article on \"The Great War's Effect papers to professional meetings,and haswritten on Schonberg's Developmentof the Twelve-Tone Method\" (College Music Symposium,1986).He has also been active as a program annotator for the Des Moines Symphony and a reviewer of music textbooks and scholarly works. As a composer, Prater has written and published works in a variety of genres and has been the recipientof numerous awards and commissions grants, for composition. le ave from Iowa the 1988-89 academic year, Prater receiveda faculty improvement During State University. where he began the translation He spent his leave time in northern Germany, from
Iowa
Music
degree
from Michigan
State
ofthis and another
book
on music.
viii
Author's Preface Which different
should be doubled?
first-inversion triad we are likely to texts,
of a
pitch harmony
If
different
ten
find
an answer in ten which lie somewhere
we seek
answers,
and Moser (\"all betweenthe extremepositionsof Bumke (\"the third should never be doubled\,1") We face the same problem if our question is about three doubling possibilities are possible\.2") if they hidden According to Bolsche,hiddenparallelsare incorrect parallel perfect intervals. forbids the two upper voices.3Lemacher-Schroeder or between occur between the lowervoices when all the voices move in the samedirection.\"4 them only, \"if the upper voices leap, for example, one case of hidden and Riemann holds that all Dachs-Sohner only special parallels,5 prohibits hidden parallelsare forbidden.6 the could be correct. The problemi s,that In specific cases, any of these individual positions from different musical examples. Furthermore, authors developed their rules and prohibitions the based these examples without sharing always generalizations they made systematic
examples
reader.
the
with
The so-called
\"strict\"
part-writing
employed as the basis for the require musicianshipexaminations
was never
example,
more
writing
three
than
Distler [whose
(strenger
style
musical
actual
to write
student
parallel
books Satz) presented in many harmony Nevertheless, nearly all compositions.
exercisesin the \"strict\"
is judged
fifths
to be
style
unsatisfactory).
(where,
for
Even Hugo
his are full of contradictions to the \"strict\" own taught compositions style] J students by this method, nobly calling it \"exercisesforthe study of harmony\" (Harmonielehresatz) to name only a single example,Distler requiresthe In one of his part-writing assignments, chord. Although this was only first considered a student to include a dominant-ninth sonority in a strict preto be written discretechord in the time of Schumann, the assignmentis otherwise B ach chorale of the reasons for this stylistic style. Nowhere in Distler's text is thereany mention however.
mixture,
exercises do not aid, but hindera good music-history education (it is a of harmony the study have not protested!). Furthermore, limiting before and after the periods to the \"strict\" written also tends to lock-out the study of music style the main The \"strict\" also ensnares dominated style composers, who shoulder by tonal harmony. often into a conformity with arbitrary rules that responsibility of teaching composition, Instrumental exams take placeon the stage, whereas entombs their individuality. effectively and lab: \"modulate from to as quickly harmony exams are heldin the theory the member barks! as [or assistant] junior faculty teaching convincingly possible,\" Such
wonderthat
pedagogical
historians
music
Harmonielehre (Leipzig: C. Mersburger, 1927). Joachim Moser, Allgemeine Musiklehre (Berlin: de Gruyter, 1940).
\342\226\240^Cfustav Bumcfce, 2
Hans
JfranzfiSisclie, 55).
Ofiungen
4Heinrich Lemacher 6 6
'
Michael
Dachs and
und'AufgaBen
and
Hannlng
Paul
SShner,
Hugo
Riemann, Handbuck
Hugo
Distler,
Funktionelle
der Harmonielehre,
zum. Stadium
Schroeder, Formenlehre Harmonielehre
der Harmonielehre,
30th
derKunst Musik
ed. (Leipzig:
(Cologne:
Breitkopf
Gerig, 1962).
(Munich: Kosel-Pustet,1951). 9th ed. (Leipzig:
Harmonielehre (Kasseland IX
Basel:
Breitkopf
Barenreiter,
und
Hartel,
1941).
1921).
und
Hartel,
time in history for the important years has been the most is so style. Furthermore, the study of these changes to understand has favored a \"strict\" fascinating, that it is difficult why the teaching ofharmony The employment is particularly of \"strict-style\" methods approach. problematic, when we considerthe major role that harmony has played as an agent of these stylistic changes. The \"strict\" even modeled after the music of style, easy to present and correct,is not usually though the greatest such as Hafiler,Praetoriusand Osiander, but rather, on composers of composers, lesser that \"strict\" chorale-style somewhat historical It is an outrage importance. exercises, which chordal sonorities from the Romantic to be presented as contain continue era, frequently the fundamental medium of harmonic music teachers, conductors, training for future instrumentalists and opera which students face such exercises is often singers. The joylessness with the silent methods. comment on the pedagogical effectivenessof these of remain better sources than this book, if one traditional manuals Certainly, harmony it is my wishesonly to prepare for the usual [German]competency examinations. Nevertheless, music schools to offer pedagogical approaches(and hope that this text will encourage in actual more closely follow the artistic practicesfound music. Modulation and its examinations)that various the course of history (with the differences in techniques exercises), during appropriate ca. 1600 and the time of Bach,the organ-mixture harmony betweenthosein practice techniques the special problemsdealingwith harmony in opera, Liszt's pathway to atonality, of Debussy, the differencesin harmonic four-tone progressions employed by Handel and Mozart,Wagner's i n the form role ofthe cadential Hindemith's sonorities, building progression Mozart, sonority classification harmonic sonorities, etc., would all system, and Schonberg'smethodsof connecting make excellenttopics for short lectures and demonstration at the piano. The materials and exercises found in this book couldbealsousedto design examination questions for those pursuing professionalstudy, and certainly, the analyses and approachesusedin this book would benefit the professional musician, music educator, or music scholar. the very beginning, the great composersare the only master in this book. I From teachers have not invented of the rules or I have derived each any prohibitions;instead, principle from actual musicalpracticeand have checked the validity of each principleagainst numerous works. This text does not stir together, in the samepot, centuries of harmonic developments, but rather a new pedagogical methodwhich discusses eras and individual composers in presents separate to specific historical developments which self-containedchapters. Each chapter corresponds rules. There are no longer any fixedrulesconcerning yieldcorrespondingchangesin harmonic it is treated differently in Chapter Three than it is in Chapter One. The first-inversion triads; seventh in does not chord major-minor late-Wagner [always] appear as a chord of harmonic and it does not dominant function like it did earlier. In Schonberg's music, tension, alwayscarry the traditional consonances are the intervals that require whereas, in earlier treatment, special considerations. chapters, it was the dissonanttones that required special voice-leading this does not insure easier Although approach may seem somewhat confusing(and it certainly to harmony reading in every case),an historical approach brings the study closer to actual The
past
development and
musical
four-hundred change
of musical
practice.
The compositional exercisesin the first two knowledge, Chapter One introduces a subjectwhich x
chapters has
are isolated from oneanother. To been made available in a harmony
never
my
ca. 1600.8 No longer a strictly art, and not yet bound contrapuntal home the domains of counterpointand between long remainedwithout this fascinating world of harmony has proved to be an effectivestarting Nevertheless, harmony. for this Bach's well-tempered music is shown to be a renunciation of pure point study. This development made possible the invention sonorities. of harmonic [Pythagorean] progressionswhich do not depend upon a nature-bound ideology. In fact, renunciation the of this for great music. ideology providedthe groundwork homophonic The secondchapter, which is the most extensive, comes the closestto other harmony texts. Nevertheless, it takes its direction from works written during the time ofBach and doesnot that was not in use during that period. introduce harmonic The chapters dedicated vocabulary to single composerssuch as Schumann, Wagner, Liszt, and Debussy contain modelsof various which certainly have appearedinthe works of other harmonic approaches composers. Although not covered in this text, the harmony of Brahms, Bruckner, Mussorgsky, etc. couldbe handled in the fashion. I wish to stress that sonorities and progressions, when in similar presented context of musical-historicaldevelopment, become less anonymous and less always for the construction of general rules. Instead,the study of harmony becomes more and more instrumental of homophony,
text\342\200\224a study
to
this
tonality,
a study
music has
of individual
inventiveness.
to systematically Up to this point, harmony texts have attempted bring together all types in its proper context. Theterm of sonorities, it impossible to consider each sonority type making that the textbook has come to mean harmonization exercises, which further harmony implies The widely-held materials presentedmust beusedproperly. doctrine that melodies are invented, but that are simply produced may not have been consciously established, but harmonizations tasks has it been sufficiently It seems to me, that one of the most important neither challenged. the of a harmony course is to point out the vital between individual and creativity relationship development
materials.
of harmonic
the assignments in this book are either excerptsfrom actual works or have been the kind of designedto match the style of the time period or composerin question. Therefore, to chapter. Standard four-voice exercisesare not examples and exerciseschangefrom chapter but their use is limited to the study of those and composers where they can be avoided, styles I am convinced that the large variety of assignment beneficial. materials in this text will be more be more to these assignments may actually enjoyable for students. Going over the solutions the usual semester traditional useful and stimulating than [or more] of writing four-part harmonizations. Most important, the analysesin this text cover a wide range of subjects and materials that can be used as reference points for further study. With three exceptions, the functional used in this text correspondto those symbols symbols must be newly in general use introduced by Wilhelm Maler.9 symbols Only the following or l\302\243v); of Bi or VII7). and tf7 (instead introduced: $ (insteadofBior D\;") 'S>v (insteadofS,?> of sothat the forms these the These were made sonorities changes employed during Baroqueand Classicalerasno longer appear to be derivations ofchordsthat were actually introduced in later of their respective also show the precise functional content symbols periods. The revised sonorities. All of
is indeed coveredin: Eric Wolf, Der vierstimmige points out that early homophony und des Kantionalsatzes zwischen 1590 und 1630 (Wiesbaden:Breitkopf Merkmale review of Harmonielehre by Diether de la Motte (Kassel:Barenreiter, 1976), Hartel, 1965); see Peter Rummenholler, Zeitschrift fur Musiktheorie, Vlll/1 (1977), 48-52. 8
note] One reviewer [Transl. Satz. Die stttistischen homophone
9
Wilhelm
Maler, Beitrag
zur durmolltonalen
Harmonielehre,
XI
13th ed. (Munich:
F.E.C.Leuckart,
1984).
I am indebted to Dr. Wolfgang Therefore, My courage does not carry me past Debussy. and careful not only for his patient and persistentencouragement editing, but above all, insistence that this book continueinto the twentieth century. Now that the work has been I believe that he was correct. A chapter on the sonorities of our own century shows completed, rounds out this study. Special thanks to a continuing of harmonic process development which Sommer for his excellent editorial suggestions. Jiirgen an article with two of entitled \"Pleading for a Reform of Harmony published Pedagogy,\" a greatdeal Birnstein and Clemens Kuhn.10 This article precipitated my former students, Renate of these two helpful of response. I had planned to complete this bookunder the watchful eyes co-workers and critics,but this would have conflicted with the beginning of their teaching careers in Liibeckand Berlin, respectively. So we remained together only until the section on secondary for me to offer Ms. triads in minor keys [Chapter 2.11]. Nevertheless, this is grounds enough Birnstein and Mr.Kuhn the most sincere thanks for being my faithful collaborators up to that point. I would also like to thank those colleagueswho are in agreement with my work and who have all gone far beyond the teaching have offered me many words of encouragement. They materials found in traditional texts to provide their studentswith analysis-centered systematic in harmony. At last, my textbook is also ready to take this step. instruction This book presumesan acquaintance with Musiklehre by Hermann Grabner.n Allgemeinen As an accompanying discourse, I also wish to recommendMelodielehreby Lars Ulrich Abraham and justification and Carl Dahlhaus.12Page 18of the latter would make an excellentforeword for this text. far as the musical examples are concerned,only those As who would rather pay a higher pricefor this book shall be allowed to complainthat the musical examples appear in my own Rehm, for his
I
hand.
Autumn
Hamburg,
10Diether
de la
III (1973). 11
Hermann
12
Lars
Motte, Renate Birnstein, and ClemensKuhn,
Grabner, Allgemeinen
Ulrich Abraham
Musiklehre,11th
and Carl Dahlhaus,
\"Pladoyer
ed. (Kassel:
Melodielehre
xii
1975\342\200\224Diether
fur eine Reform
Barenreiter, 1974).
(Koln: Gerig,
1972).
de
la Motte.
der Harmonielehre,\"Musica,
Author's Preface to the FourthGerman
Thanks
to the
D. Levin
Robert
before
noticed The
reader
following
colleagues:
Martin
Tegen, who
and Franz Zaunschirm who pointedout the third edition went to press. will also notice that my hand-copied
several
Edition
produced the Swedishtranslation, which the author had not errors,
musical exampleshave
been
replaced
by
edition. engraved examples from the Japanese A supplemental chapter on Chopin, which was dedicated to friends in Warsaw, Krakowand in preparation. will be reserved is currently for the Polish edition, which Poznan, Sincerestthanks to Dr. Ruth Blume for the diligent and careful to bring editing required this edition into a new format.
Hannover-Herrenhausen,
xiii
early
1983\342\200\224Diether
de
laMotte.
Foreword
Translator's
to visit in 1985, I had the opportunity one of the During a professionalvisit to Germany author's classesat the Hochschule fur Musik in Hannover. I wasboth impressed with his breadth of knowledgeand the loving with which he approached his lecture.As Professor de excitement la Motte sat at the piano, he demonstrated and a surprising melodic-harmonic event explained In the course of the hour, he not only discussed the musical in a Mozart concerto. materials relevant historical and aesthetic factors and comparedand themselves, but also covered the passage in question to the work of other contrasted from the Baroque, Classical composers and Romantic eras. I left his lecture exhilarated. Later that while browsing in a bookstore, week, I saw de la Motte's harmony text, which I bought and read with great interest. After returning across to the United States, I accidentally came several references to this book in the literature. no less than twelve reviewsof this text in a halfwas piqued and I was ableto locate My curiosity day's search. It was only then that I realized this book was not only a best-selling harmony in Europe. textbook, but that it had broken important ground in the area of harmony pedagogy In 1986, an articleby Siegmund Levarie in an American journal which advocated appeared the useof functional in lieu of the Roman-numeral/figured bass In this article, analysis system.1 Levarieexplainsthebasictenetsof the functional system and its benefits to the music analyst. It was after readingLevarie, in the Journal of Music and then Martin Bresnick's insightful review that this translation In fact, it was Bresnick's final Theory project began to gather momentum. is a significant statement that decided the issue for me:\"...Dietherdela Motte's Harmonielehre book and deserves a careful critical an not to provide a reading by Anglophone public, only the state of current German pedagogybut an exchange of views. That window into to begin can only raise our mutual awareness ofthe ways and teaching the of understanding exchange of tonal harmony.\"2 practice for entering music conservatory students in Europe; however, the This book is a textbook students there are often older and betterprepared in music theory and history than the average or university student in the United States. For that reason, this study of beginning college at too advanced a level for the average written American college freshman harmony is probably an enterprising use this book (or or sophomore, instructor might be able to successfully although of in a Instead to aim this at the beginning of translation it) parts core-theory program. trying musicstudent, I have directed this translation toward the professionaltheorist/musicologistand in interested the advanced music student. This translation is especiallyappropriatefor those of its more about the of and functional and because understanding theory analysis; history music for graduate-level historical approach, it would also make good reading interesting students who are preparing for preliminary or comprehensiveexaminations. To make this book as useful as possible for readers trainedin Roman-numeral analysis, and of the functional harmonic basis of this to aid an understanding text, I have added Romanthe author's analytical numeral/figured-basssymbolsin brackets[ ] underneath symbols on make it easier for those should nearly all of the musical examples.This double-annotation unfamiliar with functional theory to better understand and correlatethe comparative strengths
1 2
Siegmund Martin
Theory, XXII
Levarie, \"Harmonic Analysis,\" College Music Bresnick, review of Harmonielehre (1978),
by Diether
Symposium
de la Motte
p.324
XV
XXVI (1986), pp.66-76.
(Kassel:Barenreiter,
1976),
Journal
of
Music
and weaknesses
engrave all of
the
beencompletely edition,
borrowed
of the two musical redrawn,
systems.
In the
process of this
examples in the book. Therefore, and is not, as the author states
from the
the
in his
Japanese translation. In addition,
it was
annotation,
in this
artwork
Preface to the I have
added
to retranslation has
necessary fourth
German
numbers
to the
musical examplesin eachchapter so that the written text and the exampleto which it refers might be more easilycross-referenced. in this text are mine, although The of the notes contain citations footnotes some explanatory of sources to which the author referred parenthetically within the German text. Since this book was not originally as a scholarly resource,the author did not always provide complete designed for his outside sources, and only rarely did he include any reference to bibliographicalcitations all of the author's sourcesfor specific would specificpagenumbers. Searching page references I run the risk of have required an enormous additional of time and resources. Although outlay criticismfor lack of scholarly pursuit on this point, I decidedon compromise and have included for number references in the footnotes. complete bibliographicinformation, except page The author did not completely referenceall of the musical examples used in the book.Where sources were available to me, I added some additional such as the readily information, first line of text in many of the Bach-choraleexcerpts,or movement titles from identifying Handel's Messiah, but in most instances, the scopeof this project would not allow me to include measure-number references for every example. I took the liberty of changing the text complete in all examplesfrom Handel's Messiah to read in English rather than German. All of the texts to the non-German in opera) cited in Chapter Six (harmony were also converted to their examples and supplied with English translations. original languages the book so that The functional and its symbols are introducedgradually system throughout a lengthy will not be necessary here. For additional information on the subject, I explanation refer the readeronce more to Levarie's excellent article. It is possible, There isonefeature of the functional system that I find particularly helpful. with functional to directly indicate the chord factor that occurs in the bass. With the analysis Roman-numeral a sixth above the bass indicates that I6, one must know that a tonicchordwith the third the functional of the chord is in the lowest voice. With symbol T3, however,it is Roman-numeral obvious that the third of the chordisinthe bass.Furthermore, with immediately show non-harmonic tones when they occurin the bassvoice, analysis, it is not possibleto directly
the functional system it is only a matter ofwriting the appropriate chord factor numbers with fourth above the chordroot of the symbol (e.g., D43= dominant a dissonant right in the bass voice resolving to a third above the root). Coming from a background in Romantwo of the symbolsthat numeral taken the longest for me to assimilate arethe have analysis, chords-of-the-sixth and sonorities. six-five Following Rameau's principles, the functional a third and fifth allows triads to be constructed either from the bass (standard above system When a triad is built from a third triad) or a third and sixth above the bass (chord-of-the-sixth). to be the and sixth above the bass,the functional still considers the root ofthe sonority system bass note (and not the pitch a sixth above). In other words,the functional two system recognizes
but
with
at the lower
types of root-positiontriads.
Inorder
to
interpret
S6 (subdominant
chord-of-the-sixth)
in the
it is necessary to assume a change of root tone. Thus, S6 will Roman-numeralsystem,however, be interpreted as ii6. In the same fashion, a six-five as ii*. sonority such as Sswill be interpreted of the in technical terms in this book are both found However, Many cognates languages. the musical term parallel has a fundamentally in German than it does in different meaning
xvi
English. In English,thetermparaZZeZ same tonic pitch (e.g.,A-majoi\"/A-ininor).
the to describe major/minor key-pairswhich share however, the term parallel isusedto refer to major/minor key relationships that share the samekey signature (e.g., C-major/A-minor). In Therefore, the Germanterm paralleland the English term relative are roughly equivalent. As order to ease any confusionon this point, I have translated the Germanparallel as relative. is
used
In German,
refer to parallel (P or p) have alsobeen by Levarie, those functional symbolswhich (R and r). The six-four G-C-E in C-major, will only be considered a \"tonic six-four\" (It) if it sonority, within the shows clear tonic function its musical context. Since the sixth and fourth above as a double-suspension dominant pitch often function which then resolveto the dominant triad, this figure will be labeled of it -V. (in Roman-numeral symbols)Vl f instead
suggested
to relative
changed
De la Motte
likeHeinrich Schenker,who stand apart from reduction of entire compositions into Bresnick \"hierarchical\" and background levels. In his review, levels the following middle-ground criticism: \"The problem... is essentially the same onefound in Piston namely the setting ofnearly all harmonic at a single fore-ground level. The central ... is the overactivity deficiency a corresponding of most fore-ground (chord to chord)activity and inattention to determination the hierarchical relationshipsof the harmonies that direct the foreground.\"3 theorists have not warmly embraced other theoretical systems is a more Why most German Suffice it to say that theoretical models than this short foreword will allow.4 complex question of the Riemann charismatic in Germany. outside tradition have not producedmany proponents As my Austrian colleague, Franz Zaunschirm wrote me, \"The history of Germanmusic theory is a history of functional ... to Grabner. .. to de la Motte, etc.).\" (from Riemann theory de la Motte does defer the Riemann for his analytical procedures and to tradition Although of his symbols, as yet another traditional German this book should not be judged many Harmonielehre.Inhis Preface,delaMotte rails against the theory-minus-music approach which of harmony take; he deploresthe customary so many German manuals of partwriting teaching in actual music; procedures by arbitrary and capriciousrulesthat have little to do with harmonic and he encouragesthe reader to keep in mind the differences of approach among various Carl In promotional material for this harmony text, composers, genres, and time periods. fulfills Dahlhaus wrote: \"Harmonielehre by Diether dela Motte the need, urgently promoted for years, for a harmony text that incorporates historically accurate modelsof style in place of on abstract schemes...\"5 Dela Motte's Harmonielehre to put the study of harmony attempts with the hope of making the study of harmony more a firm historical and analytical footing, relevant to the music student, professionalmusician, or interestedamateur.
3 4
Martin
5
Bresnick, review,
For more about
Ubergange,\"
Schenker
Musiktheorie
Carl Dahlhaus,
to theorists
no reference
makes
the Riemann tradition,
and
call
who
for
analytical
p. 321-22. and
how his
V/2 (1990),
theories
have
been
received in
Germany,
see Stephen
Hinton,
\"Nattirliche
pp.101-4.
promotional statement
in
an advertisement
p.514.
XV11
for
Barenreiter-Verlag,
Zeitsehrift flir Musik, VI (1976),
Certainly support. provided
no project
the size of
this
could
translation
have been undertaken without and Brittany, who have of their usual time with
I am grateful to my wife, Jane and my two daughters, Allyson me with encouragement much and love, and who have sacrificed
several years. I am also grateful to Iowa State University, which granted me I could work on the 1988-89 academic year, in part, so that improvement leave during and her associates at W.C.Brown, the first draft ofthis translation. Thanks to Meredith Morgan saw early merit in this project, and who provided the right mix ofboth encouragementand who thanks to Professor de la Motte, pressureto see this project through to completion.My sincerest who supported this project in many ways,including a proofre ading of the draft manuscript. I am to my colleague, Gary White, indebted who regularly discussed this translation project especially with me in its formative stages, and who shared his expertise ofbothmusictheory has unselfishly and who proofread hundreds computer technology with me. Specialthanks to Sara Compton, of musical examples,and to reference librarian, Susan Knippel at the Parks Library on the been of Iowa State The and of final could not have campus layout proofreading copy University. the tireless efforts of Eric Petersen, GregWhite and Stephani Scherbart. accomplished without Finally, thanks to Rob Hauser, DougFishand Collen Willcox who helped with the preparation of musical examples. It is my hope that this translation will provide some fresh insights for the English-language readerinto the fascinating technical and historical changes that have taken place in harmony it is my hope that the reader will also come to a better understanding of the since1600.Further, and weaknesses of functional harmony and the methods used to teach it. strengths me over
the past
a faculty
Ames,
xvm
Iowa,
January
1991\342\200\224Jeffrey
Prater
CHAPTER
ONE
Cavalier!) Harmony ca. 1600(Lasso-Palestrina-Lechnerinto twelve temperament, in which the octaveis divided equal halfthe more or less universal in the time of Bach.1 Sincethat time, intervals except the octave. has done away with all purely-tuned of equal adoption temperament out-of-tune intervals. In spiteof fewer pure intervals, however, there are no longerany unusably meant renouncing absolute interval purity (the Although the adoptionof equal temperament have all triads of all earlier systems), relatively acceptable object tuning equal-tempered scales of intonation. allows us to construct and play musical Furthermore, equal temperament reasonable intonation on any chromatic pitch. fifths are constructed upward in a seriesfrom the pitch CI, If twelve purely-tuned perfect B#7 is actuallyhigher in pitch the pitch B#7 is reached.2Becauseof the comma ofPythagorus, fact This makes it impossible to than C8 (derived by pure-octave transpositions above CI). The
of equal
principle
steps, was first
established
construct a closedcircleof tuned
perfect
fifths
is constructed
fifths.
perfect
purely-tuned
from the
upward
Furthermore,
pitch CI, the pitch
if a seriesof E3
four
purely-
Because is higher in pitch
is reached.
of the syntonic fifths, perfect comma, E3, reached by this series ofpurely-tuned of El (a purely-tuned major than the E3that is reachedby a two-octave upward transposition that third above the starting pitch CI). From these acousticalfacts, it can be observed purelythat is, it is impossible tuned perfect fifths and purely-tuned exclusive; major thirds are mutually to have both purely-tuned and purely-tuned major thirds at the same time. perfect fifths to maintain After the aspect of necessity relinquishing pure perfect fifths, an important of came new into music theory in the MiddleAges(Pythagorean systems tuning tuning), vogue called mean-tone between the sixteenthand the eighteenth centuries.Thesesystems, fifths and purelyacoustical compromises between purely-tuned perfect temperaments, are actually tuned major thirds. They provide excellent (almost purely-tuned) intonation for those triads C major]. which related to a starting referencechord [usually are closely However, those triads out-of-tune. In spite of various related to the referencechordare noticeably which are distantly those triads most the compromise between pure thirds and fifths, methods usedto calculate that distant from the reference chord are so out-of-tune they are unusable for all practical
purposes.
1
over the question of whether J.S. Bach actually There has been much employed equal temperament, controversy the strongest arguments presented on the side that he did not himself employ a truly equal-temperedscale,even in the Well-Tempered Clavier. Equal temperament began its rise to prominence only toward the end of Bach'slife. with
2
The system of octave classification C at approximately 16
Society, where
employed in
this translation is the one suggested by the symbol C0 and where
Hz.is represented
1
by the International Acoustical middle-C is represented by C4.
this period, the only black keys of the were: C#, Eb, Fit, Git, and Bb. The black keys and Alt were quite unusable. For example: the representingthe pitches Db, Dlt, Gb, AJ\302\273, though when out-of-tune in-tune, the same C#is disagreeably pitch Of in the major triad A-C# -E sounds it is enharmonically employedasa Db in the triad Db -F-AI\302\273.Although it is possible to find spots in the unaccompanied vocal literature of the period where out-of-tune black-key pitches appear With
keyboard
(e.g.,
the
the mean-tone
with
acceptable
during
intonation
of chromatically related triads inthe musicof Gesualdo), music in Ex. 1:1 for all instrumental musicand vocal
juxtaposition
astounding
used
systems
tuning
universally
resources were limited to those shown We instrumental accompaniment. listen
to
can verify that old organs that are still tuned in mean-tone
certain
u
equal
Although
almost every harmony temperament is really
the number
of pitches
with
h-
\\.
Intonation
1:2
Example
4
we
1:1 with Acceptable
Pitches
Mean-Tone TemperedPitches
pitches
with
unusable if
systems.
Example
Mean-ToneTempered
were indeed
pitch
Unacceptable
'\"
1l#
Intonation =
which developed during the time of Bach, is extolled by most natural and conclusive method of tuning, equal not natural at all; it is actually a repressionof nature in favor of increasing with reasonable intonation. This increasein pitch has made availability
temperament, as
text
the
it possible for composersto develop a wide variety of musical stylesand modulatory techniques which require unlimited chromaticfreedom. musical can already be found in operas written about 1600. These textures Homophonic
texturescontain
juxtapositionof melodic the riseof homophony. which closely
sonorities
harmonic
tonal relationships.
In fact, lines
whose
a goldenage of derived
Nevertheless,
followed the polyphonic
progressions, contrapuntal
from the
ancient church
one to another, imply composition, modes,
early homophonic compositions of the time. practices
2
based was
certain
basic
on the
primarily to a closeby
brought
obeyeda number
of rules
approach to the number of homophonic from this era. Indeed, the harmonic examples vocabulary provides a particularly a discussion of tonal This is because is for harmony. early homophony good starting point was with connections betweena limited number of and chords. concerned (As primarily pitches discussedabove, the complete chromatic was not yet available to composersof instrumental In addition, an introduction to early music.) homophony may also help provide a better and of an important is rather in the understanding high-level musical style which neglected In order that
limited
harmonic
musical life
of our
become better
we might
of this
materials
through
a correct
with
and unified
study a of this period we
that
time.
style is somewhat
Because this musical
readerplay
acquainted music, it is vital
the
style can be acquired.
rules and exercisesthat
unfamiliar
today,
it is
especially important that the aural knowledge of the
examples a number oftimessothat an This should take place before proceedingto the will be generated directly from follow analysis following
exercises. of these
Example 1:3a - Stabat
Palestrina
ti
i1
i!
*i Sta
i111
i!'i'
U
Ulo -
do
Example 1:3b - Stabat
Palestrina
Mater
+-M-4
r
IW j
a
u
* r
j
iS_
m jus
a
-
ra
3
^
^
ter
bat
Mater
- mam
ge
-
men
ro
The stylistic examples.
Example
Palestrina - Stabat
1:3c Mater
\302\261
w^u-t^H^m
J
iJ
H
\302\261i
la
-
be
- die
ne
ter
Example
Palestrina - Stabat
I
I
ffi
j
feii
;W ^?
^
feB
J. J.J
,J
J ^
\"f1
u
-
- ge
m
1:3d Mater
j
j
j j
ja
ma
ter,
V
/
f1
^
n
gp^f fons
l:3e
Example
Palestrina - Stabat Mater
r\342\200\2241 \"i1 \342\226\240I
T\342\200\224r
j me
j
do
found
Triads
-
lo
fac,
triads
(root
triads
(root position):
position):
First-InversionTriads
found
'H
Bb F
g in
a
j
ut
te -
ni1
\\
j
j lu
cum
1:3 a-e
in Examples
Minor
j
tj
ris
Major
4
1 r~F\342\200\224\\ f -i111,i
j
j j
sen
J.
J
w^\302\247
C GD
d a Examples
A
E
e 1:3 a-e
jq
f^ \\TT
^ ge -
am.
1:4
Example
Gallus - Ecce quo
Jacob
moritur
modo
(15S7)
^
et
-
ne
mo
- ci pit
per
-
cor
et
de,
s
ne
-
mo
- ci - pit
per
-
cor
de.
'
IS
Tr -
Vi
ri
jus
-
itH
I
Hi
\"i1
r
r
r,
ti
tol - lun
-
>
tur,
r ne
s
i
Tr?
r
et
-
mo con - si
-
de - rat:
*
it
iHH~Hr{
Jj g J J J ,j 1
JI ^\302\273
f
pr
rr' a
i
fa
-
ci- e
r
r
r
in - i -
'f
r
qui
-
ta
sub
m i!
'!
il
il
i111
^
r
>
JU
r
r
et
e
r -
nt
Triads
Majortriads (root Minor
triads
i'
in
T
found
me - mo -
in Example
position):
(root position):
m 5
J
J
r
r
r
la
^c
F
C G
Bb
c
g d a in
|tr
r
n -a
e
1:4
Eb
First-Inversion Triadsfound
^
h
rr
r ce
pa
-
li
J14
J
J
1
\"r
Example
D
A
1:4
jus
Example1:5 Spriiche vonLeben
- Deutsche
Lechner
Leonard
S
^7
J
J
J
r
r
r
(1606)
W
J
J
s
Tod
und
J
J
g'lin
get.
=f
sich
Wenn
er
-
schwin
get
* s
^^F\302\245 thu
Gliick,
drau
bau
S J
en,
Triads
Major
triads
Minor triads
(root (root
r
j ^^
z'viel
ihm
found
i \302\243j
P^P nit
dir
S
m
I
m
das
ver
in Example
position):
1:5
Bb F d
c g
position):
No First-Inversion Triads
6
GDA
^ fr
r
Example1:6 -
de' Cavalieri
Emilio
La
(1600)
rappresentazione
^=k
I hi
riil
\"^\"W
j ijH
ii
j j J j
miJ r
0
f
gran
stu - po
^
iJ
i1
-
rf
r'/
*L ^ j
it
O
re!
gra-
ve er - ro
J
J
J
r f
p^
re C'huo- mo
mor - ta
le
^
-
le,
ch'e
-
ter - no
du
Triads
si
ra,
found
triads
(root
Minor
triads
(root position):
position):
First-Inversion Triadsfound J
po
in Example
Major
|
r r tan - to
dBh
? ma
d'un
hi
I
/1'
/
ni'
-
P
7
1:6 F C
G D
A
g d a
in
Example
1:6
E
1:7
Example
Orlando di
m
(1550? publ.
Erythraea
Sibylla
B
5
?E
I
Lasso-
1600)
^=\302\261
j
j rr
se
qui
di
-
mi
sit
frf
m
^
p
y
^f ti
- ma fe -
-
li
g
ces
-
re
P=F
IT
fer- em
tern
cum
-
po-
les.
ra
He
^t
^ -P
Ul
al
ab
^-
**=
^
^
J&:
^
P
j
(9-
f r\"\"
rr
I
J^i^ m
brae
-
a,
quern
vir
Triads
Majortriads (root Minor
triads
ret
go
found
Eb
position):
No
c
Bb
8
F
C G
g d a
Triads
First-Inversion
stir
pe_
1:7
in Example
(root position):
de
D
A
E
Exs. 1:8-9 chart all of the Carissimi, Titelouze,Sweelinck, that
those triads
only
triads
in Exs.
employed
1:3-7. Analysis
Peri, HaBler,
Capello,
Anerio,
appearing in Exs. 1:8-9were
in
general
of many pieces by Byrd, Demantius, and othersconfirms use during the period.
Example1:8 in
(.arranged
triads
The
in
circle
Keys:
Major
Eb
Bb
F
C
g
d
a
Minor keys:
(scalar
*
in
G D e
frequent.
E
A
(b)
1:9
Example
i
of fifths)
those in smaller plain type are less heard; type are the most frequently The B-minor triad, in parenthesis, is the least frequently encountered.
bold
representation)
*
ii
iii h
%$\302\273 h*
^#rv
irir
CcDdEbEeFGgAaBbb
The
roots
third omitted
or
fifth). (in
cases
major triads
of root-position
(ca.1600).In addition,
root-position
Only in the like this it
major
example by is usual
are always
triads
Lechner
to triple
doubled
are seldom found (Ex. 1:5) do we
the root). Whereas
in four-voice
homophonic style form (without fifth of the last chord of the final chord was
in incomplete find
the
the
third
in pieces written around 1550,by 1600the third an indispensable became of all M inor triads also double their root sonorities. tonesin fourcomponent closing normally voice textures, but the third may bedoubledif contrary motion is employed (seeEx.1:10). melodic frequently
omitted
1:10 Example (Lechner)
The third of a minor triad may be doubled if it occurs as a result of contrary motion between two voices (x).
9
choral music
Modern
employsthe approximate vocal
ranges
shown
in Ex.
1:11.
1:11
Example V-\"
r^zt.
=z\302\261
Tenor
Alto
Soprano
vocal ranges were not firmly established around 1600, however. Exs. 1:3-7show voice ranges seldom exceeda ninth in the bass). However, the (or an eleventh of each individual voice part varies considerably from to piece piece.
Specific
individual
that
tessitura
1:12
Example
in in
Lasso
in Gallus
in
Lechner
G alius
in Palestrina
m
9 Alto
Soprano
in another work by Lasso
Tenor in the entire Stabat Mater by Palestrina
in Lechner Jau
m Tenor
Bass
One octave is the maximum interval allowed between the soprano and the alto, as well as between the alto andthe tenor.Wider between voices in the case permitted spacingis upper only of isolated individual chords which immediately return to sonorities in normal spacing.There is no spacing limit between the tenor and bass. However, the twelfth is the widest perfect and bass in the examplesby Lechner (Ex.1:5)and observedspacingbetween tenor Lasso (Ex. 1:7).
Example in
Gallus
(entire piece)
w
The alto and
tenor voicescover
exactly
^
the same
incorrect
disposition
T
=?
i
1
1:13
in Lechner
range.
10
of tessitura;
why?
Exercises: In the samemanner other excerpts from
be constructed
Exs.
within
(e.g.,
possibilities
high
1:3-7. the
shown
as
Write down
in Ex.
as many
1:13, chart the individual
four-voiced
single
triads
ranges
of
as possible that
can
voice
ranges charted for each piece; become acquainted with etc.). register chords, chords in open or closedstructure,
all
the
or low
Example 1:14 Good
Chord
Voicing in
Gallus
d=i i:
y
j
i
(
l,
'i
r
J
j
i
P^\302\245
r
J
j
Example 1:15 Rare
or Unused
Chord Voicing
j i#^
ca. 1600; why?4
j
j r
___
TT
.1
f=r to facilitate goodvoice leading occurs a number of times and alto. To prevent all of the voices from at the ascending same time, Lechner(Ex.1:5,measure the alto above the soprano.Inthe examplefrom 1) begins Lasso written above the alto so that only the soprano (Ex. 1:7, measure 10), the tenor is already and alto need leap upward the next measure. into Voice Leading: It is rarefor all voices to move in a downwarddirection at the same time. Ex. 1:16 (1)showsan example of simultaneous downward motion. Moreconspicuousto the ear, in all four voices. In Ex.1:16 and therefore even more rare, is simultaneous motion ascending simultaneous softened voice motion in all four voices is somewhat (2), by stepwise upward leap in the same leading in three of the four voices. Ex. 1:16 (3) showsthat a simultaneous between two chords. direction of harmony by all voices is permitted if there is no change Voice
betweenalto
and
parts and soprano
Crossing
Crossing:
tenor
4 In addition to the overly-wide spacing, which occurs between two of the upper three voicesin chords 2 and 5, there are many voicing difficulties in this example. Other traditional a melodic tritone in the tenor between errors hereinclude: chords1 and 2; parallel perfect fifths between chord 2 and 3 (bassand tenor); incorrect doubling (missing third) in chord 3; double melodic tritones between chords4 and 5 (alto and tenor).
11
Example 1:16 Lechner
Cavalieri
from Ex. 1:5; m.7
from
(2)ii
Cavalieri from Ex.l:6; second
Ex.1:6; first system
*
(3) I
is
system
s
rs ^
f
^ there are three possibilities
motion: rising, falling, and direct repetition ofan entire chordal frequently-occurring to be present at the sametime it is normal for at least of melodic motion two kinds sonority, quite A between chords. individual voice parts occurs nearly constant change in the directionwithin in Ex. 1:17. This frequent of this of linear direction is an especially important aspect changing style. For
a given
chord voice,
remaining the same. Except
Cavalieri:
When
for
Ex. 1:6; beginning
separate
of forward
the
1:17
Example
voices are coupledto
other
each
for long
periods
by
motion
in the
same
it was considered tend to lose their independence. Therefore, voices direction, the individual a lengthy texture when working in four voices. For example, faulty technique to imply a two-part series line gives the impression of two opposing streams of rising chords against a falling bass of materials rather than four discrete and independentparts (seeEx.1:18).
1:18
Example
IN
r
m
rrf
=J=y r
T
J
j
J
r
r
r-
12
All moving
standard
texts recommend
harmony
one chord
from
to the
next.
As
in the same voice when tone keeping the common in Ex. 1:19, this principlealso applies to early
is shown
homophony.
Example 1:19 (from Ex.l:6)
Cavalieri
w
J
a
m m
m
-i
Common tones between chords should be kept in the same voice. The horizontal lines show normal application of the common tone rule
voices between chordswith the same root [e.g., Ex. 1:16 (3)]are is the allowed, freely important exception to the common-tone principle in of all simultaneous voices a the after cadence Ex. 1:4at (see: practice allowing leaps directly further should first Some license also be for deliberate of rest). quarter granted infringements the common-toneprinciple,especially in situations a piece might not otherwise be ableto where forward move followed the common-tone freely. For example, had Lassostrictly principle in Ex. 1:7 (measures6-8),it might have appeared as shown in Ex. 1:20. To obey the common-tone been necessary for Lasso to limit the range of the soprano to the pitches have principle, it would than is allowed by the G4-G#4-A4. Lasso's freedom (Ex. 1:7) has much more melodic soprano strictadherenceto the common-tone principle. Therefore, melodic considerationscan sometimes take over the common-tone rule. precedence Simultaneous
leaps
however.
in all
Another
Example1:20 ML
m
n
w t'\342\200\224\\'
^L
TT
r
LinearConsiderations: With
the exception of the leap ofan octave has always been (which rule the centuries-old intervals smallerthan melodic to permissible), contrapuntal leaps limiting a minor sixth can also be appliedto linear of pitch choice in early homophony. considerations of major sixths and all seventhswere prohibited.) Thereisa minor-sixth in the tenor (Leaps leap at the end of the example by Lasso (Ex. 1:7,penultimate an octave in the measure), leap soprano
13
in the example in the
Lechner
by
examplesby
frequently
in the
quite rare,
however.
Cavalieri
bass.
(Ex. 1:5, penultimate measure), and several octave (Ex. 1:6) and Lasso (Ex. 1:7). As a rule, larger
Consecutive large-interval
leaps in the samedirection, 1:21
Example
Lechner
(from
in the bass leaps leaps occur most as in Ex. 1:21, are
Ex. 1:5; m. 6-7,
bass)
^
Large leaps are most
often
and followed by
preceded
motion in the oppositedirection
(see
Ex. 1:22)
1:22
Example
Lechner(from
Ex. 1:5;
m. 7-8,alto)
^T
Sincethe top
most conspicuous voice,melodic of seconds and thirds tend intervals should be avoided predominate soprano. Melodic augmented and diminishedintervals of the augmented unison, which in all voice parts, with the allows for chromatic exception Since musical style around 1600wasgenerally in a alteration of an individual conceived pitch. should not be overused, however. Lassoemploys it very strict manner, the chromatic half-step in Ex. 1:7 (C-C# in the soprano, measures 3-4; F-F# in the alto, measures 11-12). very sparingly The chromatic half-steps B-Bb,G-G#, E-Eb (and others) are employed in Exs. 1:3-7. in immediate A cross is created when a chromatic half-step occurs or close relation Exs. 1:23a-b show how Schutz employedcrossrelations in successionbetweendifferent voices. to
a mid-seventeenth
line
is the
in the
century work.
Example 1:23a Heinrich Cross
relations
Schutz
between
different
- Es
ist erscheinen (1648)
octaves.
UJ
gEg; der
sich
14
selbst
m fur
uns
1:23b
Example Heinrich
relations in the same
Cross
- Es
Schiitz
register, but softened
by
ist erscheinen a rest.
at
w
J
ip
J
1
^
W^ ser
die
Welt,
und
appear only twice in Exs. 1:3-7,and in both cases the a rest between the softened. Gallus (Ex. 1:4) employs C# in the alto is followed related rest). pitches (see both sides ofthe first quarter is in turn rest which followed by d in the tenor voice. Lasso relations
Cross
is somewhat
relation
effect of the two
by the
(Ex.1:7)
coincidence Bit
of chromatically alto
against
Bb) by using
rare in this style, when
they
related pitchesin the first
half
cross
chromatically
prevents
quarter a
direct
penultimate measure (tenor Though cross relations are quite
of the
quarter-note motion in the tenor. for do occur, there is a preference
softening
their
effect.
Parallel Motion: Every of harmony prohibits motion between two voices study Ex. in parallel perfect octaves, unisons, or perfect fifths 1:24). It would be ridiculous even (see of such to attempt number establishing principles of voiceleading basedonthe insignificant parallelisms that actually occurin the music of the great composers. Forbidden
Example
There are two between
usual
any octave has two
explanations
1:24
for the prohibition
of parallel perfect octaves
and
fifths
voices:
and the frequencies ofits lower upper notes of the upper pitch is 100 Hz.,thenthe frequency the two tones of the octave are often will be 200 Hz.). Because of this acousticalphenomenon, as a which has the next most simple unified the fifth, perceived single sonority. Similarly, perfect to be a strong unified its upper and lowertones,is alsofrequently ratio (2:3) between perceived will tend to lose two voices which move in parallel octavesor perfect fifths sonority. Therefore, some oftheir own melodic individuality and independence.
1) The
a simpleratio
(for example: if the frequency
of the
of 1:2
between
lower pitch
15
2) Parallel perfect
perfect
fifths simply
traditional explanations are somewhat also cautioned against the use of parallel
simple ratio
explanation as shown
have
1),
why
next most
1:25
2), why is it
claimed that parallel perfect
abound 1:26, such structures style of Medievalparallelorganum,
in Ex.
in the
(Furthermore, to
(Ex. 1:25), the
fourths
?\302\243EE
i when,
In explanation
troublesome.
perfect
(3:4)?
Example
In
sound \"bad.\"
of these
Both
we not
are
and
octaves
a particularly
\"good\"
octaves
fifths
and
sound
\"bad,\"
the MiddleAges? in question are said
music of
in
the
the
parallelisms
sound.)
Example 1:26 Excerpt
f=F
m
from
Conductus
a Thirteenth-Century
JLJ
JJ
J-.-H-J
rr
rr
r
J-J-J r
^
^=6 * Parallel perfect octaves and fifths, broken by rests were also generally permitted and employed m later
P
rrr
or cadences, musical styles.
which attempt to explain why parallel octaves and fifths perfect create problems that cannot beresolved.Forthat reason, I shall attempt to of this rule a different way. explain the origin The major triad is a basic harmonic element that was common to Western music during a periodof some 500 years (from Dufay to Reger). It also plays a vital role in twentieth-century and Stravinsky. Dominant-seventh and diminishedmusic, especially in the worksof Hindemith seventh which are newer than the are quite rare in twentiethstructures chords, triad, major music because however. This is both of these sonoritiesareassociatedwith literature, century the kind of dominant-function characteristic of the Classical and harmony that is particuarly All
should
technical
arguments
be avoided
Romantic periods. By 1925,many refused to employ dominant- or diminishedcomposers in their works because these sonorities seventh chords musical evoked styles and aesthetics that In short, in the were no longer in vogue. harmonies which had played such an important part music of the past were simply of a newer age. as old-fashioned by composers rejected Parallel perfectoctaves, and perfect fifths were first considerederrorsof unisons, compositional in the of this era also manifest fourteenth technique century. In many ways, compositions 16
musicalexpressions.Sincecomposers
of the fourteenth century considered that disdain for and avoidance of earlier the rule that: establish consonances incorrect. are techniques parallel perfect helped musically Hidden Parallels: Musicalsituations where two voices move in the same direction from harmonic intervals into a perfectoctave, or perfect fifth various are called hidden orcovered unison, in many harmony texts. Hidden either or are totally parallels. parallels partially prohibited Theserules,however, are only distantly connected to actual musical practice.In spite of the fact in strict \"textbook\" assignments, the Hteral observation of that hidden parallels are forbidden to the this rule is mostly an exercisein music theory for its own sake. Exs. 1:3-7show,contrary hidden occur regularly and equally often parallels opinions expressed in many treatises, that in many musical between lower, upper, middle and outer voices. Hiddenparallelsappear masterworks ca. 1600and should therefore be considered in the style. permissible Ex.1:27shows the most frequently encountered hidden parallels. At those spots marked less often, both voices leap (1), a step of a second and a leap occurs;at (2),though appearing at both In the case of hidden even less voices often, downward; (3), appearing leap upward. the voice is moves where involved the (4), parallels, soprano soprano usually by the smallerof the two intervals; at (5), the sopranoonly infrequently moves by the larger ofthe two intervals. between the Hidden unisons regularly occur betweenthe tenor and bass(6),but seldom appear
an aversion
to earlier
the musicof
the
era to be primitive,
previous
soprano and alto
it is
possible
(7).
1:27
Example
\302\256
\302\251
\302\251
\302\251
\302\251
\302\251
\302\251 \302\251\302\251
\302\251
\302\251
J5i=:
IW
1
j
U
i
=8z
^=4
^^m hidden 8ves inPalestrina
hidden
5ths
inLechner
hidden 8ves in Lasso
hidden 8ves in Lasso
Tn hidden 5lhs
,
\302\251\302\251
\302\251\302\251
\302\256\302\251
\302\251 \302\251\302\251
tidden \" in
\302\256
8ves
hidden
5ths
Lasso
\302\251
\302\251\302\256
s
\"m
nO Ii I s m hidden 5ihs in Cavalieri
uj
=1=1
hidden
J-
ijj
J
^ 8ves
and Slhs Lechner
hidden unisons in Lechner
hidden unisons in Johann Walter
in
17
hidden 8ves in a different place in Lasso
E
^ m
hidden 8ves and Sths in HaBler
Choose a
Exercises: many
observe all of
chord (Ex. 1:28usesD major). Employing from this chosen starting sonority of partwriting discussed above.
progressions
single-chord the
principles
voicings, write as Make sure to
various as
possible.
Example1:28
4\342\200\224I
EPESF
^^k
i^k
ip
J
i \302\273J.
J\342\200\224h
m
#
\"f^F
-+-J-
f
L_i
r^F
as
UJ M=
j
^
i.
of chords From chosen starting where at least one voice afreely chord, compose a succession in eachchordprovidesa common-tone to the next chord in the progression. connection Useonly those found in all the tones as in chords Exs. 1:3-7and mark common Ex. 1:29.
Example 1:29
j=^
n
i
M 18
j
a number
Compose
the possibilities
are
of chord progressionsthat will limited (see Ex. 1:30).
common tones between chords;
not allow
somewhat
Example 1:30
$ t\342\200\224r
j
y
Complete
r
r
the outer-voice
F
\\>S
frameworksfound
in
Exs.
1:31 a-b by
adding the
alto
and
parts.
1:31a
Example
i
j
j
J- ^
J
i
J
j:
j s
r r r r
,j j
J
r r ^F
19
P
J
J
J
^
t
r
r t
^
#*
tenor
1:31b
Example
I
f
1H
F
g
d
C
G
a
e
D
A
E
list each single-line excerptin Exs.1:36a-d,tablesaregiven which in the original work from which the line was taken. Using only listed in the tables following each example, compose a stylistic (ca. 1600)four-voice each excerpt. Since there aremany solutions for each line, try completing more possible
Exercises: At all major
in the
^f
and minor
one setting
end of
the
triads
found
of each.
Example1:36a -
Lasso
9=
Triads
Major
triads
minor triads
\"
11
employed (root
Sibylla
Samia
(1600)
\302\243
in the
original setting of Ex. 1:36a
position):
(root position): 23
Et>
Bb
F
c
g
d
C
G
D
A
E
Example l:36b(l) -
Lasso
3S
Cumana
Sibylla
s
m
'r
r
Triads
triads
Major
(root
minor triads
r
r'
n
original setting of Ex. 1:36b(l)
in the
employed
position):
Example
triads
Major
(root
l:36b(2) Cumana
:m
^ employed
the
in
setting
original
position):
Eb
Bb
of Ex. l:36b(2) C
F
D
G
c
(root position):
minor triads
A
d
c
Lasso - Sibylla
D
G
C
F
Bb
(root position):
Triads
^
^
Examplel:36b(3) Lasso
^
[
Cumana
J
^\342\200\224-L-U\342\200\224^^ I
|
1
J
m~c\342\200\224A\342\200\224 j w
[I6
u
j
D.
3
T
D
xl
3
[V
V6
I
V
I
I6
Handel-
T3
j
j
J
P^ R
B:
j
\"And
2:24b Example Glory of the Lord\"
the
from
V]
Messiah
D
\302\2603
V
rv*
44
\"3
T
V5
I]
Example 2:24c Handel-'7
\302\261b
p^
\302\243\302\261\302\261t=t
E:
^
T-
[I-
2:34b
Example
Handel- \"Pifa\"
from
Messiah
1^
^m. D-
C:
[V-
Handel
-\"And
Suddenly
2:34c Example There Was With The Angel\" from Messiah
\302\273tfEEffpEff?ffff^
D:
CiffffFffrr.r
T
[I
53
always
is
enters
a
chord is created when, in a series of six-four Arpeggio Six-Four Chords: An arpeggio tri ads with the same root, the bass skips through the triad members from root or third stable The more to the fifth and back again to the rootor the third (seeEx.2:35a). harmonically make clear the function of the less triads) surrounding chords (root-positionor first-inversion chord is functionally equivalent to the chordson stable six-four chord. In this case,the six-four side and, therefore, is perceivedto be consonant either (a second-inversion triad). Exs. 3:35b-c from the and contain works of Handel Vivaldi which the arpeggio six-four. excerpts employ successive
Example 2:35a Examples
i C:
Arpeggio Six-Four
J
J
r
r
J
J
r
6 4
5 3
5 6
I
v6-
2:35b
Example
Handel-Concerto Grosso
e
i
Ur
U F:
j
k 3
5 .3
Chord
J
,1
^P^
T
tl
of the
Tj
[ I
5 3
54
6 4
5 3
6 4
6
]
2:35c
Example
Vivaldi-
\"La
from The
Primavera\"
rf*
Mi * r-
Four Seasons
M
MM\302\243
Mf
TI
b:hh
r
%
E:
T.
[I
The
by a more
six-four (T5) [I4 ] is incorrectly stable tonic-functionchord (T: or T3)
arpeggio
Example
employed [I or F],
2:36 because it is not
chord of
a different
followed
function.
2:36
J
C: T,
in Ex.
but by a
J S
[ I
IV]
six-four chord also occurs between two more-stable Passing Six-Four Chords:The passing triad with the same (often between a root-positiontriad and a first-inversion bassline The both the and six-four function). departs approaches passing by step, smoothly the less stable six-four with the stronger consonances on either side. Becauseof this connecting motion in the bass, the passingsix-four is perceived to be consonant. Exs. 2:37a-cshow smooth six-four was used in early eighteenth-century how the passing music. consonances
55
2:37a
Example Passing
. chords
^
P^ C:
T
[I
D5
T3
S3
T5
S
T
vS
I6
IV6
14
rv
i
2:37b
Example
Handel-Xerxes
n
m
f^m
n \342\200\242>h
Eb:
LJ
m
D
v!
[v
T3
D5 T D3
i6
V4
i v*
]
Example 2:37c Handel-Xerxes
\302\261sk
*
i j
a\342\200\224
j.
^ A:
T-
S3
[I
T5
\342\200\242IV* 14
56
S
IV]
and showsthe suspensionsix-four the passing six-four in combination. This in a strong metrical position whilethe occurs when a six-four chordis placed and to consider the secondbass approaches leaves the six-four by step. Becauseit is possible inversion triad in Ex. 2:38either as a passing six-four (consonance) or a suspensionsix-four two separate (dissonance), analyses are provided.
Ex. 2:38 structure
musical
Example 2:38 Telemaim-Tafelmusik
or:
D-
S,
f]
[rv* 4\"3 suspension figure in soprano and alio
Exercise:
Play
and write-out:
2:39a;2)thethree upper
for
voices
types of six-fourchordswhich in all major keys. your solutions
various play
for the given soprano line in Ex. 1) the three lower voices bass line Ex. familiar with the the given in 2:39b.Become to harmonize the examples. Transposeand are required
Example2:39a
w
#ip
6 4 G:
T
5 3
'1 6 4
[I pedal
5 3
V
1
V4
V
T
I
aipeggio
VS
I6
s
D
IV
V
5 6 n3 4
5 3
pedal
57
2:39b
Example
'
:i
i
r
D5
T3
V4
I6
>\342\200\242)\342\200\242. J \342\200\242
4
C:
T
[I
T5
T
S3
it
IV
passing
IV*
i] suspension (cadential)
passing
cadential six-four,the suspensionfigure other six-fourconstructions.
In the of the
Exercise:Play
the
\342\226\240: r- \342\200\242
\342\226\240 '\342\200\224-a
r
in all
progression
following
(D4
D\302\2604
[I
v1
rv
3 )
[Vt 3 ]
appears more often
than
any
major keys.
35
V3
I
T
ii]
Dissonances
4. Characteristic
tonal function of a singleroot-position triad is uncertain, when a minor major above its root the resultingmajor-minor chord takes on a dominant seventh If a major sixth is added above the root of the same triad, however, function. minorthe resulting seventh chord (first inversion)takeson a subdominant function (Rameau: sixte ajoutee). SeeEx. Although
seventh
the
is added
2:40.
2:40
Example
Root-Position Major Triad
i
Major-Minor Seventh Chord Root Position
in
Minor-Seventh Chord in
First Inversion
^
=r
^ 6
D7
[V7]
in F Major
6
S5 [25]
in G Major
(sixte ajoutee)
texts devote a section to these two dissonant sonorities, but the Harmony customarily differencesin their origins, voicing and distinctive features are not usually considerations, covered.For that reason, I will devote some time to a discussionof these issues. chord (sixte ajoutee) is a somewhat older Origins of the Added-SixthChord:The added-sixth than the chord. Ex. 2:41 dominant-seventh As 1600 the added-sixth had c hord sonority shows, by been an considered element in the construction of cadences. already important long
58
2:41
Example Johann
a)
Walter,
b) Leonhard Schroter, 1578
1551
^ f
M
r
^LJ. f^F^ si
D
[I6
T
V
the By employing sonoritiesare smoothly triads positionprimary
or D [V], but
never
I]
Ss [iis ] chord,
[i6
it is possibleto
a basic
construct
D
T
V
I]
cadence pattern
(see p. 29).
[I].
Exercise: Play the cadencepatterns
in
Ex.
2:42 in all
major keys.
Example 2:42
^
i*H
m
m
C:
T8
[I
Ss 115
D
T
T3
Ss
D
T
I]
I
ppi
j
;
iU
T
S5
D\302\2604
T
I
115
V\302\2534
I]
=8=
m
C:
T5 rT5
[13
where all
tones (see Ex. 2:41).This is not possible with rootWhen used in cadences,the Ss[iis ] is always followed by Eft 3
by common
connected
by T
r
r
r
t3
[V4 3 ]
I
m
Ss ..6
115
59
..6
of the implications Voicing Considerations in the Added-SixthChord:The harmonic to those associated with the added-sixth chord are nearly identical chord-of-the-sixth. As is in Ex. 2:43, the practice ofreplacing shown thefifth of a triad with a sixth is quiteold,originating from to be a harmonic structure built from either a third a time when the triad wasconsidered and fifth or a third and sixth above a soundingbasstone (seep. 42).
2:43
Example
Schtitz
a) Heinrich
b) M.
Praetorius,
1609
^ $m
r
r-f
1=4
w F:
vi
i6]
r
r
r Tr
r
r
T3
D
[I6
V
T
I]
The subdominant chord-of-the-sixth (S ) [ii ] was regularly the time of employed during Bach. In four-voice its bass tone doubled. This this sonority appears most often with settings, ca. 1600, where any chord member in a chord-of-the-sixth runs somewhatcontrary to the practice couldbefreely doubled (see p. 26). In music from before the time of Bach, it is betterto consider the Ss [iis] sonority to be a simultaneous of a fifth and sixth above a basstone,rather sounding as a triad with an added sixth. than in Ex. 2:44played a major Exercises: The three role in music of both chord progressions in all keys. the Baroque and Classicaleras. Play these progressions
Example 2:44
m^m
C:
T
[I
sw
PW
S ii0
D
T
T
S\302\260
V
I
I
11
T
S 11
60
D
T
demonstrated in Ex. 2:45a,it is easy for forbidden parallel fifths and octavesto occur with which contain S [ii ] chords.Problems fifths and octaves are best parallel the between the use of contrary motion by uppervoices and the bass (see Ex. 2:45b). of the S [other inversions ofii] do not in compositions occur of this period.
As is
in progressions avoided Inversions
Example 2:45 Incorrect problems
a)
with parallel motion
f^
(contrary motion between voices and the bass)
b)
upper
m
m C: T
[I
ii\"
T
S
D
C: T
S
I
ii\"
V]
[I
ii\"
T
S
D
if
V]
of the Added-Sixth Chord:When a minor seventh is added abovea harmonic in thirds is not of constructing sonorities principle root-position and The ofthis makes the chord root remains the same. extra addition disturbed, pitch actually of the resulting the harmonic function For i f F is added above sonority unambiguous. example, the sounding the root-positiontriad G-B-D,G remains but the F a dissonant provides root, element that clarifies the strong dominant function of the sonority. However, adding an extra pitch to a major triad in order to invoke subdominant function sixth a sonority with functional that is, if we add a major above the actually produces ambiguity; root of a root-position in two separate major triad, the resulting sonority can beinterpreted ways. chord in Ex. 2:46a,a root-position minor-seventh chord is formed Starting with the added-sixth the same pitches in thirds (see Ex.2:46b). The in Ex. 2:46b by restacking pitch reconfiguration different function than is impliedby the sonority harmonic in Ex. 2:46a. expressesa completely minor-seventh chord functions As we have discussed,a root-position (according to Rameau) to a dominant-seventh chord (see p. 30). Though the sonority in Ex. 2:46b is a minorsimilarly seventh it tends to progress to a chord, like the true dominant-seventh(major-minor seventh), whose root is a perfect fifth Because of the functional duality chord lower. associated with the the T Ss D T [I iis VI] can actually be viewed as a fusion of the cadential S\302\260, progression Distinctive
major
Features triad,
1-4-5-1 and progressions
the basic
1-2-5-1
[I-IV-V-I
and I61
v7/V
-V-I].
Example
2:46 b)
is F, Tone-D
Root is D, Added Tone-C
a)
*
l^n Root Added
(sixte ajoutee)
It is ajoutee) by
perfect
only
fifth
whether the circledchord [v /V], since the roots ofthe
of opinion,
a matter
dominant
or aRameau
twice, from
D through
dominant
the
is an inverted S5 (sixte chords progress downward
Ex. 2:47
in
following
(G) and on to
tonic (C).
Example 2:47
P#W
*\302\245
^ inversion
of Ss (S56) or II7
?
[ii7 orv7/V]
Though inversions ofthe bass (see Ex.2:48).
S5
are
rare,
also possiblefor
it is
the
third
or the
fifth
D
T
V
I]
to occur
in the
Example2:48
h
N^
W
s C:
T
[I
V6
\\
T
T
S3
I
I
iis4
Exercise: In Ex. 2:49,S and S5 chords are somewhat overused in a fashion that has very little in common with actual music literature. extra Nevertheless, this exercise will provide in these sonorities. Harmonize the four and follow the in practice handling melody voices, functional To further indicated. write-out the exercise in various progressions gain practice,
keys.
62
Example2:49 \302\253J\302\273 0 /\302\243
4&-4
C:
\" \342\200\242\302\273 * a\342\226\240 i\302\273 a \302\243.
p_E.
[I
iil
*l\"\302\273*rJ
1
d
J
p
Ss D
T
* 1
V
T, S6 D T
S*
ii6 V
iil
I6
I
T
D,
S6
I
V6
T
s'
V
I
itf V
ii6
Ss
D T,
D
J\342\200\224^
T
D64
I6
I]
Ex. 2:50,the fifth and sixth above the bass in the Sstend to act as dissonances other. In (1) the sixth (D)remains a common while the fifth tone, push away in the fifth remains a common into while tone the the sixth (C) moves (2) (C) (D) downward; D4, at the same time. Incorrect moves upward; in (3) both fifth and sixth move apart from each other the next chord voiceleadingwill result if both fifth and sixth move in the same directiontoward As is shown in
from each
which
(4). 2:50
Example \302\251
(D
(D
\302\251
Si , ..6
[115
Origins
D
S3
V
115
..6
of the
^
appeared
D64
5 3
si
D
Ss
D64
vi
5 3
..6 115
V
..6 115
vJ
Dominant-SeventhChord:Though
Ex. 2:51a-c occurred
in
in the time
,
,J.-J
\342\226\240 -J
M/Mi C:
\302\251
earlier
music,
the
harmonic
\302\251
i,J-rWi
i^ c6 S5
..6
115
sevenths
D
S5
V
115
..6
Schroter,
b)A.
c) Heinrich
Hammerschmidt,
1641
1578
r
t#tf
..j-LAi r
n
\342\226\240*'fr
63
Schiitz,
circled in
chords
of Bach.
Leonhard
v$]
like those
concept of discretedominant-seventh
Example 2:51 a)
D%
1648
first
Chord: Dominant-seventh chords are Voicing Considerations in the Dominant-Seventh one ofthe most important almost all final sonority types in the music ofthe late Baroque.In fact, cadences in the works of Bachcontain chords. As is demonstrated in Ex. dominant-seventh that the following two principles of voice be observed when 2:52a-b,it is important leading the of a dominant-seventh chords: seventh dominant-seventh resolves 1 ) resolving downward; 2) the leading tone (third of the dominant-seventh) resolves upward. Exceptionsto these two rules are certainly possible,but alternative should be made consciously,and only resolutions after careful consideration. The only chord member of a dominant-seventh that may resolve freely
fifth.
is the
2:52
Example a)
Resolution of the Dominant-Seventh
Chord
Other Voicings
b)
\302\243=\302\261 i=\302\261
W
H
n
H
m ' f
i \"i
\"r
dominant-seventhchordsin allpossible and then voicings Remember that the leading-tone (third) should resolve downward. It is important at the beginning to acquire good selfdiscipline.Sinceevery one of the four chord tones can serve as the bass note,therearethree to root position inversions of the dominant-seventh chordin addition (see Ex. 2:53). possible Exercise:
keys, write
In various
resolve them correctlyto upward and the seventh
the
tonic.
Example 2:53 First-Invension
Dominant Seventh
3bd=
Second-Inversion
Third-Inversion
Dominant Seventh
Dominant Seventh
#=\302\261
i J^j
C:
D7
3
r^
r
r
r
J
m^
r
D7 5
[vS]
[V2]
64
j
Write out and play
Exercises:
T
the following
D7
[I Vs
D7 T3 D7
T
I
I6 V2
Vs
in various
progression
T3 D7 T I6 V3
I
D7
T
V7
I]
keys:
of the Bach-era,the dominant-seventh is often motivated, as it wasin earlier chord in Ex. 2:54; pay special motion. In four voices, harmonizethe melody the passing-sevenths which are indicated by the functional symbols.
In music times,
passing-tone
by
attention to
2:54
Example
0
A
\342\226\240 rT\342\200\224r
\342\226\240
_H
&T\302\247 VW *k \302\253J
T
C:
D8
V8
[I
7 7
T
D8
I
V*
7
V5
r
'
i-- -
T
D
I
V
\342\226\240 \342\200\2423 -\342\226\240\342\200\224? 1
T V2
I6
s
D8
IV
Vs
7
7
T
I]
will normally resolve to an incomplete spelled root-positiondominant-seventh tonic is tonic triad triad desired after the dominant-seventh,either the (no fifth). If a complete can move upward seventh or the leading-tonedownward, as long as these exceptions to regular voice occur in an inner voice. Do not break normal voice leading, if either the seventh leading both complete and incomplete or the leading-tone occurs in an outer voice. Ex.2:55shows that in late-Baroque literature. tonic chordsmay follow a dominant-seventh
A completely
Example2:55 i
rt
j Correct
7th
^
w
res. upward!
7th
res. upward
i !
^
leading-tone
res. downward!
m
When
spelled
contains chord voices, a completedominant-seventh chord may sometimesbeomitted. In A dominant-seventh doubled. with a doubledroot and tonic triad (see Ex. 2:56).
in four
However,the fifth of ofthe chordis generally resolves to a complete
a dominant-seventh
65
no doubled this
tones. root
case, the
no fifth,
usually
Example 2:56 incomplete
dominant-seventh
,
(no fifth)
\\
wm
is
r r
^ complete
-
tonic triad
Features of the Dominant-SeventhChord:It isthe simultaneous of sounding scale degree and the leading-tonethat gives the dominant-seventh its characteristic sound. This harmonic tritone was certainly employed in music long before but in the Bach, this with the era dissonance b ecame associated dominant-seventh chord. strongly Baroque and In the fifteenth sixteenth the chord-of-the-sixth ft g contains a centuries , which Distinctive
the fourth
- , to be consonant in the same way as the first-inversion triads ft g \302\273 tritone, was considered which do not contain tritones. Examplesof these triads can be seen at the tritone-containing arrows in Exs. 2:57a-c. In Ex. 2:57c,notice that one of the two only pitches of the tritone actually the tone but the fourth scale resolves (circled note) does not resolves; leading upward, degree
resolvedownward. 2:57a-c
Example
a) Dufay,
b) Isaac,1541
-1450
p
M
r
r
T \302\261A
T
c) Praetorius,
1609
r J
J
^^r-rr 66
f
I
chord, the leadingincreasing importance placed on the dominant-seventh the time of Bach as an incomplete viewed dominant-seventh (i.e., a during dominant-seventh chord with an omitted root). We shall callthis sonority an abridged dominantseventh chord and labelit with the functional most symbol E> [vii ].5 Since the El appears of the
Because
tonetriad wasoften
frequently [vii
] will
with
the
fifth
dominant
O
[third of the vii
] in
the bass,
7
the functional symbol D,
the abridged how dominantmost common case. Ex. 2:58ashows to the ate in structure dominant-seventh; Exs.2:58b-ddemonstr several the D 5 to tonic.
be used for this
seventh chordis similar methods
of the
of resolving
a)
2:58
Example
Root removed from Dom.-7th; fifth of chord usually in bass.
d)
c)
b)
O-
^^
zS-
^
r^
j m
=\302\253= ^\302\245
B
Bl
D'
C:
B
I]
[V
As was mentioned above, the triad B-D-Fwasconsideredto be a consonant sonority in earlier music, despitethe interval of a tritone the between B and F. During late Baroque, were considered to be however, both the dominant-seventhand the abridgeddominant-seventh This historical an consonance to dissonance is dissonances. from tension-producing change course of time. of how over the musical interesting example practices changed In the time of Bach, abridgeddominant-seventh chords resolved either to root-position or first-inversion tonic triads. Ex. 2:59 demonstrates both types of resolutions.
2:59
Example
from
YLsnAA-\"Halleluia\"
J*
fc
J
3
Messiah
\342\226\240 J
J
r^
j
S^
m D:
\302\245^E
B
B
The slash
through the
dominant
symbol
(0) indicates
T
I]
[vii
6
-j.
that
67
the root
tone of the
dominant
chord
is omitted.
and in a The dissonant harmonic seventh tension that is normally present between root is This makesit dominant-seventh in the dominant-seventh. possible complete abridged missing of the vii to resolve the seventh of the abridgeddominant-seventh ] upward to the fifth of [fifth it is usual to double the bassin theD 3 chord of D/third the tonic. In four [i.e., the fifth voices, be doubled. of D/root of vii ] should never of the vii ]. The leading-tone [third
the harmonic
Write-out and play
Exercise:
in Ex.
progression
2:60.
Example 2:60
P^ C:
T'i
B75 \"
T
[I
All
chord
four
inversions
(D5) [vii
S
&]
IV
vii
of the
full
T
\"Ach mein
as the
abridgeddominant-seventh
2:61a-e
herzliebes Jesulein\"
D:
from
Christmas
Oratorio
D:
G:D;
[V
of the
as well
dominant-seventh
Example
One
I]
I
] are present in Ex.2:61a-e.
Bach-
[Vl
most frequently
descending melody line which
settles
T
Bl
T
&]
]
[V3]
[V$]
encountered closing gesturesin the tonic chord. on the root of the final
68
B [vil
]
choralesof (See Ex.
Bach
2:62)
is a
Example 2:62 H&ch-Nun
alle
preiset
gggg T
G:
[I
Ex. 2:63a-eshows cadences.
D87
..6 115
..\302\243 7
V
T -,
I]
the Ss [iis] and D
of ways that
a number
't
S65
can be
] chords
[V
used in final
Example 2:63a-e from
Handel-Excerpts
\"For Unto the ev-er - last - ing
Fa
-
ther
Messiah
Us a Child is Born\" Fa- ther,
Prince
the
of
Peace.
a) \302\260
d
J
J
J
J
J
m
f
#
a
r
^=nttP S
G:
V'
[IV
?
tm
T
si
D-
T
I]
..6 115
V-
I]
[Vs I
For
\"Hallelujah\" the
c)
d)
L
Prince
Unto Us a Child of
B
,
6
Bl
T, S5
6 D4
is Born\"
Prince
of
Peace.
e)
=\302\261 *=
ifeE\302\261
*4
fJ
J>
4-fU D:
the the
Peace.
,
h\302\243
till?
S
i
j>j
J J
A
A
A-
iJ
5
L
T3
D: T3
S?
D
T
G:T3 S*
B7 T
(H7)
,
..\"6
[ vii
,6 ..6
r
115
6 T74-
v
5 3
[f
f]
iil
V
I]
[I6
ii7
(v'AO
69
vii06I]
to its
The dominant-seventh function as a powerful
chord is not
contain melodies.Exs.2:64a-f
pitches
six
musical
to its role as a strong closingsonority or melodies. It can also directly generate whose melodic lines werefashioned from the
either
hmited
for harmonizing
agent
excerpts
dominant-seventh.
of the
Example 2:64a in D-major
Bach-Suite
2:64b
Example Valley
Handel-\"Euery *\342\226\240
from Messiah
be Exalted\"
Shall
\342\226\240tr
*\342\226\240
pup
i
m j>
4
m
If
i
a.
a
i=\302\243
T3
S\"
re^^f T
T3
I
tl6
Example Vivaldi-\"L'Autunno\"
* ^i
\342\200\242tr
\342\200\242tr
f * t
* f
from
Bj T vii\302\2606I]
2:64c The Four
t nt
f
*
Seasons \302\243*
w
m F:
LLLj
LOj
ILL^
T
[I
S
D
T
..6
,.V
I]
u
V7
70
Example 2:64d Vivaldi-Concerto
grosso
r
m
P
JLJ-D\"
afe A:
S
Vi.
jTlij:
\302\253\302\273
^
*
3e
fc
D
T
[V-
I]
Example 2:64e usik
Telemann-Ta/eZm
-^B4
r=r
i
m Bh
mm
T,
[I6
V^
7
T
D3
I
V5
Vl
T
S
I
IV
Example Handel-\"0
Thou
that Tellest
Good Tidings
to Zion\"
feE m P#^g
J
r^f T
A:
I]
[V
71
T
Vl
I
2:64f
hold
J>
D\302\2604
(Chorus) from
Messiah
Exercises: Set Ex.2:65in melodic
line has
provide
rich harmonic
of interest,
amount
2:65
J
J
J
J
D3
T
Bl
T
h J T
G:
the
should
variety. Example
i
solution at the keyboard.Though the suggestedchord progression
and play your
voices
four
a minimum
only
[I
V2
I
V5
J
.1
|J
I
vi
-j-^u+4-^ 64
T
i
rv6
i
vl
IVS
5 3
S5
D\302\260
T
..6 13
115
,.8 V
I]
The bass line in Ex. 2:66twice. in the ofthe tessitura change uppervoices; a soprano as possible. expressive
Write out the without
as
highly
first
much
time, the
harmonize it conservatively, time, set the bass line with
second
Example2:66
ss s ..\302\2606 ,6
[I
v:r
^
T
B
T
Bb:
f
f
s6
dS
vi
..6 115
IV
J
N
\\i
J
i3
o3
^3
i6
rv*
vl
I
rj 3
ii
4
h
4 3
I
f
V2
j=^
d:
T, Ss
D4
3
D7
T
v^
I6 iil
VS
!
V7
I]
72
Harmonize the singlelinesin Ex.2:67a-f and
solutions.
your
play-through
Example 2:67a for Strings
Telemann-Suite
\"La
Lyra\"
a)
r
r
f^
m
r
\302\273r
r
r
PfP^
'
1
D
JUL V
W
a
i
-_\342\200\224| \302\253 \342\200\2241\302\253 \302\253 ^
*
*
1
*S-
J
I
\"
Grunde
I
J J
geistliche
J J
Jlf
Hr-k^~^
\302\243
mm
^i
from
p^ 88
^
Eisleben (1598)
JI J
J
*
-II
a different
Example
Joachim Neander-T/rcser
^
2:99b
Herrscher, wiserKonig
M
\302\253
^ G:T [I
^
IV*]
Example 2:99c Johann
*\302\273J
JIJ
4
(1680)
=g
\302\243
'\"J
J-
\"
Rudolph
Ahle-\"Liebster
Jesu
\"
(1664)
wm^
rr
W^
p^
2:99d
Example
Franz
Heinrich Meyer-\"Mein Schopfer,
m
steh
bei mir\"
(1741, after an old melody)
jp-
^E^
zaczrgrg:
u. 4tfr>JirrrJiJJ':i
devices occur on weak beats Escape Tonesand Appoggiaturas:Both these non-harmonic of the beat. 1) Escape tones are approachedby step from a chord tone (like the to apassingtone then or neighboring tone). This dissonantneighbor approach immediately leaps are approached to atone of resolution. 2)Appoggiaturas followed by a leap and are immediately the resolution tone (like the resolution of passing tone or neighboring by stepwise motion into in the late-Baroque. rare tone). Appoggiaturasare extremely
or portions
89
The four tone figure;
in Ex.
excerpts
the most frequently
2:100a-d demonstrate
an upper-neighborfollowed
by
a descending
encountered
escape-
leap-of-a-third.
Example 2:100 a)
alle
ruhen
Bach-\"Nun
i^rt^l^iff1
Telemann
SS
r
appoggiaturas
passing tones that
Bach
*y^
f=rr i-XU
s The
d)
i
P
ihr Frommen\"
W^
m^
c)
doch,
J J J Ml 3S r^
J*
UA
wie selig seid ihr
b) Bach-\"0
Wdlder\"
(circled notes) that
are exchangedbetween
*s
/
*L
^
appear in Ex. 2:101areactually the
alto
nothing
more
than
and tenor.
Example 2:101 Bach-
\"Gottes
Sohn
a piano accompaniment
ist kommen\"
to the melody in Ex. 2:102in which you employ Donot write-outthis accompaniment, but rather changes sketch-in only the functional The (or Roman numerals), then sing and play the example. symbols a passing-tone suspension [accented tones, auxiliaries, melody itself containspotential passing and an escape tone. Identify and labelall of the potential non-harmonic devices tone] passing contained in the melody before it. playing
Exercise: Invent
no more than
two
chord
per measure.
90
Example 2:102
Rathgeber(1733)
crr ir cr
ffi'r
^
m D V]
s
[IV
where
harmonic
change). always
T
i
P
P r
r r
i
?
^
device that occursbetweentwo chords, the secondchord (anticipating the upcoming the pitches of the first voices maintain chord. Meanwhile, the other occur on weak beats or portions of the beat (see Ex. 2:103a-e).
Anticipations: An one or two voices
Anticipations
r
\302\273i|\302\273 rrrfif
-s-f\342\200\224(Lf-frif
anticipation
sound
is a
non-harmonic
tones belonging to
Example 2:103a-e Anticipation of the 8ve from above
b) Handel-Messiah \302\261^fc
Pip
p^
C:
D7
[v7
c)
i]
Handel-Xerees
[vH
n
nLr^u~~crj n
^fe
n
i]
Anticipation Of the 3rd.from above
Anticipation of the 5th from above
d)
Handel-MessiaA
m^
3 mm
i^rffi
tes
LLA
Mi
y-%rrrf
TTT 91
cont.
2:103a-e
Example
Anticipation of the 8vc from below
e) Handel-Messiah
I
J pi
mm
5S
mm Ex.
2:104
contains
3=^
and tonic
of both the subdominant
anticipations
triads.
2:104
Example
Telemann-Tafelmusik
frbBr
f A
A
A
E
i
m
r T
T-
F:
[I
Anticipations
2:105
contains
an
IV
I]
most often occurinthe melody-carrying voice of rare lower-voice anticipations: example
as it
Example2:105 Handel-Messiah
h
J
>
i
J
J
J
J
\302\261
r r r c_jp m
I D: T
i
imm D3
S3
T5
D,
V*
TV6 14
Vt
92
I6]
approaches a cadence.Ex.
Part One of bewein.\" of its
kind in the
Passion ends
St. Matthew
Bach's
constructed entirely from
This chorale,
literature. (Ex.2:106seearrows)
4A
J-
I
i
I
i}44^A
arrangement is probably
motives,
\"O
Mensch
the only
piece
2:106
Example
Bach-\"0 Mensch
i
chorale
the
with
anticipation
bewein\"
i J i 111
I
i
#
yfoj\"jrafN3
S
ate
Ex. anticipations.
2:107 Label
^
a melody by Rathgeber which harmonic functional changes with
shows the
on an
accompaniment
contains a number
of ornamented
sing the
symbols,
melody and
instrument.
Example 2:107
^=g fl
J
J^
\302\243h$L&
w J
Jj
I
u-
f
m
F
[__j
1
m \\ f *\342\200\224\342\200\224 jJ s
|
*un\\nr}\\&tUJ3sj-^
93
\\
J
J\"\"*\342\200\224 ^=^
play
an
drill
Exercise:
Harmonize
the correct
use of escapetones(e.t.)and
the
melody
2:108 in four voices. This exerciseis designed
in Ex.
2:108
Example
r
fy't
r
i j j
j. iil ^m
-\342\226\272C-Major
W
\302\261m
Ex. 2:124a-eshowshow and
lowered-seventh
the
major
scale degrees in
late-Baroque usedthe lowered-sixth ascending passages to create a shift of tonal center. composers
101
of the
a-e Example2:124 Purcell-TArice
a)
Happy
P
im\\ts-tf^
^m C:
D
t
V
i]
D
T
I]
[V\302\260
Concerto
b) Vivaldi-Oboe
m
m
mE
c) Kandel-\"But
t
s
[V
i
iv]
Who
=fe
C:
D
a:
May Abide
& 11
S
from Messiah
2=J=
L
F
*t V
C: S,
V6]
d) Bach-OrganFantasy
[IV6
V6;
]
[IV
102
I]
in B-minor
D
C: S
t[i
ming\"
A
D.
a:
I]
[V6
the Day of His Co
^P
[i
T
D3
VK
V]
e) Handel-\"3Vie
Walked in Darkness\" from
that
People
Messiah
fc
^
f^*
m -
dark
ness have
seen
a
light,
great
m m
C:D
a: D [V] symbol for the
The functional
Hugo Riemann
Tr
[V
Sr
D
T
IV
ii
V5
I]
has
triad
minor
used the
S
in several forms
appeared
since the
Karg-Elert employed of using small case lettersto represent characteristicminor third), and upper case letters to represent major triads (because of their characteristic major third).13 It was not until first that Maler the of letterWilhelm 1931, however, developed convincing system functional For that I follow Maler's this text. in Ex. 2:125shows how symbols.14 system reason, shall closely Maler applied upper and lower caselettersto all types of the tonic, dominant and subdominant in major and minor modes.15 chords nineteenth
century.
the symbol
T,11 whereas
symbol
early as 1821, GottfriedWeber minor triads (because of their
^\342\200\224 .12 As
Sigfrid
the
suggested
concept
Example2:125
i
I Ii
s
S
d
D
iv
IV
V
V]
I
^ [i
In the
late-Baroque allinversionsof
subdominant
2:126
the time Hugo 12 13
region
was
of
Riemann, Handbuch
Sigfrid
Karg-Elert,
rich in harmonic
especially
the progression Bach (a fact to which
contains
dominant-seventh
the
8i
ft
fSf\\ 5 -
S5-D (ii every
tenor
der Harmonielehre,
Akustische Tonklangund
St7
v
variety: s(iv),s (ii ), S5(ii
) which was
in a
were available in
chorus can testify).
9th ed. (Leipzig: Funktionsbestimmung
Breitkopf
und
Hartel,
(Leipzig: CM.P.
1921).
Rothe,1930).
Gottfried der Tonsetzkunst, three vols. Weber, Versuch einer geordnetenTheorie at a Systematically Arranged Theory of Musical (Boston: Wilkins and Composition
transl. (1817-21);
Wilhelm
Maler, Beitrag zur
durmolltonalen
Harmonielehre
16
Ex.
5), S(IV).
especially common in music during
as Attempt 14
minor, but the
(Munich: F.E.C.
Carter,
by J.P.
Warner
1841-46).
Leukart, 1931).
The author labels the minor triad constructed on the fifth scale degree of the minor scale with the letter-symbol is consistent with the conceptof the Rameau dominant d; thus the term: minor dominant. Although this terminology if a minor seventh is added above the root to form a seventh chord\342\200\224see (especially p. 30), many mu sic theorists, in both and German-speaking countries, prefer to limit the use of the term dominant to sonoritieswhich contain the English-
leading-tone.
103
Example 2:126
*
J J^J
PP 7 .n lj
r..\302\2736 ,.8 LU 5 V
was not used in chord (to which the
Ss (iis)
dominant
in
occur
the time
during
keys
Ss normally
of Bach.This is probably
resolves), would require
a doubledthird
because
the
(leading-tone),
that the raised third of the principles followed. Ex. 2:127shows forces an the resolution to lea This problem does not (F#) (G#). upward ding-tone is not altered from the key signature.16 chord major, since the third ofthe subdominant
if standard subdominant
minor
voice-leading
2:127
Example
m Ai
*
f
m
^ F
r*>
T
Ss
D
[I
iil
V
a: t [i
]
D S\302\247
iil
V]
resolves 2:128a-d, the dominant directly to the tonicin minor normally the progression D s3 (V iv ) is sometimessubstitutedfor D-T [I-V]. Though However, keys. rare, the progressionD- s (V- iv) is also occasionally encountered, but D - S (V- IV) is consistently As
shown
in Exs.
avoided.
16
The author seems to of its inflection.
be making
reference
here to the
principle
direction
104
that
an accidental should
normally
resolve
in the
2:128 a-d
Example
b) Handel-\"flbii)
Blow-
John
a)
Ode on the
Death
f
TTF
i^#f
si - lent and
and
i
y^g s6 r.6
D
s3
..\302\2606,. V 11
Li
s3
i]
[iv6
#^ D
s
V
iv]
gj
j^ \302\247s
D
[V
s3-~~ iv6
iv7
D7
t bb;
V7
away progressing lowered-seventh
of the
every
possible
in the
from a
minor
chord
dominant
scale degree
(subtonic pitch)
soprano. Ex. 2:129showsthat
voicing.
105
the
ss
t3
i] [i6
appears
u
iP
c:
it
See Him from Messiah
That
g\302\273
j
ii TJ1
when
things.
good
^
m
^m
m
When
n
of
dings
H*\302\243
##
j[j
tendency
-
ti
d) Handel-*A# They Laugh Him to Scorn\"
Fugue in F-minor
c) Bach-Organ
k
vi
^
[i
g:
D4 3
j^rrr;
5=^ glad
Feet\"
Messiah
sp J^A
list'-ning
Wf
are the
Beautiful from
ofPurcell
iil
(d) [v], must
progression
D V
j\"ijj
\342\200\242
Lr
[
s3 D* iv6
VS
I
t
35
i]
the downward-resolving be considered,
d-s (v-iv)
especially
is not feasiblein
Example2:129 acceptable
avoided
to be
n
m J
J
fc
w
iv
v
Ex. 2:130a-b showsthe typical
J
1
p^
i^i
J
pp
tds3 tds
a:tds [i
nffl
J
v
i
i
iv
iv]
a descendingminor
of using
practice
Baroque
v
scale
in the
bass.
Example 2:130a-b Bach-\"Es
a)
woW uns
Gott gentidig
sein
z4
0 ate
\302\261
Si
^f D
t, IV
[V
b) Handel-'TfooK
Shalt
^
Break
D
V]
Vll
Them\" from Messiah
^tffff
s
I
\302\243i
ff
h; tti!\342\200\224r a:
-J
:tz2
^ .6
14
Ex. 2:131 demonstratesanother descending
chromatically the
tendenciesby
i
t
[i
music of
1
B\302\253t
nineteenth providing
employed in the late Baroque\342\200\224a technique frequently scale is also important in the (The descendingchromatic where it often employed to neutralize melodicleading-tone motion in the oppositedirection.)
bass line. century, half-step
106
2:131 Example Shalt
Hande\\-\"Thou
n
^i
nr^
nrm
j
I
\302\261W
J 1
j
\302\261 a:
Exercise:
Them\" from Messiah
Break
D3
d3
S3
s3
D7
[V6
v6
IV*
iv6
V7]
in all Play the progressionsin Ex.2:132a-b
minor
keys:
2:132a-b
Example
^k
^
w^ a)
m
^=\302\261
\302\243e\302\261
D7
\302\253:
V^
i<
PW^
if
^
b)
S a:
t
S
B] 1
[i
D87
t
V87
i]
rules were derived from analysis of numerous Bach chorales and 1) minor triads normally doublethe root, but it is sometimes is rarely doubled. 2) In first-inversion minor possible to doublethe third; the fifth, however, the bass (third of the chord)is doubled as often as the root. triads, nearly Sinceminor keys are somewhat less-stable than major keys, it is quite typical for minorthe (almost key progressions to remain within key only a short time, before modulating to the relative major. effortlessly) Exercises:Write out and play four-voice settings of the melodiesand bass lines in Ex. of the examples 2:133a-j. The brevity corresponds to Baroque practices. The
following
excerptsfrom
Handel's
doubling
Messiah:
107
Example2:133 a-j
al)
> ins t
d:
D3
[i
Vl
6
t
.,06
i
11 5
t
D
S5
V
i
d3
S3
h
v6
. 6 IV
.6 14
S5
D,
t3
..\"6 ,.4 11 5 V2
.6
p
t
\302\2735
..\302\2606 .1
Vll
1
lj
a2) ^E5t
lfegE3g
i
s4
t
g:
r .6 Li
a3)
B
Soprano:
3.
s
t
.43
6
vS
i06
iv
i
i]
CB Dl
^ e:
t
D4
S B
3
..06 \342\200\236,
.6
IV Vll
[i
1
1
d
s
V
IV
b) Handel-Cantata \"Ach
f
^ c:
t
[i
*l|\302\273 ^
D3 d3 V5
t
3
D4
t
V3
Herr\"
\342\226\240
If---^
^
S3
s3
IV6 ii'J
v6
D75
D V
D7
vS
V!
I
c) Rathgeber Compensate
4tJlir
for the
lack of melodic
with harmonic
variety.
P
MiJJito
d)
3^ PHIF^:
interest
Rathgeber
^
IfiF^F
PWP d: s s-
[iv 108
\\iei\\
e) Handel-'Bui
Who May
from Messiah
Abide\"
^
\302\261*
\342\200\242nPl-TCJiJlJ
^rPirp
gmJLdi1
d:
habe
f) Bach-'TZerr, ich
'
'
u
m
r
'
'
h)
First
Johann
^
cadence on the dominant
Melody
meine Freude\" (1653)
Kriiger-Vesu
j^-jg-l^
and Last
t
r
^
f^^T^
The
' r
m
^m
i)
[it] mifigehandelt\"
half
g) Chorale
t.
Sectionsof a Chorale
r r if errJ
Melody
ir
which
J r
r
y
Modulates
in its
[\302\273J
r
Center Section.
s\302\247
^ j)
From
filji
a Chorale
r
Setting
by
Bach
^lULLrLTt^ a: t, [i6J
109
triad, which can augmented appeared during the time ofBach.17
The
Triads:
Augmented
first minor-scalecomplex, as an independent sonority. treated as a suspensionabove
whether 2:134b),
Neapolitan-Sixth Chords
Triads and
7. Augmented
be formed
from
the
pitches
of the
it was
rarely employed triad was usually
However,
the dissonant tone of the augmented or tonic harmony. In Ex. 2:134a-b, to determine the augmented triad E-G#-Chas tonic function (Ex. 2:134a) or dominant function (Ex. it is first necessary to determine which tone (G# or C) is the dissonance. Rather,
dominant
either
Example134a-b b)
a)
s *
p39p [(in+6)v]
[(inVl
the Roman-numeral III+ indicate that symbol above dominant or occurs as a result of suspensionfigures tonic and should not be considered an independent harmonic sonority.
*The parentheses
the
Ex. 2:135a-b which
imply
()
surrounding
triad
augmented
shows two
the augmented
spots
from
Bach
chorales that contain
suspension-like figures
triad.
Example 2:135a-b b)
a)
^5k
\302\245
$ J=\302\261L
r^ a:
D3
17
An augmented the contains
3
t
d:
D6
5
t
[(III+6)V
i]
triad is formed from the pitches of the minor-scalecomplex raised-seventh scale degree as the fifth of the chord.
when
[an*!)
degree
4
3 vj-i\342\200\224
i]
110
the triad
built
on the
third scale
Exercise: Play the progression given practicein the late-Baroque,the augmented
2:136 in
in Ex.
does
triad
several
minor
not actually
keys.
As was
appear as an
the normal
independent
sonority.
2:136
Example -
6 D\302\260
t
I
4
D3
5
-
3
, | t
[i
(ni+6)
v
i
,6
ii\302\2606 i (m+\302\253) vs
5
|
~3
i
t
S5
I
t'
vii\302\2606i
ii^f
i
(in+)
JBT7 5
3
i6
S5
i6 rf
D
v
I
i
t
i]
the Chord: In the biblical story, warrior Jephthah bargained with the first person from his own household whom he would meet upon returning in if God would to him battle.18 As fate the first to greet would have home, it, grant victory At his beloved the where father after was and only daughter. point Jephthah victory daughter which seems to have meet in Giacomo Carissimi's oratorio Jephte (publ.1664)a sonority appears for this spot (though it is used quite liberally throughout saved this of the been especially section as a minor subdominant chordwherethe interval of functions work). This particular sonority a minor sixth above the root is substituted for a perfect fifth [i.e., a minor chord-of-the-sixth with a chromatically used in operas lowered sixth]. Since this sonority type was commonly by it has come to be known as the NeaSchool, composers ofthe eighteenth-century Neapolitan the Neapolitan). This sonority type was originally derived politan-sixth chord (or often, simply from a b 6-5 suspension-figure which was applied of a minor subdominant above the root and third chord (see the figure labeled s in Ex. 2:137).
The
Neapolitan-Sixth
to sacrifice
God
Example2:137
i]
In the
time of Bach, the suspension form
Neapolitan-sixth s ) are symbol
3
Book of
chord. Several
shown in
Ex.
of this
possibilitiesfor
2:138a-d.
Judges 11:30-40.
Ill
the
a true sonority was regularly replacedwith use of this sonority (also labeledwith the
Example 2:138a-d
il
#Wf
fes
$m
f^
T
cross-relations
cross-relations
^ 6
D4
3
the voice which
J
fm
^#
5
D [i
Whether
d)
c)
b)
6 4 vll
N6
the
contains
b
[i
i ]
N6
r r J
t
v3 i6]
ti
N6
V7
i]
next chordby step (the so-called or by diminished third (see Ex.2:138c, soprano),
6 progresses
to the
Ex. 2:138a, \"Phrygian second\"\342\200\224see soprano) it should generally resolve downward. ThoughBaroquepracticeoccasionally
from
deviates
principle, the normal downward resolutionof this voice should predominate. that the Neapolitan-sixth was reserved,in Baroque to remember music, and woe,\" and in no case shouldit be considered expressionsof \"lamentation
this
It is alsoimportant for the most intense a simple
triadic
sonority.
The subdominant pitch (bassvoice) is usually doubled in the Neapolitan-sixth. When it to it is t o the avoid cross-relations between the two progresses directly dominant, impossible In Ex. 2:138b-c, note the Bb in the soprano of the s and the B% in tenor of the following chords. Ex. 2:139a-e contain additional excerptsfrom dominant chord. literature which employ period the Neapolitan-sixth.
Example 2:139a-e a)
[Texttransl.:
\"and in
the
affliction
Giacomo of my
Carissimi-Jepftfe
heart, I wail\"]
w
bs^fmw^ffl'i
i
et
in af-flic-ti- o- ne cor-dis
me - i
(-1645)
u-
m
i-Hfffl-p lute,
^
^E
he treble staff is a basic harmonization of ihe continuo bass and is rotated here without actual rhythmic values.
gS5E D7
65 D43 s\342\200\236
[V7
iv6 V43
112
u-
W
lu
-
la-
^^ ==m 65
Scarlatti (-1700)
b) Allesandro transl.:
[Text
\"if
only a life
*
of
sorrow\"]
i
vi
m.
wr~hl
m
^m
va nel
-
dolor
7 7
-TMr-
1 1
P
{U-P_
VJ
w
\342\200\242iv6 V]
[iv
Matthew Passion
c) Bach-Si
$
r-
err
r
f^r-i
\342\200\224
^ J\"
S^ D
c:
[
3
1
D^
V6
V-
Vl
d)
s
t
i
Bach-Organ
5
N6
Passacaglia
7
i^I
T
=i
h
EF
S
Ji
AJ2
S^ r
J
nJ>
-f\342\200\224^-
^S
^
F
c: D-
D
v2
[V-
113
7
t
3
i6
1
i]
e)Bach-Well-Tempered i
IsiJ
t
f:
mm
[i
s'
s
iv?
N6
Exercise: Complete the following [Text Transl.;
on, Draw on
\"Draw
\342\226\240L
k^S:
U
&
U
LJ
p
Clavier
D
four-measure
grieving year;
on with
3
by adding
phrase
Draw
t
7
my
the altoand tenor voice on with
Draw
afflictions!
\342\200\224-A. Gryphius
gtit^rg -
tes
triib
Zeuch
Jahr!
\302\2736
ii 5
g_L_c/ mei
^
^^
-
nen
,J
^
Schmert-zen!
Zeuch
III
+ 6*
m^m hin,
mit
t
D'
t
i
V
i
V i
mei - ner
Angst!
m^m^ -D
7
t
\342\200\242 1 V2
3
mit
i
mm
^
hin,
B1
t 5
Vll
114
111
s6
D4
3
t
V4
3
l]
my
dread!\"]
s
a four-voice setting on at the climax of your
Compose appears
sonority
the
text;
following
und bliit, kann nochfiir Abend Was ist derErden Saal? Ein herber Armen! ach wie ist's so bald mit uns
Wasjetz Wir
[Text transl.; earthly
\"What
space?
8. 9-8
make sure that
gantz
The
sonority,
werden.
zutretten
Thranen-Thal! \342\200\224A. Gryphius
gethan!
now blooms can be completely down by evening. What is trampled of tears! Poor humans! Alas, how quickly we are undone!\"] vale
this
A bitter
Suspensions
Applied
and Leading-Tone
Chords
fully diminished leading-tone seventh chord can of the minor-scale complex.Though all composers it is especially characteristic of the music of J.S. Bach. Example
2 diminished
be constructed in the
from
the
pitch
Baroque employedthis
2:140 fifths
- diminished
figured-bass
Chords
to Dominant-Seventh
Diminished-Seventh
materials
a Neapolitan-sixth
setting:
seventh
3 minor thirds
symbol
to the brief figured-basssymbol [ ] and the relatively simpleRoman-numeral as is not to an functional symbol for the leading-tone easy design symbol appropriate chord.19 In minor keys, it is often viewed diminished-seventh as an abridged dominant-ninth with chord (dominant-ninth an omitted and for that it is labeled with the often root), reason, D or D .20 The diminished-seventh leading-tone symbols 7 chord, which first appeared in the Baroque,should not yet be termed an abridged dominant-ninth, however,sinceit did not acAs opposed vii
, it
19
There is also diversity among the authors of English-language harmony texts in the choice of the Roman-numeral for the fully diminished leading-tone seventh chord. Someof the suggested Roman-numeral symbols for this Aldwell and Carl Schachter,Harmony and Voice Leading, 2nd ed. (New York: Harcourt sonority are: VII - Edward symbol
Brace Jovanovich, -Bruce Benward and Gary White, Music in Theory and Practice,4th ed. (Dubuque, Iowa: 1989); vii W.C. Brown, 1989),and Stefan Kostka and Dorothy Payne, Tonal Harmony, 2nd ed. (New York; Alfred Knopf, 1989); vifin Tonal Music, 5th ed. (Needham -Paul Harder,Harmonic Materials Mass: Allyn and Bacon, 1985); V^-Walter Heights, 4th ed., rev. and expandedby Mark Devoto (New York: W.W. Norton, 1978).This translation will Piston,Harmony, since this symbol is the one that this translator employ vii\302\2607 regularly uses in teaching, and because it fits with the author's use of upper- and lower-case functional symbols. 20 The small letter [ ] which is applied to functional symbols in German word verminderte; which is literally translated into English as diminished.
115
harmony
texts is an
abbreviation
for the
tually
the time of Bach. Ex. chord) complete form (as a true dominant-ninth during chord resolutions which employ ninths added above dominant-seventh The resolution in Ex. 2:141a was not yet in use during the time of Bach,but the in Ex. 2:141b and 2:141cwerequite common.
appear
2:141a-c
shows
chords. resolutions
in its
three
2:141
Example
m4&
*
!
4
r
\302\273f 9 8
D7
t
t
[V7
The 9-8 Suspension the true dominantAbove the Dominant-Seventh Chord:Although ninth chord (Ex.2:141a)was not yet employed in the Baroque, a melodicfigure which strongly chord in the dominant-ninth the form of a 9-8 implies regularly appears suspension above the Ex. 2:142a-d shows four musical excerpts (in both dominant-seventh chord. and minor major contain such figures. Note that the minor ninth the dominant (above keys) which pitch) normally appears in minor keys, whereas the major ninth is most common in major keys.
Example 2:142a-d St. Matthew
Bach-
[V? 6
5
Passion
[V
I]
116
9 8 7 6 5
V7
9 i
5 8 \342\200\236,) 3 [V7 6
*This
9-8
of F# -minor
.78 I 4
3 ]
[V?
7
i]
resolves to an Fit-major triad, even though the key by use of the minor ninth at the point of the suspension. Qui tollis from Bach's Mass in B-minor;measures 4, 6.)
suspension
is implied
(Seealso
The 9-8 suspension abovea dominant-seventh that the seventh ofthe chord chord requires alsobepresent.Infour voices, the fifth of the dominant-seventhisthe chord tone that is normally must the chord root. For omitted. Furthermore, the suspended-ninth be at least a ninth above that reason, it is not feasible to voice a 9-8 suspension figure as in Ex. 2:143a; possible configurationsare shown in Ex. 2:143b-f.
Example to
be avoided
\342\200\224
possible
r
hjn
143a-f e)
d)
c)
-
&
g
f)
W
IT Ti
ff
ff
9
V7
will
7 6 6
V5
7 6 6
V5
]
for FN. In this case, the tonic triad which follows 2:143a-f, F# could be substituted in be rather than A-minor. If the occurs the bass,it suspension figure normally A-major resolve and be labeled as a 2-1suspension circled downward (see sonority in Ex. 2:144). In Ex.
would
4
117
Example2:144
[v-
In four
Exercises:
play
at the
settings
your
the sopranoin Ex.2:145aand
voices, harmonize keyboard.
the
inEx.
bass
2:145b;
Example2:145a-b
a)
$m\302\261m
987
7
d: t
[i
D98 3
t
Vj
i
D
s
t
7
D765
V2
D
t
3
4
i
3
iv V7
2
1
V
i
i6
V7
N6
V
D2
>
V7
\302\253
i]
b)
a
^g
It should
suspensions
S
~\"
T Make
^
T
sure
to employ
or 2-1
9-8
T
t
suspension
at the
figures
T places marked with
T arrows.
be quite evident from the that the use of too many 9-8 exercises, preceding can create a hackneyed musical texture that is not at all typical of Baroque
literature. The
may
also appear
As is shown
Chord:
Diminished-Seventh
as a suspensionsonority
which
inEx. 2:146a-c,the diminished-seventh chord to the dominant-seventh chord.
resolves
Example 2:146a-c Bar
- ab-bam!
b) Bach-Chorale Excerpt
ttJ~3J \302\273
\302\253 \302\253:
J
a) Bach-
ff^
\302\273
w
Si. Matthew \302\253n
Passion
i \302\245
^mm 9
^
PfT
9-
e: D7
g:
t3
7 6
D7 7 6
[i6
118
Vf
t43 D i4 3 V
Toccata c) Bach-Harpsichord
jS
fin
^
*
J>J m g:
J
j>
>
If
p ff
D^ 7\"
[V?
The
preceding
treated asa suspension in Ex.
examples also figure
when
i]
suggest that
the
a change
of harmony
diminished-seventh in the following
leading-tone takes
place
chord is chord
(as
2:147).
Example 2:147
does
Bach
Instead, metrical
positions
diminished-seventh
suspension
diminished-seventhchordasa suspension however. figure, it without a weak beat on or always employs (those preparation portion where suspensions are normally or resolved). In fact, Bach's prepared chords often function as harmonically consonantpreparations for dissonant
not usually
he almost
figures
which
treat the
follow
(see
Ex.
2:148a-b).
2:148 a-b
Example a)
from Two
Bach-Excerpts
Chorales
g
25
^ T.
119
Clavier, Book II
b) Bach-Well-Tempered
i
gag
M
s
i
\302\2434
*
^
M
P*P
H**
PT
2:149a, the leading-tone diminished-seventhchord (vii most and subdominant harmonic elements. However, this sonority only in terms of its dominant function. For that
In Ex. of dominant
displayed as a mixture have chosen to are the 0? orD reason,
) is
theorists
explain it. However, as Ex. 2:149bshows,Wilhelm Maler usual functional symbolsusedto represent a to the mixture of dominant and subdominant tendencies (D ) employs special symbol represent is the only theorist which occur when the subdominant pitch appearsinthebass (vii 3). Maler a chord who this to diminished-seventh hybrid symbol represent leading-tone regularly employs (second
inversion).
Example
a)
2:149 a-b
b)
j|i\302\247j^ m
t r. [1
D.
D4
6
..04 .,j 3 Va
I
vll
in function, that the leading-tonediminished-seventhis basically dominant the but to go a step farther with of the subdominant triad in the bass. I intend The third subdominant attributes of the leading-tone diminished-seventh chord, however. measure in Ex. 2:150not only shows the influence of the subdominant the chord within pitch Ds indicates with the root
itself,
but
measure. diminished
a predominance of subdominant function within the entire also demonstrates In fact, dominant function, is normally associated with the which leading-tone seventh chord, does not occur until the fourth measure ofthis example.
120
2:150 Example Rameau-Les
ninth
in the leading-tonediminished-seventhchord isjust as clearwhen dominant (seventhof vii ) is found in the bass (vii 2). Ex. 2:151 shows how
function
Subdominant the
Cyclopes
above the
this third-inversion
diminished-seventhchord producesa retardation
Handel-'BwiWho
May
2:151 Example the Day of His Coming\"
Abide
into
figure
from
S5
(ii
3).
Messiah
k re:ard.
fi he
ap
pear-eth?
$=k
^t d: s
'
',
4 3
[iv
During
the time
T
of Bach,the function
of the
;6 ii\302\2736 ,,04 11 i\302\260 4 n\"i
V V6]
diminished-seventh
leading-tone
chord was
establishedbytheactionofitscomponentparts,whichbelongtoboththeD (V
Of the four pitches of this subdominant (see Ex. 2:152). chords.
sonority,
belong to the dominant
three
and three belongto
Example 2:152 -
Pitches contained
intheD'(V) 4>
1 rr
L=\302\261\302\261
r
0'
*^
*
t Pitches
contained
in the s6
121
(ii D6)
r^
-} s6
)andthes
f
(ii the
)
In places like those shown in Ex. 2:l53a-b, there is so little an interpretation of the diminished-seventh chord as dominant should end in stalemate. theoretical argument
difference
between
subdominant, that
all
b)
id^
\302\243
n
era w m
or as
2:153a-b
Example a).
analytical
mi
pffp &
4
9
6
a:
? s6 5 4-=
3
t
4~=
s5
?
s6
t3
&l
6
5 4-= D4
5
3
7
]#3?
3?
7
g
7
5
As
we have
observed, both dominant
leading-tonediminished-seventh shown in Ex. 2:154also
support
the
and subdominant
The
chord.
leading-tone
of dual
concept
s
harmonic functions
within
this
sonority.
2:154
Example
t
in the functions come together and Phrygian leading-tone motions
t
D
t
be particularly careful when the leading-tone diminished-seventh interpreting our contemporary ears, since we havebecomeaccustomedto those neatly stacked sonorities of the second-half ofthe nineteenth are characteristic (built in thirds) which These later century. diminished-seventh sonorities are almost always consideredto be dominant in function). Therefore, we shall label the Baroque leading-tone diminished-seventh with the symbol $ . tendencies as they occur 0 standsfor a mixture of subdominant [/>] and dominant [D] harmonic v the fully diminished-seventh within sonority [ ].) In functional used to define harmony, the number-symbols3, 5, 7, and 9 are customarily the chord factorsof the leading-tone as they appear abovethe omitted root diminished-seventh of a dominant-ninth chord. However,a true dominant-ninth was never in its employed complete form we shall number the chord factors (i.e., with its root) during the time of Bach. Therefore, of the diminished-seventh chord from the leading-toneupward with the numbers leading-tone Ifthe third, fifth, or seventh of the diminished-seventhchord is found 1, 3, 5, 7 (see Ex.2:155). in the bass, a 3, 5, or 7 should be written at the lower of the symbol EJ . right We should
with
122
2:155
Example
^\302\261
^M
^4
to
3^4
nu
?
m
rrr
mr &
&
d:
mm
1
&,
1 5
&l
*1
1
hk 6
&i
m
TTf
rrr
D4
J
X
'9 3 D?
5
6 or: s5 4\342\200\242 6 ..04 X 2 14 *\\-
Vll
or:
A<
write out and play (in studying the following voice-leading principles, chord in Ex. 2:155. keys) progression We discussed the correct resolution of both the leading-tone have (third) and the already seventhof a dominant-seventh chord (see p.64). As is shown in Ex. 2:156, the leading-tone(root) in the same manner. resolve and the seventh of a diminished-seventhchordshould normally After
Exercises:
various
the
minor
Example 2:156
Bach
Although
In order to downward
avoid
by
allows
occasionally this
diminished-seventh,
hidden
step (as
kind
fifths, though
the it were
hidden
Fifths
in
leading shouldremain
of voice
fifth
chord
of the
the seventh
the the
(subdominant
of a
leading-tone rule. pitch) should alsoresolve
resolution exception
rather
than the
of the dominant-seventh). 2:157
Example
'
4
As is shown in
Ex. 2:158,the third
\342\226\240'
of the
resolvefreely. 123
leading-tone
diminished-seventh
chord may
2:158
Example
J
avoided
JL
*
i~
be
-\342\200\242\342\200\224a \342\200\242 a
\342\200\242 m \302\261
~*~fi~
4, betweenthe bass and
*
;
m
fr\\
Ex. 2:159 shows two seventh chord. Note that
to
resolutions
acceptable
-^
ways to resolve the bass voice second of the two producesa set of
different
of the
the
rare
diminishedleading-tone fifths (see measure
hidden
alto).
2:159
Example
Couperin-L'Ame en peine
IiaJl
^
m
3EJ3\302\243
-J> k
^S
jj>
m p
b: t [l
Ef>
^N \302\243*
^ B7
t
B7
5
Vll
&
5
3
t
D
3
V6
i
Ex. 2:160 summarizes the standardvoice-leading diminished-seventh chords.
associated
principles
1
V]
with leading-tone
2:160
Example
i^r
$
Exs.
2:161a-d
are excerpts
3*EE?
,^
S^*
from chorale settingswhich
seventh chords.
124
D.free
contain
leading-tone
diminished-
Example2:161a-d Four a)
m d
d:
3
&
l
e: t
r.,6 vll..\302\2607 -i 1] [y
1.) Write
Exercises:
at the
settings
your
d)
4= ist
J
,
s5
b:
t
D6
214333
t
..\302\2606 .6* Vll 5 1 ]
out four-voice chorale settingsof keys. keyboard in various
the
melody
D
r-.
[V
[i6
3
D
V
t
i
T?
D
t
vii\302\2607 i
t
[i
2.) Compose keyboardaccompaniments harmonic progressions suggested; make
J#2 ' t
D4
334
viiD!6
sure to
3
t
melodic and
sing
37
Matthew
down
sat
Haupt
da
er zu Tisch-e
head ofthe
table\"
safi
Lr \302\253 I*V
r.
Uv
..04 vll 3
t
.6-1 1 ]
Ex. 2:162a-cand
}i 3
..u4 vii 2
V?
125
87
m s
3
i6 iv
D4
3
t
vn,7S
excerpts in Ex. 2:163a-e. Follow play your settings.
Passion
at the
f&^'cf d:
1
t
[iv6ii\302\2606vii1 V
Example 2:163a-e \"he
53
m
d: s\342\200\2246 T? D
V437i)
i6
to the
Bach-Si.
a) Transl.
D^v
c)
b:
V]
,6
lines in
wz^m t
t
3
Passion
St. Matthew
b]
b:
F^F
r
2:162a-c
Example
Bach-ThreeExcerptsfrom a)
b:
1
D^v
TTT+6 .6 HI 1
--\302\2607\342\200\242 i r-.06 Vll l] [ll 5
[l
Ff
w^w D^v
r-
U^ J
LL
m
&\"
I
FT=f
rm
m PFP
_
|
I. J J *f^=^=4
~
I
m
play
c)
b)
m
Chorales of Bach
from the
Excerpts
\\
i]
the
b)
\"with salve
Transl.
mit
sein-en
Sal-ben
to prepare his body zum
Leib
for
burial\"
will be- reit-en
Grab-e
9
8 \342\200\224
D?3 7
,,6
c) Transl.
small
pieces
Sil-ber-
ling-e.
\"thirty
drei-Big
6
of silver\"
*E mm E\302\273v
[iv
d) Transl.
e -
cock crows you
the
\"before
der Hahn
be
.\"
du
wirst
kra-het,
mm
i
will..
3=S
\302\273\"
e) Transl.
\"there is no da
comfort,
not anyone
ist kein Trost,
at all
kein Hel-fer
to
help\"
nicht,
ff^P
mm
&
D7
..0 6 Vll 5
Exercises:
Follow the
same instructions as in 1.)using
126
the
materials
of Exs.
2:164
Example2:164 He
ed for
look-
fir
4,[l b:
some
Broken His
Hath
Rebuke
Handel-'Tfry
to
have
-
pit
Messiah
from
Heart\"
y on Him,
but
there was no man;
rjTTU^=g^^^P
&
N6]
sameinstructions
Exercises: Follow the
in
as
He
was
wo un-ded
for our
trans-
gres-sions
T* \342\226\240
9
8 6 \302\2535
s
| i\342\200\224 9 g 4 3
P\302\273V
.9 14
er the earth
the Earth\"
and gross dark-ness
the
from Messiah peo-ple
#v
e: d
i]
[v
the materials
8, 3l
2:166
Example
Handel-\"For Behold, Darkness Shall Cover
Complete
given in Ex. 2:167a-bby
composing
ensemble of stringedinstruments. 2:167a-b
Example
for Strings
a) Telemann-Suite
n^
2:165-166.
from Messiah
Our Griefs\"
Borne
1*
cov-
Exs.
2:165
Example
Handel-'SurelyHeHath
the materials of
2.) using
\"La Lyra\"
^m &.
t
..\302\2604 . l VU 3
127
j*' ,fiS Vll
.6
1
s5
D
..#6
_, V
11 5
four-voice
settings
for an
b) Hande\\-\"But Who May who
Abide
the
Day
of His
when He
stand when He,
shall
1
j
i_*JHL2S.
S
Coming\"from
Messiah ap
-
pear
- eth
^PpfeJN j
nr\302\261HT\\
*
jrnjrn
i
Tf
g: s.
Vll 3
Triads
9. Secondary
The key ofA-minor that
minor
have
third
this
lower than the
chords,it follows be relatives
that
the same
key signature
are called
relationship
a major key is always tonic triads of relative Since the tonic
also
has
minor keys
tonic pitch
(see Ex.
as C-maj
relative keys. The of its
and minor-key
pairs
minor key is always key. Conversely, the tonic note
of a
or. tonic
relative-major
All majornote
of a
third higher than the tonic of its relative-minor can also be considered relatives of one another.
chords in a relative each
(Parallelklange)21
of the
major/minor
key-pair
key. Therefore, the
are considered
respective primary triads in those two
keys
a
(T, t;
to be
relative
S, s; D, d) will
2:168).
Example2:168
a:
t
[i
21 One of the most significant in music terminology between music theorists and their differences German-speaking most German-speaking authors and instructors English-speaking counterparts is found in the term parallel. Whereas refer to the pairs of major and minor keys that have the same key signature asparailel keys, English-speaking authors and teachers is worsened by the fact that English-speakingtheorists use the prefer the term relative keys. The problem term parallel c-minor). keys to stand for major and minor key-pairs that are based on the same tonic note (e.g., C-major; To avoid as many problemsas possible for the reader trained in the Anglo-American system,the German term parallel will be changed to relative in this translation, and the symbols [P] and [p] will be changed respectively to [R] and [r]. See: \"Harmonic Analysis,\" College Music Symposium, XXVI (1986), pp. 66-76. Levarie, Siegmund
128
the terms:relative
parallel tonic], relative subdominant [orig. parallel dominant] for those minor whose roots are, respectively, a third belowthoseof the tonic, subdominant and dominant triads, triads in a major key. This nomenclature, still in use today, employs the symbols found in Ex.
Riemann introduced
[orig.parallelsubdominant]
tonic
[orig.
dominant
relative
and
2:169.
Example
C:
The
symbols
sonoritiesin minor
shown
in Ex.
2:169
T
Tr
S
Sr
D
Dr
[I
vi
IV
ii
V
iii]
2:170 were employed
Riemann
by
to represent
the relative
keys.
2:170
Example
Tr
a: T
ffl
[i
\302\260Dr \302\260Sr\302\260D \302\260S iv
v
VI
VII]
Riemann uses the symbol [\302\260 ] to indicate = the minor tonic, minor chordquality; e.g., \302\260T \302\260Tr= the minor tonic's relative major. Wilhelm
Maler slightly
represent major triads and Ex.2:171shows Maler's revised minor-key
revised Riemann's symbolsso that upper-case letters were used to letters were used to represent minor-triads. revision of Riemann's minor-key symbols.We shall employ Maler's
lower-case
symbolsin this text.
Example2:171
4s a:
\302\247 U
\"
t
tR
s
sR
d
dR
[i
HI
iv
VI
v
VII]
The symbol tR should be interpreted as the relative major triad [III] of the minor tonic [i].
129
have two
with their respective primary triads. This is higher (rel.maj.)or lower (rel. min.) than the root that two of the three relative triad with which it is associated. Riemann showed ofthe primary triads within a key possess ambiguousfunctions, since the they share two common tones with triad a third and two common tones with the primary triad a third lower. Ex. primary higher, 2:172shows how Tr (vi) can also have a relative to S (IV), and how Dr (iii)can have relationship Sr common tones with only one primary triad (the a relative to shares T(I). (ii) Only relationship a since the triad third (vii\302\260), below, is not a primary triad. subdominant), leading-tone Relative triads because the root of a
in common
tones
is a third
triad
relative
Example2:172
C:
Sr J1j73
cj S' [IV7
d
LLU
r
D
Tr'
Sr' D'
V]
[vi7
ii7
152
V7
T I]
f)
Bach-\"Jesu
nun sei
gepresiset\"
~B8.ch-\"Schmiicke
g)
4=\302\261
1
^=k
\302\245
:f^
I
^k
du
~gt
J-
J
J3 T
Dr'
...7 UI h) Bach-\"0
r
,1
J
Sr7 6
T
^^ Sr' D
Sr'
C:
^
J
w
^s
B1? 5
I
r
SU
dich,
Seele\"
o lie.be
Ewigkeit,
i)
.7
-6-. I J
Bach-\"A//ei\302\253
Herr Jesu
Donnerwort\"
Tr7 Tr
zu dir
natus
Hach-\"Puer
j)
in Bethlehem\"
Christ\"
1
B
I . 5
^4
# UlS
I
J
\302\2611
nm
J
m
^fff^ Dr7
Tr7
Sr7
...7
.7
..7 11
111
Exercise:
W
rr VI
Write out and
play the
T
T
[I
I6
t8
ii7
t7
T
V
following
sR7
two
dR
S7 D
7
d7
'
t
7
,1
Dr7 S
tG
IV
iii7
a: [
in various
progressions
IV7 V2
I7
\\\\
s
D
a:
3
,6-, I J
D7 T7 5
Sr7
3
6
T
Tr7
I
vi
s7 d
s'
d'
IG\"
iv
v
vlJ
keys:
JQ1
Sr
5
.7
vn::\302\2606 I]
ii
dR
tR7
s
Vn
IE
iv
t
1 2
[i8
i7
iv
VI
VII
v7
VI
153
iv7
v
T
i]
13. Expansion
of Tonal
Space
melodic contour shown in Ex. 2:198was developedsometime around 1640. form consistsof four phrases. The first phrase, which forms a melodicarch ending third is pushed toward the on the tonic pitch, is repeated in the secondphrase.The phrase the means of dominant dominant's This leading-tonebelongsto a dominantby leading-tone. The fourth function chord in the key ofthe dominant. phrase completes the formal structure by occurs in the fourth Ex. 199a-e contains tonic melodic climax often to the (the phrase). returning exhibit this kind of of the seventeenth century which complete melodiesfrom the literature melodic-harmonic phrase structure. The
important
This melodic
Example2:198
Example
a)
\"O
Gott,
2:199
du frommer
a-c Gott\"
(1670)
/T\\ g\342\200\224 TJ
$^m
^
pp
nicht
h)\"Strafmich
in deinem
gfej
m
154
^
Zorri\"
(1694)
Si
alle
danket
\"Nun
c)
Gott\"
(1647)
ri
^fl^-iiipLg^B
i=
PP
f^TT
m
7 Dl
[I
iii
v|/,
6
V^
D
i
|
I
(G: S
V/^ D
( IV V
V
&1 3
D
T
v
I
S>
7
D
3
T
6
V5^
T)
i)
155
V
V3^
V2^
V6
I]
As
in Ex.
is shown
2:200, l9 frequently
for the
substitutes
chord in a harmonic
subdominant
progression.
2:201
Example
^ T
C:
V5/
[I The
through
V
I]
between a dominant half-cadence and a illustrated in the melodiesin Ex. 2:202.Both
differences iP are
employed in the
Baroque.
progressionto
the
are
constructions
Example 2:202a-b ich tausend
a) \"O dap
hdtte\"
Zungen
(1738) half cadence on the dominant
gS=
gg-
j^m
^r
^?
The dominant as an imermediaie tonic (secondary key area)
m
T
D
[I
V]
mm? D
g>
V]
[ V/
b)
\"Ich
freu
mich
in dem
Herren\"
(1635) half cadence on the dominant
te \"Eb:
J
^-hJ\342\200\224TTtJ~J
f-f
[I The dominant as an intermediate tonic (secondary key area)
m
5
T^f^ fi>
[V/y
D
V]
# 156
V]
dominant
regularly
Exercises:Analyze label the you
study
the
melodies
harmonicfunctions, these
then
in Ex. set the
for 2:202 and Ex.2:199
harmonic
their
melodies in four voices and play them
make sure to keepin mind to the new tonal area. In some
more
that
melodies,
than just
implications, piano. As
at the
the dominant'sleading-
section of a phrase may best in a secondary-keyarea. To facilitate of such be analyzed analysis spots, we will adopt the all within functional found ( ) will be chords that symbols following procedure: parenthesis area the chord As is shown in Ex. the of which follows. to 2:203,severalinterpretations key belong a w hen a return to the original tonic area be for may possible particular progression,especially can
be related
is relatively
gradual.
tone
an entire
cases,
2:203
Example
m
PPl
i3E
m D
g>7
D
T
D
g>7
D
T
T
S
D
The the
two
chorale
labeling several
(D7
D3
(T
T,
T
fi>
D
S
D)
D
S
D)
D
melodies in Ex. 2:204a-bimply
tonicization
in dominant does not appear the harmonic functions, search for the most and choose the best option. possibilities
of the
leading-tone
-l^rj
i
-J
*~JTj
convincing
ich dirgeben\"
of the
itself.
j
j
(1615)
157
^^H=^ff^
dominant even When
though
and
analyzing
spot to apply the
:\"*r5 3 D 3
(D7)
il
%
Vv^vl
c)
r
K F:
U
[r*
(D7)
J
i
J
\302\243D
(ilr Tlr^U
I'ui^l'r T
S
S
fefi
\302\253
Sfi
vJrA9!
(D7
9\"
H>
161
3
*)
Sr4
6
..4 3 .6 11 VI
^
D79
8
,r6 V
6
5
7
T4
UlLljW
i1
,n|'
|?\"
^ 7 \302\256 1 3-T\342\200\224
-Tr
T-
D:
[I-
7
f
V6/
/v
D
(D 4
V
VV.
)
3
Dr
iii
e)
^
s
Harmonize
excerpts
T
\342\226\240(D^S
I6
[V
Sr^(D)
(D^>
l6
IV
^
jjj. ^T r
p
irtr^r D:
three
ffff
V5/.
S
(D^>
iv]
\342\226\240% nv IV
the bass lines in Ex. 2:21Oa-b in four voices and play them at the keyboard.The in several in Ex. 2:210a also demonstrate the use of secondary subdominants
forms.
Example 2:210a-b a)
al)
Bach-Chorale
'
S B1 (D5 3 5
I6 vtiv
[I
*
^m
P\302\243
El: T1
Excerpts
D
V
vii\302\2606
xrv
(s76)Dr
(S5
(ii\302\26076)iii (iii
Ds7)
D
V87>
Vl
a2)
a F:
(D3)
Tr
iii [V/\342\200\236
D
V
T
Sr^-
6
I
V5/. Ml
162
ii
a)
b)
t
t
^
m
Efe
s
rr\342\200\224r
^
^
-
D
[wii>7
6
3
vl
I
parts
r
5
D4
The two excerpts from Especially note the voice
Hi
p^F
tTt= t _ v fi>
xM>
f:
t
[i
tS'V
D4-
'%
be
at the keyboard. organ works in Ex. 2:218should played marked since with, they contain clearly defined tonic
Bach
elements.
170
a-b Example2:218 a)
E^
J, Jy^M
5
m
p
f=5r
nn 3 ij. j. ^m T
f
-\342\226\240\302\2607
Vll/
b)
j- ^
'4^j-j
J1
r
*L
ZUJ
^
^^ D
t
D4
T I]
Ex. 2:219
contains a typical
Vivaldi-Concerto Grossofor
example
Four
of a
dominant half-cadence
Example Violins in
t]5>v
2:219
B-minor, op. 3, No.
10; Movement
/~\\
Largo
Ml
w HJUU
J. m
ZJUU
r D ..\302\2607
171
preceded by
Vl
II (end)
Ex. 2:220
shows a rare exchangeof
elements in the elements)
in the
tl5)v
chord.
the tonic
between
position
places the
Bach
Here,
lower voices, while the third and fifth
seventh
and
fifth
and secondary-dominant of the chord (the tonic elements)
(secondary-dominant
are in the
upper voices.
Example 2:220
jf
Aural
Analysis:
t
D
t
&m
m
inn
\302\261=\302\261=\302\261
r
r
f
r
r
#v
#7
5
Aj
Af
discussed the role of the diminished-seventh chord as it resolves to tonic and also be applied as a secondary keys, but the diminished-seventh may to any scale degree in major as well as minor keys. chord in a major key. 2:221 shows an adventuresome use of the diminished-seventh
We have dominant dominant
Ex.
in
minor
Example2:221
r
jpiCg
'U
T\"
m O.
Book II
Clavier,
Bach-Well-Tempered
w
T
T
S6
172
&1
2:222a-b demonstrate how diminished-seventhchordsmay to note, in Ex. 2:222b,that the bass pitches of interesting two diminished-seventh chords chromatic actually frame the dominant pitch (G)with leadingwhich tone motion from aboveand below.Ex.2:222c shows is voice leading quite rare during the time but which became very important in the Classicalera. The normal of Bach, downward resolution of the seventh of the E?\" is delayed by the presence of an intermediate D4 [V4 ] but the the must be first because of Eb raised suspension figure, approaching major-key cadence, to EM before the voice can finally into the fifth of the resolve downward dominant.
Theharmonic
precede
T [I],
in Ex.
reductions
Sr [ii], and D [V].
It is
2:222 a-c Well-TemperedClavier,Book
Example Bach-Prelude
from the
in C-Major
a)
b)
ps
C:
I (harmonic
w
f
Sr
(I-P) 4
3
T?
D7
*,
.6
L vu/
f
..\302\2607
V7]
Mi
c)
*
^P
f
m 6-
D\"-
r
(D7)
S
%,
\342\204\242
.-\302\2607
- Dominant Pedal -
173
reductions)
Ex. 2:223
shows: a) the usual practiceof
the
resolving
of the'
seventh
l5)V
(Eb)
directly
to the
dominant chord; b) the frequently minor-key delay in proper resolution of employed caused by the insertion ofa D% I suspension the the seventh, rare (Baroque-era) c) figure; upward chromatic motion in the seventh ofthe' l!Pv (Eb) into the radiant third of the major tonic (E \\) before of the
fifth
resolution to the
of the
fifth
dominant.
Example
2:223a-c
1
\342\226\240
'
X
4=\302\243
T=^
6
[vig
To prove out
of context,
Bach's
time,
V]
[vii/
D4
T
V3
I]
that the kind of chromaticmotion and to demonstrate Ex. 2:224
&
v\\
in Ex.
shown
that the powerof
presents a clearexample
this
of a
chromatic
progression
thell5>v.
Example
2:224
Bach-ChristmasOratorio
~JF^iF
sehn,
nach dei - ner
/3E
F^Bf T
3
[I6
S
D
Tr
IV
V
vi
.6
14
174
D4
2:223c has not been interpreted figure was known even during in major
mode which
employs
wish to correctly imitate the Baroquestyle,
If we
it is
however,
not to overuse
important
the
chord.
diminished-seventh
Notice,
expression
in Ex. 2:225, that the of the wounds of Christand
either beforeor after
this
diminished-seventh chord is so representative human sin, that the sonority is not used for
in
its
a long while,
spot.
2:225
Example
Handel-\"Surely He Hath BorneOur
from
Griefs\"
Messiah
-J-TLL-X^l\342\200\224i
k
TXrrr*M^=ed for our
wound-
trans-
J>
X
M
S
^m
\302\273 8
r .9 I1
the short
Harmonize
Exercises:
in various keysand
play
them
at the
sions,
gres-
8 5
L
UV
..\302\2607
6
8
9* d4
t \342\200\236v
8 i 3 J
Vn4
Vll/
melody and basslinesfound keyboard.
2:226. Provide
in Ex.
settings
Example 2:226a-h a)
c)
b)
d)
F=^
vm
fcj
^
i Sr
T (J?)
C:
Tr
8 7
'fi^
D
D^v
5
T
Tr (I^v ) Tr
3
3
S5'S|V
D4
3
T
U15 vii/
V4
3
IJ
3
6
LI
vii/
11J
Lvi
vi2 VU/
V raj
I]
Ivi
vi
vii/
e)
J
h)
g)
^1r^J-^5d^-^H c:
,
tfv
cr
t_(^)
^VII
D4 s\302\273 'g\302\253v
3
5
%V4 175
t
t
(^)
Sj
[iv
J*v 3
t
viil
i6]
3
16. Chords
Borrowed from the Minor-Mode
the minor-scale pitchcomplexprovidesa pitch inventory have discussed, that makes both major and minor of the dominant and subdominant triads (D, d; S, s). forms subdominant Occasionally, members ofthe minor-key [iv, ii\"6, ii'i, N6] family (e.g., s, s6, si, s\302\260) are borrowedby the parallel-major with the 2:227 showsan same Ex. [the tonic]. key major key si as Bach usedit in of the a chorale. (iil) example minor-key major-key As
we
possible
2:227
Example
Bach-aChristus
u
Lj
F:
T3
r.6 LI
der ist mein
Leben\"
^L=
S5
D8
7
T
..16
,,8 V
7
,,lj
11 5
that \"the seventh scale degree ofthe theory states, as doesLouis-Thuille, raised \"in order to maintain the chromatically major dominant triad,\" the raised seventh was \"from its very origins, and that an alien element.\"27 Such then authors the to an between chromatic of the sixth scale i n attempt provide analogy lowering degree major and this theory concerning the raisingof the seventh scale degree in minor. It is often postulated that the lowered third of the subdominant triad in major generates a strongerpull to the dominant because of the upper(Phrygian) to the leading-tone relationship dominant (e.g.,Ab-> G in C-major). The strategy of writing textbooks \"from simpler to more difficult leads to such unfortunate theses. [concepts]\" Just the oppositeis actually the case. The leading-tone is older than the notion of either the raised and seventh is more the \"midwife of tonal an than major or minor, clarity\" \"embellishment\" in minor In the time of m inor subdominant sonorities which Bach, keys. appear in major-key were not held to be colorful enrichments of some simple original structure, passages but rather were considered rich and full sonorities from earlier musical style. Ex.2:228 borrowed contains an early example of a minor subdominant which chord occurs in a major-modepassage.
The traditional
natural
minor
Rudolph
scale\" was
Louis
and Ludwig Thuille, Harmonielekre
(Stuttgart: C.Gruninger, 176
1906).
2:228
Example
Hassler(1601)
fT=F
4
^
^ G:
Exercises:
T
s
D
T
[I
iv
V
I]
the following
Write-out and play
6
T | [I
T
sn
| N6
in various
progressions
|
S5
D87 | T
iif
V87
I6 |
|
6 T
|
[I
|
s
(D7)
iv y}ly
l!?7
[I
T
[I
I I
D7
T
s5
ul
E^v
^
nfi
177
3
T
I I]
|
T
V| | I]
V| | I6
| ii*3
5
D4
| vS
V^
T | s5 D? |
I
I]
I i
T.
i6]
keys:
CHAPTERTHREE 1770 and
between
Harmony
1810 (Haydn-Mozart-Beethoven)
1.Introduction The
change
style
3:1-3)
works
from
that took
by Johann
place about 1750is made
in the
clear
Stamitz (1717-1757) and his son,Karl
(1746-1801):
3:1
Example
Johann
following excerpts
Stamitz
in G-major
Stamitz-Symphony
Allegro
a
m
,UUas
lifflyyitfiifc,
J J i
J
[I
m
^
rrr G: T-
i
J
J
65
s6 ..6 11
S6
D43 T
.,6 5 ,I V4 3
11
V4 3
I
Stamitz-Symphony
in
..9 8 117 6
A-major
T
m
A:
\302\24333
j^
fi: T-
rv
[I-
178
..\302\2607 ,.i VJ
Vll/
Presto
hi
^
\342\200\242
3:2
Example
Johann
9
9 8
65
Q4 3 T_
(Exs.
Example 3:2 (cont.)
H'\"'ffl
i
j\342\200\224n
&S
JU
^^
J
j-n j\342\200\224j-}
J\342\200\2243\342\200\2243
m D
D
rv
V
v
Example
3:3
Karl Stamitz, Orchestra Quartetin
C-major
Poco presto vln.l
B^\302\247
* -* -J-*l
...j-
iil
j.
#
p
pff#Pi fem&4\302\243
was dominatedby four separate voices is over. The melodylines voices, movingin parallel thirdswith each other, suspended over a simplefundamental The viola part, located betweenthe melody-line and the bass bass. pair is so insignificant it is hardly appropriate to speak of it as a separate voice. Noticehow the that viola part regularly doubles the bass line in octaves in Ex. 3:3. In Ex. 3:2, after with beginning into the pure barbarism of parallel some independent character, the viola part degenerates at independence in measure seven.(For octaves with the cello, exceptfor another feeble attempt more like these, look at the early string quartets of Haydn!). Those who expect voice examples to say about works like these. leadingto be clean and contrapuntally correct have nothing good 1.
The
musical
intheseexamples
era which
consist
of two
179
2.
to the three lines are limited primary pitches ofthe key [tonic, to find places in Bach's music that Though it is almost impossible but the most rudimentary feature such simple bass lines,it is difficult to find anything of tonic, subdominant and dominant in the basslines of this new musical era. presentations is characterized occur Classicalmusic over Early by a large number of melodypitcheswhich is one the in bass of reasons for few fundamental (this many light, graceful changes relatively harmonic of these melodies makes of early Classical melody). The obvious quality simplicity in countless compositions ofthe them to comprehend. is found This lightness and simplicity easy several and once a listener becomes acquainted with time, pieces in this style, the samedevices over and over again in nearly every appear piece. a new tempo is alsointroducedin the 3. Along with a new compositional superstructure, a Classical Almost carries early period\342\200\224the presto. every pitch in a flexibleBaroquebasspart In
Exs.
chord change,
dominant].
time. For that
need reason,
determine
to be the
function. Since today's terminology) a change of harmonic by the brain], they require perceived by the ear [andthen processed number of functional changes per measure [harmonic rhythm] it (in
with
bringing
changes in function actually
the bass
3:1-3,
and
subdominant
the tempo
at which
a melody
unfolds.
The eighth-note in the Allegro movement from Bach's Brandenburg is essentially in the three Stamitz a longer that which occurs than eighth
No. 5,
Concerto
6
6
examples
(Exs.
3:1-3).
3:4
Example 'Bach-Brandenburg
Concerto No.5 (Ex.3:4)
6
6
Allegro
6
rate of two chord changes per beat. This the that harmonicrhythm forces a moderate is, the relatively movement; tempo upon frequent tends to produce a sense of harmonic Above all, it was the change of function weight. of this harmonic abandonment ofharmonic that created weight, produced by the slowing rhythm, the new, magicallylight and graceful Classical-era melodic line. In
Ex.
3:5, the
harmonic
rhythm
proceeds
at a
180
Example 3.5 Concerto
Bach-Brandenburg
No. 5,
Allegro
sro
L. ^m^ D:
of measuresor groups
T-
D
[I-
V]
an important role in the three Stamitz This kind of repetition is typical for music examples. during the early Classicalperiod. In Ex.3:1,Measure 3 repeats 7measure 2; in Ex. 3:2,measures3-6arethe same as measures 10, with the exception of a few minor details. In Ex.3:3the viola and cello parts repeat exactly the same materials in the secondfour measures that they played in the first four. The second measure which do not enter until was introduced violins, five, repeat the same material that by the first violins in measures 1-4, while the first violins continue in the secondfour measures with a line that is scoreda third higher than before. On one hand, suchjoyful of musical materials are courageouslyuncomplicated repetitions textural solutions that reflect simple, slowly changing harmonic On the other progressions. these time the in additional for ear to the harmonic hand, repetitions provide perceive changes the characteristically fast newtempo.The repetition of melodic materials also helpsguard against the presentation of too many divergent musical materials in too short a spanof time. 4. Repetition
of
measures
181
plays
We shall
now
compare
the
and harmonic
melodies
settings that
appear
in Ex.
3:6-7.
Example 3:6 K.V. 589,
Quartet
Mozart-String
Larghetto
vs
i v*i
i
3:7
Example
Bach-Si.Mark
5
Aria1
Passion,
( V\302\260)ii
The
melody
a middle-voice most important does
not require
in Ex.
3:6 is played by
accompaniment, fundamental
a fourth
while bass instrumental
the
in a
]
The second violin provides on a tonic beginning pedal point, provides the The first viohn does not play here, sincethis texture cello
high
register.
the viola,
pitches.
voice.
1 The musical manuscript for the St. Mark Passion is lost. to Christoph Wollf, the music survives According original form in Cantatas No. 54 and No. 198, and one movement was revisedfor use in the Christmas Oratorio. music for the reconstruction in Ex. 3:7was taken from the alto aria \"Wse starb die Heldin so verniigt\" from Cantata (\"La/1 Fiirstin, la/i noch einen Strahl\.
182
in
its The
198
Ex. 3:7consists another.
At
the
highly individual voices which of the Tr9 (vi9)chord (measure
of four
form
1,beat
entry
3),
bass
with one
dissonances
strong the
a stepwise,
line begins
later by the which is imitated just two eighth-notes harmonic Bach develops a rich and varied texture, two basic functions (T and D) in Ex.3:6. within It is only necessary contains all of its harmonicimplications itself. Mozart's melody to sing through the melody in order to know what all of the underlying harmoniesmust be. Bach does not always choose the harmony most immediately by the melody, however. Instead implied of belonging tonic the D m easure to 1,beat 3) sounds as the third harmony, melodypitch (Ex.3:7; is the first to present the is that the of submediant chord also interesting, (Tr). It accompaniment
descendingeighth-note
passage
top voice ofthe accompaniment. whereas Mozart employs only
the tie figure, which It is important rudimental
harmony
(B-A-G-F#)
Ex. 3:7,
In
an important rhythmic element understand the secret of artistic simplicity
becomes to
that
in the melody. that
in the
is hidden
employs only the three it is not so much the variety however, interesting harmony. In the Classicalperiod, that is important, rather how each sonority structure connects to the larger formal number of actual chord changesthat take place within various sections ofthe form. Table
3:1 shows
seemingly
which accompanies Classical-period themes. A chord progression with basic functions (T, S, and D) producesmusic only minimally
the correspondence
betweenthe contour
of the
changesper measurein Ex.3:6.
melody
of sonorities
and the number
and
the
ofchord
Table3.1 Mozart,
No.
of Chord
Larghetto
from K.V.
Changes
Per Measure:
MelodicContour:
1
2
Middle
589 (Ex. 3:6)
Range
Low Point
1
4
Descent to
High Point
Middle
Further
3:2.
data on the
harmonic phrasestructure
183
in the
Classical-period
Range
are given in
Table
Table3.2 Harmonic
KV
305,
KV 306,
KV 301, KV
376,
KV296,
IstMvt.
T
IstMvt.
T
IstMvt.
T
3rd Mvt.
T D7 T3
378,
1 st
KV 380,
IstMvt.
KV481,
2nd
S6
T
113a
1
T t
D?
T
D'_|
T
\302\2732
T D7
Mvt.
violin
the
S
S3T5
s
t
Mvt.
eight-measure themes from
3
TS
2nd Mvt.
KV 377, 2nd Mvt. KV
in nine
progressions
3
T
S
3
D7 D7
T S
D87
l3
T
T S
t^6 D4
3
of the nine examplesin Table
T3
s6 D
3
T D7
s
vlV
T
1
T
dS
r>7 D
T3
S6D437
S3
D7T
D7
t
T
657657 \342\200\236
S
T
T
T
^657 43
D
T
T
D7
T
1
T B7
T3 5
S
T
T D7
D
T S5
D7
T,
sonatas of Mozart
D 43 43
T
T3S6D4,37
T
the harmonic 3:2, changes are more highly than in the two of the nine examples antecedent; o nly consequent phrase the and consequent phrases; and show the same number of chord changes in both antecedent none of the antecedent active than the consequent phrases. The phrases is more harmonically in closeconnection and form harmonic between activity Classical-periodmusic is quite evident in these eight-measure periods. 2. Sincemelodies almost chord are imperceptibly joined to just a few possible changes, the basis of melodic invention; that is, the harmonic progression in the Classicalperiod became listener is unable to separate out the harmonic implicationsfrom the melody. At the same time, harmonic become the most important structural elementswhen however, progressions forming concentrated harmonic cadences. Table 3:2 shows a highly activity in the seventh closing measure of each excerpt! The chord progression T IDg7 IT3i S IDS I II T I I I I would, This progression be an unimaginable harmonic pattern for a Classical-era theme. therefore, createsa situation where the closing cadence would take placein the centerof the period, leaving in the consequent phrase. no room for a harmonic/melodic climax 3. The progression triad (IV-V), from a root-position subdominant triad to the dominant much in in is less common the Classical the Baroque, period. The rootfrequently employed subdominant to T or D4 3, however, and a root-position dominant triad often progresses position is regularly preceded by S6 (ii6) or Si (iif ).
1. In seven
concentrated
in the
184
2. The
The
Role of Harmonic Progressions
Form-Generating
progressions can
of chord
role
form-generating
movement ofMozart'sHaffher contain several complicated
harmonic
The following
are employed in
cadence
Symphony
types
T [iilV I]; Si D the beginning ofthe the cadence is used to produce the form.
V7T]; s^D occur before
The first
(K.V. 3 85).
this
Although
it employs
passages,
be clearly
only
in
observed
magnificent a few
[iil
first does
formulas. I]; Ss D7 T [iil
basic cadence
the movement: S6 T S6 D T [I h6 V I]). Only six S D T section (measure 125). We shall now recapitulation a sense of harmonic closureand articulation between T
D7
the
movement
T
[ii6 V
V I];
full-cadences discuss
how
sections
of
13 at the end of the theme. The next cadence is a of the theme. dominant This half-cadence 33) which follows the secondstatement (measure second statement contains which are freely developedfrom the canonic transition materials, theme. theme enters once more (measure 35),this time Following this half-cadence, the main in the dominant key (A-major). orchestrated at a lower dynamic level(p) and presented freshly second theme, Mozart uses Haydn'stechnique of restating the (Here,in placeof a contrasting movement's first theme in a changedphysiognomy.) The first hint at a closingcadential gesture is fashioned out of motives of a fullfrom the main theme and confirmed by the appearance cadencein measure66.A second closing gesture follows almost immediately, asthe oboes and bassoons in measure 74. In a third closing carry the melodic line into the next full-cadence
gesture,two
harmonic
similar
measures 80-84(Tr
progressions IT(D)
ISr31D
closelyby yet
another
full cadences
enter in measures
the
dominant
key.
cadence
ISr3,D
(Tr ISr3iD
are joined IT) [vi lii6
IT) [vi
90 and 92 above Past this point, there are flow of
complicated
harmonically
in measure
occurs
full-cadence
together to iil
ii6 iil
I
VI
a pedal-point
one
long cadence in
I ii6 ii! V II], followed in measures 86-88. Two more I] in (A) to close-off the exposition
V II V/ii
cadences
more
no
the development
form
sectiondoesnot
until contain
measure any
125. The
key-confirming
cadences. At
the
beginning
of the
exposition, the main
the main clearly defines and sets-off tend to break-up the flow of [preparation for the following development
This cadence following
approaches these
full-cadences
later full-cadences
follow
one
another
theme the
to a closewith
a full-cadence.
from its surroundings. The five as the end of the exposition
materials
It is interesting to note that section]. nears its end. more closelyasthe exposition or to close-off sections used more to articulate a section. within progression
more and
formulas are cadence By the time of Mozart, materials than to carry the burden of harmonic
is brought
theme
185
Seventh 3. TheLeading-Tone
Chord
( J$7)
in Major
in harmonic sequences, the leading-toneseventh chord in major Outside of its appearance only as a passing-chord sonority during the Baroque.By the Classical keys (vii*7)was employed The half-diminished leading-tone function. period, however, this chord carried is own specific dominant seventh(I?7)representsa mixture (D) and subdominant (S)functions, in the sameway that the fully diminished seventh-chord in minor a mixture of D and s. Ex.3:8 (Ef) represents shows the similarity between these two sonorities.
Example 3:8
r --\302\260 L Vll
[vll
a true seventh (like the seventh The seventh of a if7 is clearly of the E)v) and this sonority in the should not be considereda dominant-ninth chord with an omitted root. It was only first chord was recognized as a discretesonority ninth Romantic era that the abridgeddominant (see Five). Although the Classical perioddid not generally Chapter regard this sonority as an it is sometimes possible to understand it as such, in certain musical abridgeddominant-ninth,
contexts. The
between
sequence Ef
in
construction,
minor
and if7 in
which occurs in
Ex. 3:9, makesclearthe
similarity
of function
major.
Example 3.9 Haydn-
Quartet,
String
op. 76
no. 3, Minuet
J
i^L \342\200\242
I
S
I
u
I
htm
EJEEfc C:
Tr
Tr (l\302\243v)
-\342\200\242\302\2607 r VI\342\200\242 VI Vll I vi6]
G:
S6
[ii6
The how
the
if7 (vii*7)isa Classical-period
3
I6]
very frequently employed chordin the worksof if7 was typically employed.
186
Mozart.
Ex. 3:10
shows
Example3:10 from
Mozart-Excerpt
(dialogue between Don Giovanni Don
and
Leporello
Don Giovanni in front of the statue
of the
Commendatore)
Giovanni:
-
-dia
v:t\302\273
mo (etc.).
lr7
p
r
r
ff^rrrWJ^
^ttmm
a*
^m-
w*$ $\342\226\240>
4. Modulation
Before coveringthe Nearly
every Baroque the
approaches
place
that
central
topic ofmodulation, dance-suite movement
double
returns the
bar line.
pieceto
the
After
original
it is
necessary
modulates the
central
tonic key.
187
to discuss
double Within
a few
from the
away
bar, a the
preliminary
secondmodulation
opening
points.
tonic key, as it movement
takes
of Bach's
on every step of material is actually presented order to accomplishthe shifts in tonal center of harmonic here, required descending-fifth sequences. In not as but rather were 2:12 harmonic were of modulation, sequences represented agents Chapter considered a meansby which the secondary triads of the key couldbe tonicized. of A modulation-producing sequence, however, might consist ofthe following progressions \342\200\224> in the chords: in the direction of increasing flats\342\200\224 Bb -\342\226\272Eb F or a, d, g, c, f, Bb; a, d, G, C, E ->A or A, D, G, c#\302\260,F# ->B ... etc.2 direction of increasing sharps\342\200\224a, d, G, C, F, b\302\260, In compositionsby Bach, we are not particularly troubled even when the continuo bass line traverses pitch areas that do not belong to the diatonic of the key. Between measures 13 pitches and nur\" from the St. Matthew Passion, no less than eleven different 17 of the aria \"Blute major and minor triads occur (B, C, C#, D, E, F#, G, A; b, e, a). Considering the strong concentration in the first part of this aria (B-minor), of varied it is meaningless to speak about a harmony in the second part. (This methodof establishing modulation tonal-center changes in chorale style was alsodiscussedin Chapter 2:12. Bach employs secondary dominants in sucha fluid manner, that it is often difficult to decide a real modulation is actually whether (or a taking place modulation on the way to some third key, etc.), or whether the change in tonal center is only a tonicization within the original key. temporary In Classical-eraworks, a particular is confirmed by the presenceof simple tonality that a associated cadence For a change of tonal center becomes formulas. reason, thematically much in the works of Bach. Classical more easily perceived event in Classical compositions,than are expressed sonatasand symphonies statements and by means ofharmonic/thematic of and developmental areas. The differences betweenthesethreetypes restatements, transitions, the and they were also increasingly less materials were not so large or well-defined Baroque, in the Romantic of the simple cadence conspicuous period, because the form-defining power to be formula was exhausted. perceived the statement of the first theme in a Classicalsonata, materials from the Following loosened and until form an established theme are often repeated, they developed, split-apart texture. This transitional material is the task motoric-like of anonymous establishing a given new in will enter in the key ofthe preparation for the secondtheme, which key center usually if the movementbegan in major; orthe relative if the movement began in minor. dominant, major,
BrandenburgConcerto the
F-major
No.
2, the
main thematic
the leading-tone. In Bach employed number a great
scale
except
The goal-oriented modulations that take
modulations
of transitional
placein the development
section.
materials Modulation
function
differently
within
than
the
exposition sections
create a direct pathway
within between one strong key area and another, while modulations development sections tend to shift the tonal center from placeto place in order to avoid any strong of key. Since these two kinds of modulation or lasting are different in both means implication and intention, we will discuss them separately in the next two sections. 2
Upper case letters stand
for diminished
for major points
triads. The arrow
triads; lower case letters stand for minor triads; lower to the goal key of the modulating sequence.
188
case letters
with
\302\260 stand
5. Modulation to the Second Theme Ex.
an example of the simplest,though contains modulation in Classical-periodliterature. After
3:11
transitional
most
employed, in the half-cadence
infrequently
a dominant
is repeated triad followed by motion into its own original key and a grand pause,the dominant dominant chord This motion the to new dominant and triad). (D-major produces actually stabilizes a shift in key from C-major to G-major.
Example 3:11 Quartet,
Haydn-iTaiser
i
op. 76,
No. 3. (Mvt.
T
[I
D
D V]
V
T
D
T
[1
V
II
G:
In most being
cases, the prepared
tonicizing
12-13)
r
C:
without
I; measures
I??
of the dominant in
ahead
appears
simply
by a common chord (seeEx.3:12). 3:12
Example
Mozart-Jupiter
Symphony K.V. 551 (Mvt.
I; measures
35-37)
s /h\302\243 1
1
*N
a
\\.JH
\342\200\224 L\302\273
T C:
jT7
S7
[
IV7
3
XV
ii6
G: B7
[
189
:
-J
vii\302\260
d V]
T I]
the new key
if the approach to the key can be especially convincing 'r will also be heard a T6 (vi ) in the original key. Since the as S (ii ) inthe new key, the new dominant is prepared by particularly cadential action. strong Ex. 3:13 contains an excerptfrom Haydn's which shows this No. 104, modulatory Symphony of the slow (Ex. 3:13 shows measures 34-36; or measures50-53if the measures process. introduction are counted.)
to the dominant
Modulation
new key
in the
dominant
begins with
Example3:13
1
J J J
104
No.
Haydn-Symphony
J
\302\243j
^
*%^
^*F
-W-
D:
Ts
A:
S6
|
V B1 5
T9 3
Ex. 3:14 containsa similar modulation. 3:14
Example
Sonata
Mozart-Piano
in
Bb-Major
KV.
333
m
mw
^fffi^j
W^\302\245
Bk T-
[I
vi6]
F:
S6 [ii6
To is only area
change
the function
necessary
to prepare
of the
new key
before the goal
of the
will
of a chord from the new tonic by
actually
modulation
D V
\342\200\224 \342\200\224 ]
initial key to tonicthe new key,it chord. its dominant Often, however,the dominant be prolonged for some time (by application of its dominant) is finally Ex. 3:15 demonstrates reached. how this process is dominant
accomplished.
190
of the
Example3:15
]}
\342\200\236 u.\302\253> h> B\302\273iuR #\302\253
M \"v 8 B 8 fm
T
C:
shows another prolongation
11
XT
S17
of the
Example KV.
Symphony
MozartrHaffner
III tto
\302\251
G: D
Ex. 3:16
-g
JH>
#8
D
T
V
I]
dominant-area.
3:16 385 (Mvt. I; measures41-48)
m D:
T
[I
D
3
V'6l A: T
Tr3
B1
3
5
D
B1
3
5
D
T \342\226\240I]
The
most
the submediant supertonic a series
frequent chord
Classical-period method ofmodulating (Tr) in the original key. The Tr chord
in the
(see
Ex.
3:17
j
itj
1 \302\243* m-4\342\200\224*\342\200\224a\342\200\224-\342\200\224
C:
r
r
wr T
[I
f
Tr
vi]
G:Sr
D
V
[ii
191
thematic
are as
employs
old key is common with then resolves to the new tonic through
chord chord (Sr) in the new key. This common of two root movementsby descending perfect-fifth
Example
between
T
Ii
3:17).
the
There are of Ex.
retrospect,however,
this
chord
of this basic modulation type. At the as a dominant half-cadence,but by the endof like Tr3 chord in Ex. 3:18 sounds (temporarily) its chord. In dominant-seventh by preceded
variations
different
several
actually
triad 3:18, the Bb-major the excerpt it is clearly the newtonic. The (vi6) in C-minor, because it is immediately
beginning
is heard fourth
functions as
actually
Haydn-Symphony
I; measures 58-64)
103 (Mvt.
m
3\302\247
Ek
f
r
T
D
[I
r
F
FT
Tr3
vj
vi6]
Ss
Bt
[ii6 Exs.
3:19-20
show two
^
5
(D7.)
V
Bb -major.
3:18
Example No.
S (ii ) in the key of
more modulations which
TV 3
T
vt
I6]
employ
3
the
first-inversion
submediant/
subdominant common chords.
Example3:19 Mozart-
Linz
K.V. 425 (Mvt. I; beginning
Symphony
T3
D3
I6
[ V6
Tr
\302\251J
vi
Mozart-
Symphony
in Eb
T
V]
D3
T (D3) Sr I
[ 1
(Vs)
3:20 Example -major K.V. 543 (Mvt. (E^V)
Tr
(viH)
vi6
S6 [
ii
D3 Vi
I; beginning
T
I]
in measure
S>
vyv D
47)
D
V5/
[ V?
in measure
7
\302\253\302\253 i,4 ii6 v!
192
] T
7
D
T
vii\302\2606y
u
3
t6 r
'v
71).
its way
In Ex.3:21,the
the new
key. Once the change of
is substituted
triad
preparation for
the
minor
that
variation
Haydn-Symphony
Tr
vi
[I
\302\2567D \342\200\224lr
V^
V
I; measures 29-68)
g.7
Tr
vi
\342\200\224JI
a
3:21
94 (Mvt.
No.
tonic functions as
minor
This
tonic.
follow.
soon
will
Example
T
been made, however, the dominant of dominants. In a surprising move(!),the
has
key
tonicizedby two secondary for the expectedmajor
key is then further
minor-tonic
submediant chord (Tr) twiceon
through the
progresses
actually
harmony
dominant
to the
4V]
D7 T 3
I
[V^
6
Tr
S5
]\302\247>7D
vi
iif
VV
\302\247)7 D
3
3
vvi
/y
V
t!
D
i
V
/y
secure to the dominant key has beenmade (with the aid of the dominant and dominant chordsin the new key) the harmony may actually pass again the original tonic chord without the new key. In this case the old tonic will destabilizing through be heard as the subdominant (S) in the new key (see Ex. 3:22 ). Once
of the
a modulation
dominant
Example 3:22 No.
Haydn-Symphony T
(D^) [ I(V$V)
Tr
vi (Vs)
[||: Ex. 3:23showshow
V]
vi6(Vs)v|/
||:
Beethoven
D7
I; Measure 46-58)
D
]5>7
(D7^ Tr3(D7)
102 (Mvt.
3
T
D7
T :||(D7) 3 3
S
I
vS
i6:llvf/
rvvii>7
vf
adopted
5
this same
'
(]\302\243v)
4i
/rv
Sr
\302\251D
Sonata,
T [I
op. 102;
Tr (D7) Tr
V7
vi
(V7)
[ 193
v
i]
7v
modulatory technique.
No. 2 (Mvt.
D7
T
a v/ v
Example 3:23 Beethoven-Cello
'D
I; Measure
\302\2567 D
vi
Vl
V]
Sr
D7
T
ii
V7
I]
18-63)
No. 101 was Although the key at the beginningof the first movement of Haydn's Symphony established by standard cadential procedures,after measure this 40, Haydn moves away from a dominant half-cadence (see Ex. 3:24). After procedure (fermata), the main straightforward is restated, theme but this time it is ledinto and actually cadences on the supertonic chord (Sr). the harmony once more through the original tonic chord (T) and then on Finally, passes Haydn to the submediant chord (Tr). After this, a conventional modulation to the dominant key follows.
Example 3:24
^
^v
D
[V
(DT)3 V
c6 (vii
5)
Sr ii
(s
3
fi
7 D7) '
,
(D)
Sr
W
D7
_
D7
Sr\342\200\224
7
Civ V7)
101 (Mvt.
No.
Haydn-Symphony
\" Vs
ii
3 6
T
I; after
T
Tr 87873
I
vi
measure
_.
S>7 6 V5/ ]
V7 I
40)
D7 T [Vs
I
S6 (S7)
D
...
ii6(vii\302\2607)
V
...
T I]
of minor keys as opposed to major, remains the samefor music of eras. of the lesser stability inherent in minor, Because period as it wasin previous it is quite easy to modulate from aminor This shift of tonal center (tR). key (t) to its relative major the presence of a dominant-function chordin the relative (dR). only requires major The problem with tonal-center in minor-key sonatas and symphonies is just the change of that encountered in major-key works. In a minor it is rather easy to produce a opposite key, but it is somewhat difficult to establish a theme that maintains modulation, convincing The relative instability
the Classical
consistentminor-key
implications
throughout.
Beethoven's Piano Sonata in E-minor, op. 90 showswhat The relative major key (tR) is actually reached after only four measures of t-dR-tR. Since such the a firm move to the relative by way major progression is a goal that should normally be reachedafter it is necessary for the 40 measures, perhaps minor to modulate back to the original that (It should be noted, however, composer key. Beethoven's goal key in this particular sonata is not the relative major, but rather, as in a number can
The first theme at the openingof easily befall a minor-key theme.
of his
pieces, the
minor-key
In Mozart'sG-minor within
the
takesa direct
minor
minor
Symphony
dominant
(K. V.
(B-minor
sonata).
statement of
the
first
theme
remains
after a dominant the repeat of the thematic materials half-cadence, to the relative Ex. (see 3:25). major path
key, but
harmonic
in this
550), the initial
194
3:25
Example
in G-minor K.V. 550
Mozart-Symphony
'
j
Hi
JJ
Sj
Sr'
S5
Bk
chooses a longer modulatory path. Betweenmeasures9 and the following progression moves through sequence of chords: F-major,d-minor, A-seventh), D-major, G-major beforereaching the new goal tonic (C-major).
As is shown in Ex.3:26,Mozart 22 the A-major
Notice
harmonic (actually
that the
C-dominant-seventh chordwhich
in second inversionsothat
the
the F-major
proceeds
triad\342\200\224(Dj)
triad can appear completely
C-major
root-position
tG [VVVI] new
occurs
at the
end
of this modulatory process.
Example 3:26 Sonata
Mozart-Piano
a:
t
D
[ i _Vl_
t
in A-minOr
K.V. 310
s
(D7) tG 5
j
(V4)
iy j
yj
d:
t
[i
T
D7
I]
VS
C: 51 D7T [ V/
In Ex. 3:27, the theme settles this modulation, repetition of this
in the first
Vs
I
D { D {
f7
Tr
S6
vi
ii\302\260 V5/
V
v
i V
D ..
i
relative-major (tR) in measure 9 (fermata). constructs a large minor-tonic key
theme
.T \342\200\242 I]
spite of After this
In
area.
repetition, however,the path to a second stable key area follows a very convoluted path through C-major, a-minor, many distantly related triads (d-minor, G-major, a-minor, G-major, e-minor, F# major). It is difficult to know before hand that the goal of all this intense A-major, B-major, will be the major dominant (E-major). harmony activity
195
Example3:27 a:
D7) r
tR (D7) v r
(IV6 vf)
m (vf)
t
[ i
v(S
3
for violin
Sonata
Beettioven-Kreutzer
s
S>7 d
d
S>7
3
3
v6]
ivV^v
v}w
t
E:
3
[ i6
6. Modulation The
and
modulatory
goal-directed
convincing,
but
modulations
surprising and unexpected.In fact,
and piano, op. 47
within the
||:
s S> D iv
v l|:
v/
t
i
'\302\251v
D
:|| T
vii7
v
:!l i]
/y
7V
Development Section
path into the key area of that take place within development-section
the a
needs to be clear are often often have no immediately
second
theme
development
modulations
section
the development section evolved into a large where a composer might freely explore many harmonically unbounded area of a movement, marked connections and possibilities. Though the end of a development sectionis generally by in the main key of the movement, the modulatory the reestablishment ofdominant harmony path toward this dominant is often indirect and highly convoluted. texts The kind of modulation exercises found in most harmony do not generally apply to the of when theseassignments kind modulation read: required by development sections, especially \"modulate (as quickly as possible)from the key of... to...\" If weexaminethe development-section of Classical-era seems to say: practices composers, however, their self-administered assignment in areas without a true tonal center.\" \"modulate! move freely, and remain for long stretches For that reasonthere arenot many Classical development sections where oneor both of the successions of following devices fail to place sweat on the brow of an attentive listener: 1)Rapid that the listener is not sure how to find the confusion key references that create such harmonic centers which take the listener 2) the entrance of unexpected tonal way back to the main key; it the time how these events relateto t o know at completelyunawares,making impossible just
perceived harmonic
the
goals.
This
is because
whole.
would be a contradiction in itself. Hundredsof study the art of surprise in their sonatas and symphonies take nearly the samepathway sections to the key of exposition the secondtheme,but every successful development section must be studiedasa singlecase.By
To systematically
at many development sections, however,wecan acquire someknowledge of the way they are designed.Table 3:3is a pictorial outline of a typical Classical-era developmentsection.
looking
196
Table3:3
The key at the end of the exposition is gently expanded into other tonal areas
Beginning of
Increasing
the
acceleration
modulatory
A decrease
rhythm coupled with a goal-directed path toward the dominantseventh chord in the
the
of
process
in
Undefinable
continuation the
of
modulatory
modulatory
process
process
main
harmonic
key
of modulatory to cover the greatestnumber the examples which follow procedures, will be represented in condensed form and only briefly described: As is shown in Ex. 3:28,aninstantaneous of mode between the tonic-majortriad (T) change the same dominant and the tonic-minor triad (t) is facilitated by the fact that both T and t have chord. After this basic shift of mode, the tonic chord in C-minor is then functionally reinterpreted as the subdominant in G-minor, etc.
In order
Example 3:28
K.V. 332
in F-major
Sonata
Mozart-Piano
ft:
-8\342\200\224t.
C:
M
^
^nr^irx4*^
E\302\273v
T [ I
..\302\2606 Vll 5 i6]
[ >v
&l
g: s
t
D?3
[iv
i]
contains a modulation that is producedby an abrupt shift of mode\342\200\224the G-major chord chord (D) becomes a G-minor (d) without any preparation. Near the endof the a first-inversion major triad (\302\2473) in C-major is then reinterpreted as the [IV'/TV] chord (s\") in A-minor.
Ex. 3:29 dominant example, Neapolitan-sixth
Example 3:29 in C-major
Sonata
Mozart-Piano
I\".
M
sa r C:
K.V. 279
r
r
D
d
s6
D
[V
V
ii6
v2
d: s
D
[iv
V!
7
t
3
i6] 197
7
r
r
T3
^
16
T
^ a:
sn
[N6
D V
U
In Ex. afterwards,
C-minor triad 3:30, the initial a Bb is added to the C-major
is changed to chord
turning
C-major in the secondmeasure.Shortly it into a dominant-seventhin the key of
F-minor.
3:30
Example
Haydn-String Quartet, op.74,No.
*
3
^^
3
f When
only
fifth
and
of a triad are presenttherecan
two tones
key. In Ex.3:31,B seventh
and
of a
D, the third
and
fifth
of the
dominant-seventhchord built
Ex.3:32contains
a similar
becomes reinterpreted
triad
on
possible
of
interpretations
triad, become reinterpreted as the
E.
op. 76,
Quartet,
No. 3
The root (C)andthird (Eb)of the C-minor the substitution of Ab for the expected
reinterpretation.
as an Ab-major
G-major
several
3:31
Example Haydn-String
be
with
triad
G.
Example 3:32 Quartet,
Haydn-String
r
T**f
a change
of triad
and third of the E-minor triad.
quality
triad)
from
No. 3
?r-T3Jl-l
4J4-TiJi| After
op. 76,
E-major
are juxtaposed
Ex. 3:33,the pitchesE the pitch C,thereby against forming to E-minor in
198
and
G (root
a C-major
Example 3:33
TiijnlJinn^}^
are reduced to only one pitch, still. In Ex. 3:34(measure3),the root
major triad. first
the possibilities
sonorities
When
are greater the
*^t
i=t
i
104
No.
Haydn-Symphony
Notice the long restinthe lower could be forgotten, or just
sonority
of a
voices.
C-major (Were
bridge-over the
to smoothly
Example
of harmonicreinterpretati
triad becomes the third of these voices allowed to rest
an
on
Ab -
sothat
triads?)
two
3:34
Haydn-Symphony No. 103
.I7TJ
d
m
>rm
m
>nm m
p
T
ft
There is considerable confusion is again reduced to 3:35, where the initial sonority onepitch.The second measure could either be heard asa sequenceof the first measure's melodic (A#) as the leadingpattern or the first pitch of measure 2 (Bb) couldbeheardenharmonically tone of B. The C in measure 3 proves that the secondmeasurewas only part of a chromatic of B. It is still unclear, however, role the C plays until what the passage and not a tonicization of end of the third measure, when it becomesthe third of an Ab -major triad and then the fifth an F-minor triad (measure 4). in Ex.
Example 3:35 No.
Haydn-Symphony
U
i
*
-
m
ffi The
same
kind
102
of confusion
I j i
s^f
'}t
\302\243
n
is present in Ex.3:36.
Example3:36 Beethoven-Rondo
in C-major
for piano,
op. 51, No. 1 5
w
fL^^LCT^fffl'ffl-ffl'l-^^l
199
There are many
in Beethoven, and most of them of unison pitch-modulations examples in motive in which the lower of the two pitches functions asthe leading-tone the new key. In Ex. 3:37,all four of the instruments samelineineitherthe the exact play higher or lower octave. (For a further example ofunison pitch-modulation, see the first movement of No. 98 in D-major; measures 139-142. Herean ensemble unison Haydn's Symphony produces a modulation to Eb-major by means of the half-step, D-Eb.) a half-step
employ
3:37
Example
Quartet,
Beethoven-String
op. 18,
No. 1
$Sjs^w^m4
TOgmf^
In fact, the composermust The exact moment of a tonal change is often quite imprecise. plan ahead for a tonal change, whereas the listener only hears a modulation after the fact. in Ex. 3:38. This spot exhibitsan interestinglackof smooth Observethe curiousnotation linear connection.
3:38
Example No.
Haydn-Symphony
\342\226\240m
i
A word
nltm
rr
Luta
oneor function
more
which
of its
from
Altered
of introduction is in orderbefore
chords
I; measure 190)
m
7.
altered
101 (Mvt.
appeared
in the
voices chromatically
which it
Chords
proceeding
Classical period.
raised () as
chord
compared
of the many types of sonority that has to the basicharmonic
is a
Ex.3:39shows
most
the
appearing in the Classicalperiod.
altered chords
important
Example3:39 nrr^ozzoz
fr#^-t\302\253MMft ^
^i\302\273J\302\273 |IJ,\302\273J \302\247
\\
Y
6
C:
D5
D; 4
[V
T3
T
D'3
I
B^T
5>T
D5
V3
kin Bass
T-
are usually inflection.
tones
Altered
chromatic
As is shown in is lowered
pitch.
a half-step,
will
ATI. If the [vii\302\2607
an upper
produce
The most remarkable feature
of this
altered
6
T
6 ii5
\302\243 5 !
6<
T
S
J& \342\200\242;6
and generallyresolvein the directionof alteration
important
dominant (' W)
of the
it
I
6<
S5
built on lowered2nd scale degree
outer voices
Ex. 3:40,a particularly chord
diminished-seventh
in the
found
It.\"
J
[ft.*]
their
'\342\200\236\342\200\242
\302\247^8=^
was made to the leading-tone third ofthis secondarydominant
(Phrygian) leading-tone tone to the dominant chord is that this upper leading-toneand the
in the dominant the dominant pitch key both occur simultaneously,thus framing lowered from aboveand below.Sincethe chromatically voice (third) of this sonority sixth occurs betweenthe bassnote and often appears in the bass,the interval of an augmented This altered chord is generally known the root of the chord (leading-tonein the dominant key). as an [in the English countries] augmented-sixthchord,regardlessof its inversion and speaking whether or not the seventh of the diminished-seventh chord is actually present (as in the W^; leading-tone
by half-step
see
Ex. 3:40c).3
Example3:40a-d
IJ:::
d)
,
b)
iijji^\\\\iJE C:
[Gr.6
3The '5>3> is called the German texts.
D4
3
V4
3
sixth (Gr6) and
r ?
fc^D* Gr.6
the aP75>
V4
3
is known as
201
&1 I
the Italian
D Gr.6
sixth
It.*5
V]
(It6) in English-language
harmony
Starting from the & (vii German-sixth chord ( E?3>).
/V),
Ex.
3:41 demonstrates
the steps involved
in
deriving
a
Example3:41
m
4^-jJ-ifE:
X
*\302\251;
\342\200\236 -.\302\2606 fi r \342\226\240\342\226\240\302\2607
Starting purposes
with
of analysis
chord (
German-sixth
the
in Ex.
Gn
vnK?
[v%
E?3>), the derivation
process
is reversed
for
3:42.
Example 3:42
;te
f*'
#\302\253fH-
D [Gr.6
Note
that
both
\342\200\242 \342\226\240\302\2607
vii\302\260i
Ss* and
'tf1^
\"V
sound
V
like dominant-seventh
chords.4
Since augmented-sixthchordsemerge from chromatic made to diatonic sonorities, changes their function is perceived to be similar to the sonoritiesfrom which they were derived. For that an altered chord with label the same basic functional symbol that is used reason, we generally for its non-altered It is much more difficult for the listener (and certainly the counterpart. becomes if a so-called turns functional altered a a chord symbol questionable), pitch sonorityinto that sounds like some other diatonic sonority. Could the pitch Ai>, which functions as the root ofthe first chord in Ex. 3:43, actually be an alteredA*| in the second chord? Is it also possible, in the second chord, that F# might be a are often encountered in developmentchromatically raised F*l? Since multiple possibilities section we should be carefulnot to jump to conclusions about the correctfunctional progressions, analysis
4
of such
The author
sonorities.
refers to the
theorists English-language C-D# in C-major) refers to
augmented-sixth
seem to prefer the less-frequently
chords that resolve to the dominant as secondary dominants, though them as altered subdominant sonorities. The author's Ss^F-Aconsidering chord built on the fourth scale degree. German-sixth employed
202
Example 3:43 Haydn-String
op. 74,
Quartet,
No. 3 (Mvt.
I; measures
94-96)
J %-
^^=^ l#J
Ex. is taken from the exposition section of a string-quartet 3:44 movement (all other sections). examplesin this discussionare taken from development Here, the middle voice is to move in between the peaceful allowed outer to believe that the final voices, making it difficult C in the lowest voice is actually an altered tone of an F#-A#-C#-E chord ) [It6]. (^J,
3:44
Example Quartet
Mozart-String
K.V. 464
(Mvt. I, measures29-33)
(It.6)
Two passages in the same tessitura (Exs.3:45-6) show how the dominant's leading-tone diminished-seventhchordwith an added upper (Phrygian) leading-tone ('S^) [Gr6] progresses to the
dominant:
Example 3:45 in F-major
Sonata
Mozart-Piano
J
J
J
K.V. 533
Se
T=T
i J
aUd:
t
[i
d3
(
v6
s65
H
J#v3>)
(ii\302\2607 It.6)
203
1: D V]
3:46
Example
in A-minor
Sonata
Mozart-Piano
s ^ ^*
i
m a:
-j\302\260
t
s*
m k*
&\\^)
v6
(ii\302\2607Gr.6)
the
dominant
Example
3:47
[i
Ex. 3:47
(
d3
shows a similar resolution to
Haydn-Symphony No. 104 (Mvt.
K.V. 310
D V]
via the
I; measures
t9'\"i>
[Gr6].
154-158)
in Ex. 3:48. The root tone of the dominantAnother altered-chord possibilityis shown Db is a chord which leads as \"S>v seventh chord in diminished-seventh -major raised,producing The surprise here is perfect, the same raised half-step in the bass because (vii\302\2607/V) to Eb -major. (Ab -Bb b) was previously j ust an inconsequential upper-neighbor.
204
Example3:48 103
Haydn-Symphony
measures 136-138)
j
,num
Dk
(Mvt. I;
hi
D7-
[V6
D4-
h
[Gr.6
shows another method of changing a dominant-seventh chord into a diminishedthree the voices are lowereda the while bass tone remains the Here, upper half-step same.The function of this diminished-seventh chord is madeclearthrough a further half-step descent (C-B) in the alto, which then produces the dominant-seventh chord in the new key of Eminor. A simplified which harmonic reduction of the chromaticalteration takes place in Ex. 3:49 Ex. 3:49
seventh.
is shown
in
Ex. 3:50.
Example
Mozart-PianoSonatain
i
ii
205
3:49 D-major
K.V. 576
3:50
Example
D7
B/b:
E/e:
[vu
[V7]
D7
^ 5
V3]
is a 3:49 works becausethe diminished-seventh chord an actual sounding root). symmetrical sonority, constructed from three minor thirds (without that in a diminished-seventh chord can act as a leadingFor reason, any one of the four pitches of that is, the composer can chooseone of four possible root tones for the following chord tone; resolution. chord so that Classical-period composers generally spelledthe diminished-seventh note which as the root of the sonority lowest (the appears pitch of four stacked thirds) actually it as the leading-tone to the following functions chord (see Ex. 3:51). For the listener,however, of a diminished-seventh is not possible to know before its resolution, which note chord will The
altered-chord
as the
function
device in Ex.
leading-tone.
Example 3:51
^ m
m
IPlii
=E*feSI
n ^tm
5=\302\253
If a necessary chord,
it is composer wishes to help clarify the resolution goal of a diminished-seventh, a half-step. to lower one ofthe four pitches This procedure creates a dominant-seventh
which
expresses
the goal tonality
with
less
ambiguity
(see Ex.
3:52).
Example 3:52 \302\247
II
ftp
IH
II
II t**\302\273J
$
ft&J
\\J
Tf Resolution
goal:
D
G\302\273
206
Al.
only
chords
Altered
progressionsthat
within
are
The marked
ambiguous.
connectionsbetweenchordsinEx.3:53arelikeupper
op. 76,
Quartet
Haydn-String
also employsthis samekind
labellingwe have agree
always
what
with
Gr.6
V]
motion between chords. The functional not contrived, however,becausethe symbols may run therisk of destroying perceived. Indeed, we sometimes
is actually
analysis ofthe top voice
A listener's
leading-tones.
ofleading-tone
is somewhat
here
events, if we are too
musical
exciting
chosen
lower
No. 3 (measure 61)
vii\302\2602
[i6
and
3:53
Example
Ex. 3:54
often produce functional
sections
development
Classical-period
intentionally
with
concerned
applying
the
\"correct\"
functional
be somethinglikethis:\"D-C#
3:54 might
in Ex.
symbols. -C!,
no D-Db
!-
C.\"
Example 3:54 Sonata
Mozart-Piano
i d:
*
*
\302\273
t
D
d
[i
V
Tg
E?3
[ill
In Ex.
3:55, the
clearly
its resolution to seventh
chord
listener can beeasily
refers back
the
must
(as vii
dominant-seventh
~
\342\226\240
5
o\\ ,.6. V5J
as well. The diminished-seventhchord, but considering or triad in the first measure, in third measure, the diminishedchord (C-E-G-Bb) (vii\302\2607/C). reinterpreted as B-D-F-Ab
\"VA) to
be enharmonically
t
..o6 IV . 46 Vll
....
-B-D-F
m
#
K.V. 280
v] F:
G#
in F-major
lead
astray,
the A-maj
207
Example 3:55 in F-major
Sonata
Mozart-Piano
^^
-^ti-i^-f In
Ex.
(vii\302\2607/F).
3:56, The
a C-major
resolution
triad is followed chord
by
K.V. 280
f
^^
a diminished-seventh
of this sonority (a
chord
second-inversionF-major
built
on triad)
the
pitch E is never
Instead, the bass note
of the diminished-seventh chord functions here (Db) of in the chord dominant-seventh suspension F-major (C-E-G-Bb). the pitch Bb ofthis dominant-seventhis enharmonically In the fifth complete measure, changed to A#. The sonority then resolvesas an augmented-sixth chord (' iP^) [Gr6] to the dominant of
reached, however.
likea dissonant
above
the root
E-major.
3:56
Example
Mozart-Piano
9
fe
C:
F:
T
[I]
FP^P
Sonata
in
A-minor
ii^\302\243tf^W
Dl. [Vll 2
D
1
V]
(K.V. 310),
[Gr:
208
V]
is often too stable to function as a good transitional its first-inversion form. An added composersoften substitute benefit of the first-inversionmajor triad is that it can also function as the Neapolitan-sixthchord is the Neapolitan-sixth triad chord in the keys (s\") in two other keys (a first-inversionC-major of B-major in and B-minor). The three condensedharmonic Exs. 3:57-59 are extracted excerpts Piano Sonatas. These excerpts demonstrate leading-tonechromaticism Mozart that does from not resolve to stable root-positionmajor rather but to their less-stablefirst-inversions. triads, Since
sonority
major triad
a root-position
in a
modulating passage,
Example 3:57
\302\247
tm
s
&
nffi
fa e:S\"
b: t
in D-major
Sonata
Mozart-Piano
..\302\2606
&
g
d: S6
s vi
3:58
Example
C-major
K.V. 309
|HH|4-r^
ftB^=
Example3:59
^f i
s
7
..\302\2606
Mozart-Piano Sonata in
Mozart-Piano
^
v\\
t.
..\302\2604 .6, Vll 3 1 ]
[N6
is^g
S
[i] \302\273:s
K.V. 284
Sonata
in D-major
*
209
K.V. 576
8.
The
Introduction sectionsto
first
Sections
Introduction
of Slow
Harmony
symphonies and sonatasrely
of large-scale
movements
on
than the thematic and less complicated, harmonic processes of the In a slow introduction, the clear-cutharmonic areas follow. sections are often avoided. For that reason, an later-appearing exposition and recapitulation section of the development section,where introduction often has more in common with the spirit to tonal to the limits of its ability pushes the system offunctional ambiguity frequently analysis
somewhat
though
different,
developmentalsectionswhich
clarify
details. In many late-Classicalintroduction
harmonic
an expression-rich,but will be
opened, the entire composition) few
but
the work,
but
closed. Introduction with
introductions
a promise
generally
Instead, a slowintroduction yet to
harmonic
non-conclusive
will
structure;
sections,
the listener
that is, many
sectionsprovide
the
forgo the
a hint
gestures of of musical
movement
following
musical
weight
doors
harmonic
of things to come; an enticement to
give us only
will experience
into
step
fulfillment
and a
will be
(and often the world
of
and closure.
foretaste of
events
come.
The basic harmonic
function
of a
Classical introduction
sectionis to
establish
the
in major or minor, slow introductionsoften are related either to or directly controlled by the present strongly tonic. This feature gives the introduction section a senseof broad harmonic scope. Central tonic harmony T [I] or t [i]) and its primary areas (Tr (whether relative-sonority Sr Dr [vi, ii, iii] or tR sR dR [III, VI, VII]) normally dominate introduction sections. In spiteof numerous perceived tonicizations, however, auxiliary tonalities in introductions are generally as secondary areas which do not threaten the overriding influence of the main tonic key. The composercreatesthis broad sense of harmonic scope within a central by tonality touching upon key areas that are closely related to the tonic (T or t), while avoiding strong cadencesin the tonic itself. Once the tonic key has been established at the start of an that the dominant half-cadence to tonic is generally avoided until introduction, strongresolution moves directlyinto the main body (allegro) of the movement. cadences within the Intermediate introduction often rely on pedal-points,half-cadencesor deceptivecadencesto avoid a sense of closure or finality. We shall established by Wilhelm Maler (Ex. 3:60)in our symbols employ the functional unquestionable
dominance
a variety
analyses
of the
work's tonic pitch. Whether
of tonal centers that
of introduction-section
harmony.
210
Example 3:60
ifcb \302\273\"'lt
C/c:T [I
Tr
TR
Dr
DR
vi
VI(^\302\260 iii
III'
sG is the major
movement
3:61
tR
M)
sR
sr
tG
viihl\"'*\302\273|HM
a harmonic
contains
progression found
section to the first
introduction
the
in
position].
Linz Symphony.
of Mozart's
Example 3:61 Mozart-Lmz
T6 I DJ3 [I6 sG [to
I
(DJ 7
I
SJ3
liv6l
v6l
yyiw
in C-major
Symphony
I
D7
I
t
D
I
I
v?
I
i
v
Uvi
T
5
if
tG
I
S6
I
ii61
I
D7
I
v7v?
I
3
T
3
t, 3
I
i6
i6
I
K.V. 425
\302\247>7 I D7
T
t
I
D7
i
i
I
v7
3
vf
(D7)
v7l
I
v^
I
v|y
'
|
s
|
I
iv
I]
T
t
I
D
t\302\256VI
D
II
i
i
I
v
I vi\302\2437
v
II]
The spots marked with an [*] indicate important places where a resolutionto tonic but avoided. In spite of this local bypassing was strongly implied, of the tonic, the of the tonic key remains influence controlling effectively unchallenged.
211
In Ex.
3:62,the major
tonic
moving into the dominant the minor-tonic area (t).
twice (fermatas), presented and confirmed double bar, the introduction moves
(T) is
key
area.
before
the second
Following
into
Example 3:62 T -f^-lD^ IrvSI
[i
T
I
v\302\247i
No. 102 in Bb-major
Symphony
Haydn-
3
ID*
S3
i
liv6lvt
II
T
II
II
i
II(v|
(D7,
I
3
) Tr
l
vS lv7)
S>7
Id7
I
vi
I
I
[i
S>7
(s3
Id)
tR5
v)
ImS
-major
] is
(iv6v^l
tR [III
I
\342\200\224 Db
I
d^
I
vH
I
8I
'
d'
i
l|:vS
vii>7
II
I
v
II]
:||
D
=11
v]
v/
l|:
W
D
\302\253
8
t
I
Bb -minor'srelative triad
in major-key symphonies begin in the minor-tonic This action introductions Many key. saves the major-tonic sonority for the start of the following allegro section (see Ex. 3:63).
Example3:63 >7
I /SN\342\200\224I\342\200\224I\342\200\224I I D*
^
I
iv
I
vy
I
v
d7
I
t
I D7-4-t\342\200\224I
[V7
I
i
I
V7^-M
i
(E^)
I
D-major S
(D7
I
T43
I X\302\256\\
h
D<
I
tR I
L 7
^
6
[i
101 in
No.
Haydn-Symphony
I
I
d7
V7
--\302\260\302\253 l\302\2534 3 3
Ivif^
I
I
t3
i6
lv4
vif^Jv4 3)lm
\342\200\236;;\302\2606 I TV Iiv r3 v3l T43 viiT (f V*l
Is
(E^v)
vi\302\243 I \342\200\242av
IV
'S\302\245
vii>7
Id
I
3\" \342\200\236!;\302\260SJ V4
V
I
Gr.6
I
V-r\342\200\224II
xv
* This T does not refer to the The dotted-line bracket indicates that all these key of D-major. the relative major this bracket as (Dj) (tR). We could have labeled the material within major, it seems to me that one set of parentheses is sufficient to explain this tonal excursion.
212
Id^\342\200\224II
1'^
harmonies
function
tR43 ] D* f7)
in F-
tR, but
After this discussion
Exercises:
to require compositional in a
benefit
individual artistic
are really
harmony
study
brought
already
exercisesthat
like
this,
to its
ofClassical-period harmony, The
exercises.
invention
achievements.Copying we even want to
and why would
apexby the mastersof
the
it is
really quite
meaningless
materials and developmental of the Classical style is oflittle writing in a style that attempt
of thematic
eighteenth
century?
real was
We might consider
some
of developmental techniques, however, a rote formula. exercises deal more with how to handle transitional materials than following Great value can be gained from the harmonic of Classical analysis works, as longas the For that reason, harmonic is always considered in its appropriate formal context. progression harmonic analysis can bebestusedas a tool to help confirm certain form-building processes or our understanding to complement of those processes (the uncovering continuing modulatory tool in developing a critical processes, for example). Harmonicanalysiscanalsobea valuable a set of functional to structure. commentary about a work'sformal complete symbols Applying an entire Classical movement is not only monotonous, but it also often showsa certain laziness of thought on the part of the analyst. Rather than every harmonic progression, it might labeling be
help
might
to answer the
better
us practice
following
since
these
kinds
questions:
between the stable is the harmony of the first thematic area? 2) Isthe modulation second theme area straightforward or is it and and confusing goal-directed, developmental in nature? the most prominent key in the exposition, 3) Is the dominant [orrelative major] in importance followed by the tonic (the secondthemeareaand the closing section are usually in the dominant the relative weights found make [or relative major]),ordo insertedmodulations two in ofthe rest the development section? polar keys less clear? 4) Are there planesof harmonic If so,where? are often found at the beginning and endof the development.) 5) How is the (They rate of key change established in the developmentsection?6) Which modulations are and Which the action of lower etc.? take unambiguous? upper place through leading-tones,
1) How
first and
A
harmonic
analysis
should
include the functional
symbols and their attached
Arabic
The complete specific symbols in Ex. 3:64state the function of all the chordsin the exampleexceptfor two places (see the key center is changedfrom C#-minor empty boxes). It is debatablehow boldly or tentatively the to C-major, and then from C-majorto B-minor. The chord in measure 2 couldbe considered in could be the sG the ofCand the in measure 4 considered II or first chord N) in (b Tg (iii) key B-minor. Ifwe fill-in the empty boxes with these respectivefunctions, we will have labeled these chordsin old both and new keys. pivotal numbers
(the
Arabic
numbers contain
information
213
about
voice leading).
Example 3:64 in C(t-minor,
Sonata
Beethoven-Piano
op. 27, No. 2. (Excerpt
from
Mvt. I)
-#i
^rir]
6
[V3
3
h 5 11 3
t
i]
8 7
5
[V3
6
^
I
12]
Although composing a complete movement in the Classicalstyle prove to be little might more than senselessbusywork, it may actually be useful to design a modulating harmonic plan and then write-out a slowintroduction section. The scope of such an assignment will depend on the length of the introduction, since an introduction of five measures will unfold much differently than one of thirty measures more involved harmonic (the latter will require a much plan than the former). It is especiallyimportant that the dominant-seventh chord at the end of the introduction is reached at just the right time. Those who wish compose an introduction a piano version,but besure may try sketching-out to maintain not a strict four-voice texture throughout. Another is to write-out the possibility and bass voices in such a way that the melody consists of two separate instrumental melody which alternate voices with one another. It is interestingto observe the differences that occur betweenan introduction that follows a preconceived harmonic plan and one that is created more intuitively. Using both methods, sections of about the same length for piano. After having written-out composetwo introduction the intuitive then compare the harmonic version, go back and add the correctfunctional symbols, version. path with the totally planned-out
214
CHAPTER FOUR Between
Harmony
1828 (Beethoven-Schubert)
and
1800
1. Triads Relatedby
The
of a
Interval
Third
term mediant chord has not been standardized. Instead there of this term in use Some today. separate commonly analysts consider working a mediant or third or chord be triad whose root is a minor above below the root of to any major some other triad. Using this a complete set mediants for a C-major triad would definition, include: A-major/minor, and E-major/minor. Other analysts Ab-major/minor, Eb-major/minor between T and differentiate the term diatonic mediant, a chord relationshiplikethat between Tr [I-vi];Tand Tg [I-iii]in major, or between t and tR [i-III]; t and tG [i-VI] in minor, and the term chromaticmediant, which refers to all third-related chords that are not diatonic mediants. I suggest that we avoid the term mediant and instead try to determine the altogether with each other. that the various third-related triads have precisekind of relationships A. Relative/Counter-Relative Sonorities: Thesethird-related chords have two pitches in common with a starting chord. Beginning with a C-major triad (T) [I], these chordsarethe Atriad (T) [I], they are minor triad (Tr) [vi] and E-minor triad a C-minor (Tg) [iii]; starting with and (tR) [III] Eb-major Ab-major (tG) [VI]. B.Relative/Counter-Relative Sonorities of the Parallel Chord? These chordshave one a C-major a starting chord. pitch in common with triad, the two chords in Beginning with These two chords are questionarerelatedby diatonic third to C-minor (the parallel of C-major). in question and are related Ab-major Starting with a C-minortriad, the two chords Eb-major. These two chords are A-minor and Ediatonic third to C-major (the parallel of C-minor). by
The meaning
of the
are two
musical
definitions
minor.
pitch
C. Parallel
Chords of
in common
with a starting
are A-major,
the
parallel
the
major of the
counter-relative
parallel
sonority.Beginning relative minor (TR)
a C-major
with
(TG). Starting minor of the counter-relative
with
a C-minor (tg)
and
These chords have one triad, the chords in question E-major, the parallel major of the
Sonorities:
Relative/Counter-Relative
and
the triad, the chords in question are Ab -minor, of the relative Eb -minor, the parallel minor major
(tr). Parallel D.ParallelSonorities of the sonoritieshave no pitches in common with the chords in question are Eb-minor (tr)
and
chords in
E-major(TG).
1
question
are A-major
(TR) and
Chord's the
The author explains that Riemann called the parallel with standard terminology, English-language chord in this translation.
keeping
Sonorities These
Relative/Counter-Relative
starting
Ab-minor
chord.
Beginning
(tg); Starting
with
with
a C-major
a C-minor
major or minor form of a starting triad the the term parallel chord will be substituted for
215
triad, triad the
In chord. the term variant
variant
Earlier we discussedthe harmonic whose chord roots are related by fifth. Now that system we have alsodiscussed a system of harmony whose chord roots are relatedby third, it might seem, that third-related chordsshould beableto build the same kind of universally useful harmonic as fifths. However, third-related chordswereused much less structures in the frequently
Romantic era than
fifth (dominant)
relationships. This makesthe occurrenceof
thesesonority types became special practice. Nonetheless, of certain composers,who used them in a variety of compositional It should be kept in mind that third-related harmony is not the norm. It is possible dominant-tonic but third-related progression to a harmonization, harmony must be a somewhat
trademarks
stylistic situations. to
with
chords
sonorities
third-related
a
apply
invented. During
the
Vivaldi, plagal
a composer's
Baroque,
would be
materials
harmonic
various
stylistic traits already
individual
applied in a composition
cadences[S-T]in Handel,and
the
employment
actual
progressions.
compositional
Remote Harmonic
For
situations
reason, we as possible.
that
Relationships:
The
will
study
development
sequences
in
dominants in Bach). individual use of composer's grows into a font of inspiration Because we wish to discuss
of secondary
an it is no longer sufficient to discuss only Today, however, at first is just a tool, which either particular materials.Harmony, or is considered only a set of formulas that shuns any real invention. in the context of musical invention, it would be absurdfor harmony of-context
determinedhow
(descending-fifth
us to
examine
third-related
section of
only single outin as many
harmonies
the
first
movement
in
but the harmony returns to D-major Haffner Symphony (K.V. 385),beginsin A-major, bass holds out a long pedal-point on the pitch A. This texture then leads to a halfcadence on A in measure is a three-beat grand pause 104 (Ex. 4:1). Directlyafter the half-cadence
Mozart's while
the
marked forte (the previous tutti by a double surprise. The first surprise isanorchestral and the second surprise is the new The keys of A and dynamic was piano) harmony: F#-major. F# are not actually heard as third however. The to the third of the resolution relations, expected F# tonic triad the becomes the of the root This half-cadence) (after D-major -maj or triad. suddenly is both distant and The tonal center for the rest of the abrupt key change averting. development remainsin F#, until the section finally empties-out into the recapitulation through a series of fifths to (B, E, and A, then back descending D-major). followed
Example
216
4:1
use of third-related A completely different Structurally MotivatedThird Relationships: Sonata in G-major, op. 3. twenty-one years later (1803) in Beethoven'sPiano appears The first movement with an embellished downward-inflectedG-major followed scale, by begins rhythmically accented tonic chords.Thecadenceat the end of the theme has already modulated to the As is shown in Ex. 4:2 this dominant key (D-major) in preparation for the second-theme. modulation to the dominant takes place by way ofthe Tr (vi) which acts as a common chord. harmony
Example 4:2
G:
T
Tr
[I
vi]
6
D:
Sr
[ii 12, however, the first secondary-subdominant
In measure F-major
is the
theme (\302\247) key
T
V4
I]
suddenly area
5
D4 3 3
in the
returns
of G-major,
but
the
surprising key of immediate
F-major.
juxtaposition on p. 215 (the
of keys (D-majorto F-major) creates the type ofthird relationship describedin B. relative major ofthe parallelminor).This new entry of the first theme is an exact transposition in F-major, and the theme ends, once again, with a modulation to its dominant key (this time CThis modulation is that leads to the dominant followed modulation major). directly by another from to Unison work from the derived embellished downward scale, C-major G-major. passage in measure 45 confirms the followed by a dominant half-cadence key of G-major. The theme entersonce more (again in G-major), but another modulation is appliedand the harmony moves quickly to the key ofB (seeEx.4:3).
Example4:3 G:
T
[I
Tr
vi]
B/b: s [iv
D
s,3 ^?75
D
V
iv6
V]
viy6
It is not clear whether Beethoven prepared B-major or B-minor The second theme here. begins in B-major(measure66),but then is immediately repeated in the key ofB-minor. The first B-minor, then B-major, and plan: closinggroup of the exposition follows a similar ambiguous finally
closing
in B-minor.
217
I hear the repeatedentry surprising as the F#
-major
of the
chordinthe
first theme in exposition
F-major (measure 12)to be
of theHaffher
(Ex.
Symphony
just
4:1).
as remote
and
The question
is the role of B-major as it is employed in the second themeof this G-major sonata. Is it a remote or closely related key?After cadenced in having G-major, D-major, F-majorand C-major,to what should measure 52? The surprising Beethoven have modulated after key key relationships statedby the first theme's materials allows Beethovento dispense with the traditional polar key of D-major. to prepare our ears for the second these initial key excursions function Further,
theme'snew
key
area.
is able to relate the key of B-major/minor to harmonic plan, Beethoven of the theme becomesthe second as a direct F-C-G-D-major. B-major/minor key the area. Therefore, consequenceof the modulatory plan used by the composerin the first theme third motivated. between relationship G-major and B-major is structurally
By employing this
the key-complex
a Stationary with Change Applied to a Central Pitch (Melody theme in the first Schubert's second movement of StringQuintet
Pitch): The transition ends with an is dominant, followed spot
Color to the
accentedchord by an auxiliary
in C-major
at this 57-8. The harmony chord over a pedal-point, returning again to dominant diminished-seventh The fundamental (D\342\200\224D). by the viola (pizzicato), while the harmony is then carried forward violins chordal on the weak beats. The first cello sings in a high register, provide interjections in thirds and sixthsby the ribbon-like accompanied predominantly legato of the secondcello.In is a this which is later repeated by the first there melody, noticeably frequent recurrence violin, it of the which causes to texture. dominatethe pitch G, In measures58-81(24 measures) the pitch G occurs in the melody for a total of 56 beats If would total fourteen of these G'swere added all notes). measures, more (quarter togetherthey than half of the entire melody. Regardless of the limited motion of this melody and the way it so highly on a chain of single depends pitches, many friends of chamber music perceivein this theme a sense is why no one either seemsto of wide space and deepexpression. The question sense for the passage to moveaway from the limited pitch materials or feel a necessity this nearly constant central pitch. In measure58themelody pitch G is heard as the doubledroot of a G-major triad. This same is heard as the third of an Eb-major 60. In measure 65, the pitch triad in measure G, however Gis again heard as the doubled root ofa G-major triad after having been preceded by an F-minor which creates a dominant half-cadencein C-minor relative minor of Eb). G isheard (the chord, once as the third of the Eb-major measures 66-70 and then is harmonized more triad between in C-major (see Ex. 4:4), a further as the fifth of a C-majortriad in measure71. After arriving is modulation to the dominant of C is applied reached and again in measure 79. Like G-major in the third an Eb -major triad inmeasure it was the beginning, the melody-pitch G again becomes of passage
(tutti)
in measures
81.
218
Example4:4
of the different sonorities that harmonize the often-repeatedG arerelatedby third. The D-T is not the to C utilized. (i.e., simple relationship major) G-major resolving pitch G Though It is harmonized as the fifth is stationary in this melody, it appears in several different colors. All
of the
C-major
triad, as the root
of the
triad. Because
the pitch G is harmonized
the
of wide
given
impression
G-major with
of the Eb-major triad, and as the sensitive third so many third-related sonorities, the listeneris
melodic motion, when the
actual
melodic
line
is quite
limited in
scope.
Breakoutfrom Symphony
No. 4
is in the key of
end in Cb
Prevailing
of the Tonic Area:Schubertcomposed Enrichment years old. In spite ofthe fact that the last movement start in Eb -Major and are two modulations in the expositionthat
when he was only
C-minor,
there
Harmony; nineteen
-Major.
finale begins with a four-measure followed by an Allegro melodythat is introduction, The harmony is also quite different from one Haydn might have written. ' straightforward This initial melody (the most complex progression that occurs here iss -D-tG [N\"-V-VI]). In measure is repeated, followed a the relative 33 a pleasant modulation to (Eb -Major). major by but the original melodysoonreturnsinthe key of C-minor. (Schubert enters, connecting melody often composes histhemes sothat they approximate the closed structure ofthree-partsongform and modulation (the The first theme group endsin measure63,followed [A-B-A].) by transition of times I? [vii as the active chord, leading-tonediminished-seventh ], is employeda number The second theme enters in measure 85. It is more sonority in the modulation process). varied harmonic devices. than the first theme group,but there arestill no unusual harmonically The closinggroup begins in me asure 129, and is clearly from the rhythm of the first theme derived in . The consists four measures Eb of [I-I-V-V] (T-T-D-D) J J JJJ -major, repeated closing group is as this four measure phrase is hearda third harmonic listener but time, catastrophe!\342\200\224the this breakout the without into the remote of Cb from thrown, -major. Although key warning, The
not very
219
was not prepared prevailing tonality motoric eighth-note pattern which always present in at least one voice
it certainly is strongly throughout the
harmonically,
in intensity
increases (see
supported
by the
movement, and
is
Ex. 4:5).
4:5
Example
\302\243m
frih^ After
this
\302\243E
^ the
key change,
surprising
scale passagesproduce
more
becomes
harmony
in Ex.
shown
modulation
the
* active.
Ascending chromatic
4:6.
Example 4:6
-
J *J4i)J
jij j W^jjj
r
i
r
!
T
t
tG
[V
1
VI]
f:
D
t
tG
[V
i
VI]
T
'
T g: D
D
e:
1
[V Ek
t
i] Tg
[iii
f* D [V
t
tG
i
VI]
T
\302\260l
vl
T
I]
enharmonic cl major triad
The key of Eb
-major
is confirmed by
a cadence.
passages
the
with
strings.
strengthened and clarified
is reintroduced
thirty measures
Now, by
the
beats (seeEx.4:7).
Example
4:7
\\ij-{TTlrFTtfm
f^Xn Ek
tG
T-
[I
\"
beforethe endof
the
exposition,
and
the movement,the winds have shared the melodic however, the harmonic progressionof the closing group is winds who reinforce the harmony by playing only on strong
Up to this point in
D
VI
V
220
In Ex. 4:7we alsohear
an
again
triad followed by
Eb -major
a Cb
-major
triad.
This time,
rather, enriches the key of Eb. This is because that the key the two chords occurs in the bass. It is clear, the common tone (Eb)sharedbetween chord Cb -major of Eb is not endangeredin the sameway that it was earlier when the following and the in This time Eb is confirmed as the tonal root following center, position. appeared occurrence. of its earlier, more dramatic reminiscent (inverted) Cb-majorchord is only slightly
however,Cb
from
not breakout
does
Eb
-maj
or, but
of Unanticipated Sonorities:The first movement of Beethoven's The APiano Sonatain Eb-major, (A-B-A). op. 27, No. 1, is constructedin three-partsongform Table of six four-measure 4:1). phrases which are joinedtogether(see part of the form consists of one another. These four-measure repetitions groups are either literal or variational The
Pleasant
Surprise
Table 4:1 of the
(Diagram
|:
Al
:|:
in Eb -major,
Sonata
Beethoven-Piano
phrase structure in
A2
:|:
the first
:|: A4
A3
:|:
op. 27, No. 1 section of Mvt.
Al
:|
A2
:|:
these
I)
phrases are
variation of repetitions earlier
their
counterparts
As is shown in Ex. 4:8,the major element between connecting occurs at the beginning of the of repeated quarter-notes, which
Group A3
begins
with
a pickup
i i J
J \\ty\\
pattern
^p
and carriesthe repetition of A3
is a
measure.
4:8 A2
Example
Al
fl
groups Al and A2 first
Example 4:9
221
pitch
one note
further (Ex. 4:9).
Both the eighth-note pickup and the elongatedrepetition arecarriedover to group A4, but is introduced. As is shown in Ex. 4:10, the eighth-note a new harmonic connection (G) pickup functions as the third ofthe previous of the Eb-major chord, but it also functions like the fifth of the relative minor, becomes an attractive following C-major chord. C-major,the parallelmajor color in the piece. new harmonic
Example4:10
m
^m
rf?
kEEEl \342\226\240sit
t-T?
i^^i
\302\247g -m
Because be
might
tempted
should
notion
of the
-m
-m
straightforward way in which this harmonic C-major chord as a secondary
progression
to analyze this
be rejected,
dominant
(see
is continued,
we
Ex. 4:11).
This
however.
Example 4:11
\342\226\240* \342\226\240*\342\226\240
Ek
(D
T [I
The C-major referencing
other
pickup-note
figure
triad in group A4
V/.
is stable,
7) Vl
neither
This concept of stability its counterpart group A3 with
tonalities. in
-m
Sr
D7
T
ii
V7
I]
seeking resolution to other sonoritiesnor if we compare the is further reinforced in group A4 (Ex. 4:12).
Example4:12 A4
A3
I f'\342\226\240
The
entrance
of register
1
\302\273
W
C-major chord is breath-taking.No set of functional symbols, whether really clarifies the surprise wehear in this spot. Thedramatic at the entrance of C-major chord must also be considered. As Ex. 4:10 shows,
T-TR[I-III]orT-(D)-Sr change
II
of this
[I-V/ii-ii]
222
the relatively triad enters without registral preparation, after the bright C-major material at the end of A3. The best way of experiencingthe surprise,however, A3 and A4 (Ex. 4:13). between attempt singing the melodicconnection groups
low register to simply
is
Example 4:13
jtlLU3\302\261i: in such a way, that istaken The unawares. next, unanticipated that of a third-relatedsonority good example is constructed
connection
melodic
This
the
what will come
anticipate
and its repetition
is a
to who is trying listener, of the chord entry C-major
a sense
produces
of pleasant
surprise.
Schubert's Progressions
the
around
Circle
of Fifths: Until
the beginning ofthe
lengthy
op. 10,No.3, the in measure 13 is to Cmodulation movement quite close to the key ofD-minor. The first stays 21. The key changesto F-major (dR) [VII], followed by a move to a-minor(d)[v] in measure major is (tR) [III] in measure 30, and then returns to D-minor (t) [i] in measure 44. BeforeD-minor confirmed (measure 60) by a strong cadence, Beethoven briefly tonicizes the key of Bb -major (tG) (VI) in measure 56.
coda
section
with
the
A
in the
broader
tonic,
Largo e mesto
from
Beethoven's
harmonic plan unfolds in the following the movement's most remote sonority
measure 67. This measurealso 4:14 contains an excerpt from
contains this
spot
the
in the
lowest
Piano
Sonata in D-major;
23-measure in the
however.
coda,
circle of fifths
sounding pitch in
As compared occurs in
(Eb -minor)
the movement
(Gb).
coda.
Example 4:14
pm
*r5
w
mm
www^
mm 223
^\\
Ex.
the smoothest voice leading will prevail, uses an enharmonic F# instead Beethoven diminished-seventhchordon the downbeat of measure 4. (Beethovenclearlyintends the root of this diminished-seventh to be the root of Ef [vii\302\2607].) In measure 5, however, he spells the seventh of the chord without using an enharmonic the so that harmonic sequence equivalent is correctly notated. that follows The seventh of the applied diminished-seventh chord in the i when the seventh resolvesdownward. )D*! T[viiC7/V-V4 progression(E)v -I], normally However, of the diminished-seventhis forced in as measure 4 of the enharmonic (because F#), upward, composers will often resolve the sonority to Dt i [Vt I ] rather than directly to D. This principle is not either uniformly or systematically applied, however. a progression all the way around often sequence the circle of fifths, but do not Composers rather think of the distance(in fifths) two keys as straight lines with a low end and high between end. In Beethoven's Eb -minor from (six flats), is a very long distance Largo e mesto,the low-end the key of A-major end. at the high (three sharps) Outside of development-section tend to modulations, most Classical-period composers maintain a linear key organization,wherethe central tonic a rather stable equilibriumbecomes the central tonic, even in nonoften destabilizes producing element. Schubert, however, music should be regarded as hisown personal sections. (This aspectof Schubert's developmental In Schubert's music, the entire circleof fifths is often style and not as a generalstyle of the times.) means harmonic that include many third relationships. traversed completely by far-reaching Schubertwill frequently a particular tonic and launch into one of his complex circular abandon progressionsthat will end precisely where it started\342\200\224back on the tonic. So that
of Gb
in the
4:15
Example
Schubert-PianoTrio
D
t
[V
i]
B:
op. 100
Eb-major,
46
38
34/35
E|>:
in
G:
(Mvt. I)
58
48
57
Dr
T
t
I
i]
[iil
Ek Dr
Tg
D7
t
[iii
V7
i ]
[in
chord
[measure
66
T I]
enharmonic D#ttiinor triad
In the
fifth
perfect
a Gb
piano trio excerpt (Ex.4:15),a Bb -major to an Eb -minor triad (a circle-of-fifths
G-minor
new
from
2b to
34-5] resolves 6b). Within
downwardby
this new key area,
and is enharmonicallyrespelled(measure46) to form an chord appears (6b=6#),which then resolves once more (down by fifth) to a B-minor triad (2#). Within altered to form a tonality, a G-major triad appears(measure57),but it is immediately
-dominant-seventh
F# -seventh this
jump
triad
(1# to
2b).
224
There has been no modulation a goal key. In spite toward the original tonic stillemerges intact on the other end. In fact, the tonic area is actually revitalized by this process and is preserved a while longer. Earlier the closely related composers would have attempted this sameharmonic by tonicizing process chordsof the relative key. The difference betweenthesemoretraditional in the relativesojourns in Ex. 4:15, is that the controlling observed force of the tonic key area andthe harmonic processes is not really challenged by the usual relative-keytonicizations. Suchtraditional tonicizations do not weaken the influenceof tonic, but rather enrich and enlarge the tonic area before the tonic What
of
much
happened
actually
key is confirmed
here?
tonicization,
remote-key
by
a cadence.
effect. The first movement of the progressionsproducejust the opposite the in same that a written 70 Eb-major piece begins years before (in the early way have Classical period) might with a simple cadence-definedinitial After measure theme. begun; In this new 66, however, Eb -major is heard again, but this time as a pleasant and fresh sonority. is heard as a floating, independent sonority tonic without guise, Eb -major any old-fashioned secure music of (at least at the foreground level) stability. Here in this beautiful and tonally we can begin to sense a quiet revolution taking place. The concept of tonic as the Schubert, functional center of tonality is being questioned. Ex. 4:16a containsa schematicdiagram of the same modulatory technique used by Schubert in the first movement of Symphony No. 4 (measures 85-105).
Schubert's circular Trio
Piano
Example 4:16a-b At
a)
At:
d|,=c|
t
s
[I
ivl
E
a
C
f
Al>
:
:
:
;
:
;
i
I
I
;
iv]
[I
At: Tr [vi
225
T I]
contains a schematicdiagram of the harmony changes in the developmentsection in C-major, movement of Schubert's String Quintet op. 163, (measures 228-251). Herethe circle of fifths becomes traversed one-and-a-halftimes,starting on a B-major triad and chord on the G-seventh that leads into the (fermata) ending recapitulation section.The major its parallel-minor tonic triad becomes altered to form chord five times within Ex. 4:17. This a motion in each downward the circle of fifths within of (direction flats) produces large three-step T to t requires the addition of 3 flats). from The actual key changes tonal area shown (moving the in D-major). take placein relatively small within t inB-minor=Tr steps circle, however(e.g., Ex. 4:17
from
the
first
4:17
Example 6
B:
T
S D4
7 5 3
T
t
7
[I
IV V* 3 I
i]
6 D:
Tr
S D4
7 5 3
T
t
3 i
i
D t
7
[vi
iv
v5
v
F:
i ]
Tr D
T
At
t
enharmonically T vi
V At
I
notated
i 1
Tr
D T
t
[vi
V
i]
I
to G t
E: Dr T [iii
I
t
D
t
i
V
i]
C: Tg [iii
section ofthe first
D7
V7]
to Schubert's Piano Quintet in A-major, op. which onintermediate enter Trout], planes stepsasthe harmony makes a large single descent around the circleof fifths. At the end of the expositionthe key is at the beginning of the development but section the key is changed to C-major(the E-major, minor in E-major). At this point we will list only the key planes, counter-relative of the parallel their beginning measure numbers and the number of flats or sharps in their key signatures their in the circle of In measure fifths). respective positions 147, C-major (Ob); (indicating measure 161,C-minor measure this last plane is of longer (3b); 164, Eb-major (3b). Note that
The development
114[The
contains
movement
short melodic
226
away from the tonic pitch of the entire (4b),measure 193, Q>-major(7b),but as B-major (5#). Measure 196,E-minor notated (1#); measure 197, C-major (0#); enharmonically notated as C# -major measure199,F-minor (4b); Measure 200, Db -major (5b), but enharmonically in (7#). Measure202,F# -minor (3#); and measure 203, A-major (3#). The recapitulation begins in the the measure 210 in the subdominant key ofD-major. Schubertoften begins recapitulation subdominant sothat the tonic will not be worn out with use through the entire section. The tonic often appears only with the restatement of the second theme in the recapitulation section. than
duration
the
and its
others
work. Measurel85,
F-minor
The
Cadences:
Deceptive
contains an unusually
tonic note
attractive
is a
189,
(4b);measure
first movement
tritone
Ab-major
of The Trmit
cadence
deceptive
created
104-110)
(measures
Quintet by
third
relationships
also
(see Ex. 4:18). in the piano part
The ascendingpassage A-B-B#-C# in the cello is presented in longernote values andis shortenedtoA-B-B# (the B# is enharmonically spelled as C,here).The sudden pianissimo underscores the unexpected character of this resolution. The modulation from this spot backto in the progression (the dominant) E-major employs the German-sixthchord(C-E-G-A#) '6*^ D5 3 [Gr6-V$3].
Example
4:18
M \302\243
PW
2
=
t if
irv-w
pp m
4\302\261
\302\243
m
pp
^
_J^
2. Leading-ToneRelationships have
We
already
developmentsections.
works,
not
in
discussed there
Though all
of them
Beethoven's
key area,but
the process ofleading-tonemodulation are many examples of such leading-tone
are intended to act as agentsof modulation. and recapitulation sections,where they
exposition to
enrich
it.
227
in Beethoven's
in his late relationships are These devices also found do not
function
to abandon
a
At
the
beginning
No. 2, the main a grand
pause,
these
consider
the F-major
its
theme
way
Notice
of the
beginning
movement to Beethoven'sStringQuartet broken-off
with
this same melodic/harmonicfigure two
motific
seem
the
progression
is repeated,
to
in E-minor; op. 59, Ex. 4:19. After [i-V6]-see t-D3 a half-step higher. We should not from t [i] to sG [b II], since motion
of a largeharmonic progress further as a representativeof
as part
variants
chord doesnot
to tonic
oftonic.
of the first is abruptly
subdominant
(A) on
the F-major chord appearsto enter as a chromatic embellishment this leading-tone chromaticism is continued logically on to F# at the entrance (after the next grand pause).
(E). Rather, how
viola
Example4:19
In
the
first
movement
of Beethoven's
String Quartet in F-minor,
op.
95 [Quartette
Serioso],
the celloentersinmeasure5(againafter a grand pause) with the theme a half-step in the higher extension of the theme enters, once again backin the key of Gb-major. In measure18,a third tonic references both the original tonic key and its (see Ex. 4:20). This passage key of F-minor Gb -major variant. As we observedin Ex.4:19, Ex.4:20shows leading-tone both into and motion raised thematic motive. away from the chromatically
Example 4:20
This
same
kind
of chromatic
process emergesa number
a unison A-major example(measures38-41), major is then abandonedby an additional
scale
of times
Example4:21
228
the movement.For
from the precedingAb [enh. motion D-Eb (see Ex.4:21).
emerges
leading-tone
later in
G#].
A-
In minor)
the
movement to Beethoven'sSymphony a short time (see Ex. 4:22).
of the first
recapitulation
to Eb-major for
is raised
area
tonic (D-
aunison passage (seeEx.4:23).
to tonic through
returns
9, the
4:22
Example
Afewmeasureslater, the Eb-major
No.
Example4:23
f^T^P 3.
At this point, we will take another our discussion of third relationships.
Transformation
Chromatic
Note-for-Note
look at
several ofthe Schubertworks
covered
earlier
in
of Schubert's PianoTrio in Eb -major, Ex. 4:24 shows another excerptfrom the first movement Inthis passagewe find a strong dominant-tonic cadence in the key op. 100 (measures 106-112). of Gb -major, followed by a chromatic alteration of the tonic chord (chromatically raised root) not function diminished triad. This alteredsonority does like the which creates a root-position of the root of the traditional chromatic chord (see Ex. 4:25), but instead the alteration passing chromatic alteration in the following chord tonic chordinitiates a further (the fifth of the Gb-major tonic chord is also raised). chromatic The constant element in this unpredictable two-step transformation is the pitch Bb,which functions both as the third of the Gb-major triad and the third of the G-minor triad. Example
4:24
*
m
*
Pf^ qfz
tfz
cresc.
i
s
sfz
rfz
&-
~^
Gk
T
[I
Ek
v!
Tg
[iii 229
5
I]
4:25
Example
Another excerpt
is found
from
Piano
Schubert's
Trio, op.
100 (final movement, measures 666-679) from the main theme passes through an
derived Here, a simple melody transformation. Also of interest,is the fact that the harmony seems to C, the sixth scalechange from t to D3 [i to V6] in the \"wrong place\" (the weakbeat of the measure). third of the minor-subdominant), becomesunexpectedlyharmonized (the by degreein E-minor a chromatic descent to Eb in the bass. Once again, the third of the tonic chord (G) becomes the if its axis of a tonal shift. The melody, in E-minor, does not appear so straightforward, isconsidered. In measure of local tonic chord was to E \\. the root the raised (Eb) 661, preparation is first established. The excerpt in Ex.4:26 At that point, the unexpected tonal area of E-minor to Eb-major.) shows the unexpected chromatic return from E-minor only in
unexpected
Ex.
4:26.
chromatic
4:26
Example
| jjjji
i
m
e:
t
J- j-
i
Ex. 4:27
shows a harmonic
Quintet in C-major,
i
\342\226\240>\342\200\242
JjJPT-uT'r-i'r-
J-n
J-1
t
D3
V6
[i
String
J,i.
reduction
i ]
of a
passage in the
second movement
in
Schubert's
op. 163(measures47-8).
Example
4:27
^ Piano
8
h
\302\253\302\247
Ex. 4:28 containsa harmonic reduction of a passage in the Quintet in A-major, op. 114(measures80-84).
Example4:28
I h K
us
230
i
\302\273\302\247
secondmovement
of Schubert's
The beginning ofthe famous
well worth studying in Ex. 4:29).
is also extract
Glen\" scene in Carl Maria von Weber's of this kind of harmonic transformation
Der Freischiitz
\"Wolfs
in terms
(see
harmonic
Example 4:29
in this chapter were all discussedin their respective musical of chords related by thirds cannot be abstracted into because the employment rules of the dominant-seventh (like, for example, the resolution simple chord, whose resolution remains basically the sameacrossall composers and time periods in tonal music). The best of passages containing chordsrelatedby third case to case. analysis may be quite different from The statement, \"one applies a dominant-tonic but one invents a third relationship, does to compose not mean that we should attempt relationship,\" complete pieces in the style of Schubert. the following assignments may provide extra practice in mastering the Nevertheless, remote we have studied in this chapter. key relationships Because the circle of fifths can be so quickly traversed by these modulatory processes, it is that of the progressions we to become more aware that are taking learn important consciously The in and exercises place. following ear-training may provide practice understanding and help third
The
relationships
This is
contexts.
hearing theseprogressions.
PracticeExercises:
Invent
keys(for
from
example,
of sonority (e.g., T-t = 3
progressions such as D-T by
1.) At around at
the
the
following
circle
goal
by a
the
plan like After
of steps
of fifths,
the circle offifths
If necessary, [iii-I], or combine
you
between remote
modulations
circle-of-fifths
also
may
with
(for
each
use one-step
change
circle
large-step and small-stepcircle
procedures:
the direction of your goal key with large-step progressions to the goal key, checkto see if it is possible to arrive get closer
move in you
large-
and
several
upward
small-step
from D backto
4+1+3+3+1\342\200\224the
inventing
around
4 steps).
or Dr-T
one- or two-step circleprogression
circle
this:
these
of fifths. As
2.) Plan a strategy of around
[V-I]
harmonic progressions
of B and Eb)or invent
steps,T-s=
beginning,
the
modulating
C) that j ump a largenumber
C to
progressions
the keys
between
example
own
your
solution
progressions
D again,
or downward.
circle progressions. The descending distance is twelve steps. Traversethe circlewith a step-
plan is shown in by the methods above,
to this
231
Ex. 4:30. play
them
at the
keyboard.
Example 4:30 D:
T
[I E\\,:
1
3
13
4
s
iv]
T
Dr
' t
I
[iii
i] Tr
T
t
[vi
I
i]
Gt/F\302\273:
D: Dr Tr S D [iii
vi
IV
V
T
I ]
the and Ear-training: Without help of an instrument, read through try to imagine the harmonic changesthat occur in the musical examples and harmonic reductions given in this If not, play them at the chapter. Can you follow these harmonic progressions in your head? harmonic the same to the keyboard and listen carefully changes. Try thinking through in but sonorities from the on different those shown modulatory patterns, begin examples. on your listening skills. Always concentrate check Actively your mental imaging of the sounds each progression at the keyboard. Certainly, the most difficult of the modulatory by playing to hear are the chromatic transformations. I admit that progressions processes note-by-note such as those in Ex. 4:31aredifficult for me to hear and that it is necessaryfor me to practice
diligently in order to improve
my
skill-level.
Example
4:31
1 t* ft such as thosein Ex.4:31,1 recommend
^ In
order
to practice
progressions
the
exercise
in Ex.
4:32.
Example 4:32
best method of discovering and understanding should not limit to the works complicated modulatory your analytical inquiry processes, cited in this chapter. Theseexamplesareonly models of the kinds of modulatory processeswhich in many works. occur A
constant
habit
of score study
is the
but you
232
CHAPTER FIVE
Harmony between1830
and
1850
(Schumann)
1. Introduction
It was in
only
the
repeat performancesof
second successful
quarter works,
of nineteenth century that it that the concept ofa \"repertoire\"
aware citizens createda
into being, and that a group of artistically criticism (based on abalancebetweentraditional
public
of
this
period
was well-acquainted
come to know the great works of masterworksbecamethe standard This
artistic
only was it of
Beethoven,
J.S. against
became
practices the
with
It
Bach. which
and
creative
came music
innovation).
The artistic
soon Classical period and would was also during this time that traditional all contemporary compositions were judged.
works
of the
put the nineteenth-century composerin a completely to write music that was intelligibleto a public that important but most of all, it was important to become original. climate
literature of modern
music school
to hold
customary
new
situation.
had learned
Not
the style
For these reasons,the enrichedexpressive materials of the new Romantic style did not the elements them. In harmony, of older formal structures, but rather supplemented replace basic cadence continued to define specifictonalities, even these formulas formulas, though in earlier the risk used ran of worn-outand trite. In orderto already heavily works, becoming to these add a cultivated sense of embellishment and charm harmonic patterns, standard that were either slightly nineteenth-century composersdeveloped progressions disguised traditional or from \"tried and true\" This clever older formulas. progressions digressions to not a but new musical also resulted in approach harmony only produced completely style, severalnew ways of connecting Since the music of Robert sonorities. Schumann contains so of the we harmonic innovation within bounds of traditional many examples (although practice), of some will devote this chapter to a discussion of his more important contributions. Schumann was an incomparable to interpreter of poetry, and had an uncanny ability of the poetic texts he adopted for his art songs. various musically clarify and intensify aspects Schumann's songs often exhibita highly to harmony, but first we will consider creative approach his use of more standard harmonic processes. in Ex. 5:1, the traditional cadence seemsto celebrate its own In spots like the one shown deine nature. No.4 from the Dichterliebe \"Wenn ich in [Poet's Love], imperishable song cycle I Look into Your Eyes] begins simply in major with the alternation ofthe voice Augen seh' [When and the piano part. Only in the settingof the fourth line of text (Ex. 5:1),do the voice and part inthe subdominant key with a progression piano parts cometogether. Here,the phrasecadences that had been usedby composers for over a hundred years.
233
Example5:1
ri\342\200\224b
So
=\302\261
a werd
m und
ich
ganz
gar
T
ge-
sund
S^
in Ex. 5:1, \"So werd ich ganz und gar gesund,\"literally means \"therefore will Ibe or sound and Here word is the harmonized mind].\" (sound [in body gesund healthy) completely is also employedto express This same traditional construction by the old and reliablecadence. and purity in No. 3 fromDichterliebe, die Reine, die Eine\" \"die the [the delicate, Feine, simplicity The
pure, the
text
only
Sinn and to express loveliness and kindnessin thetext \"heller und soul and strong courage]from No. 2 of Frauenliebe und -Leben [Women's
(loved-one)],
fester Muth\" [hardy
Loveand Life]. not even use and clear under
does
Schumann
is simple
harmony
uralter Melodei'n[Ancient harmony
in Schumann
the Beloved Wandersmann
can be
Melodies] found
in das
Once Sang] (Dichterliebe, [The Happy
experimental materials when
the text \"aus
alten
Mdrchen\"
he
sets
[from old
fairy-tale
texts.
The
tales]
in the
song
fairy
No. 15). Other examplesof traditional das einst die Liebstesang[The Little Song that 10), and from the Eichendorf song, der frohe
(Dichterliebe,
Liedchen No.
Wanderer], where the lark sings\"aus
vollerKehl
undfrischerBrust\"
breast]. lusty throat and vigorous The fact that Schumann employssuch traditional ssions makes the entry ofunusual progre harmonies all the more conspicuous. Before we lookat several spotswhich contain these nonsense of the dramatic. Schumann's traditional techniques, however,we will discuss Schumann often two different musical styles when he setstexts that are spoken employs as opposed to the birdsin der frohe the singer, by different poetic characters (for example, wanders \"im Garten herum\" No. 12). Though the singer(seeEx.5:2) Wandersmann; Dichterliebe, \"Das Flusternend die Blumen\" [around the garden] in the key of Bb -major, [the sprechen of Onthe of the is the between seta in flowers] key Cb-major. whispering half-step higher way to Bb the two key areas, the root of the Bb triad becomes the leading tone in Cb. At the return the aber\" of where text \"ich there is an shift root tones [but I] enters, major, abrupt half-step on C. between a dominant-seventh on B and constructed another
[out of a
234
Example5:2
jua
i* j~n -
flu
*k=*\302\261
sters und spre - chen die
ich
Blu
aber
wan
-die
A-
S
a
T
T
Btc
D'
[I
V/v Ct/B:
This abrupt
the flowers 5:3,the Bb
T7
[V7
I?
V7]
change of harmony
at the point of the shift in voice between the narrator and more clearly before the next speechof the flowers. As is shown in Ex. triad becomes a dominant-seventhchordin third inversion with a raised
even
appears -major
D7
tonic
is not the third of the Eb-major however, goal pitch ofthis sonority, rather turns out to be G the root ofa G-major triad. In this spot, the oldtonic pitch functions like a leading-tone(enh.A#) to the third (Btj) of the G-major triad. fifth
[V+2]. The
(D^)
(G), but
Example i.\302\253 Jim
S
(Bb)
5:3 Jlfc
we could interpret Schumann'ssettingof the line, \"Sei unsrer Schwesternicht btise, blasser Mann\" [Don't be mean to our sister, you sad, pale man] as an act of
Perhaps du
triad
trauriger,
In Schumann's consolation; thus, a suddenmodulation. song, it is just possiblethat from the flowers does help the man to change his mind, if we considerthe The return to Bb -major is not abrupt, but rather follows a well conceived piano epilogue. plan: is altered to G-minor; G-minor becomesTr [vi], and Bb-major itself is directly G-major
unexpected the
encouragement
approached
by
a
D [Gr6-V]
'\302\251^
progression.
Schumann also creativelyhandlesthe changeof poetic voice in his song on Heine's text, Ich wandelte unterdenBaumen who wanders [I wander under the trees], op.23;No. 3. The narrator, alone in his sorrow, in forms of dominantand various sings G-major, accompanied by tonic seventh while the birds sing in Eb -major and are harmonized exclusively by T [I] and harmony, here are the phrases which Ss [ib].Also conspicuous end on false tonic chords (T,) [K ], which 235
are neither inversion
approached nor
left
voice-leading rules. The secondwhich is certainly inspiredby the
to traditional
according
produces a hovering,
tonic chord
sound,
suspended
Hoh\" [birds high The speech of the birds is completely up in the air]. the after defensive of the singer. As is [be quiet] here, unexpected especially \"Schweigt still\" in Ex. 5:4, an unprecedented harmonic shown ninth (Eb) of the D? technique appears\342\200\224the dominant-ninth becomes the new tonic pitch after the fermata chord (more about sonorities \"Voglein
in luftiger
later).
Example
The ears of
5:4
rustle and the earth silently kisses the wave, the woods lightly The tender scene is [Moonlit setting of Eichendorfs Mondnacht Night]. full of ecstasy, especially in the line, \"es war als hatt\" [it was as it had been].An interesting, free vocal style is suggestedhere(especially if the singer pays close attention to the metrically of traditional harmony is that chordsshould changeon piano part). One of the main principles or beat portions within the meter. If Schumann had followedthis rule, the transition strongbeats to the second line of the text in Mondnacht have looked something like that shown in Ex. might heavens
gently
grain
in Schumann's
5:5. 5:5
Example
ttu^-in
i
Him
ife
w
die
mel
^
i Er-de
\302\253E
**
f
t_^J
f
The strong syllable \"Er-\" (from the word, Erde [earth]) falls on the downbeat of the third measure in Ex. 5:5. To see how Schumann actually set this passage in Mondnacht, see Ex. 5:6. Notice that the tonicchordis already a rest in the introduced by the piano on a weak beatduring vocal part. This allows the singer to enter gently without a strong metrical accent. creating
236
Example 5:6
ft mel
Him
ISSi si
\302\243
In similar fashion, the initial by the piano in entry of the voicemMondnachtis prepared such a way that the music literally glides into the singer'sopening The pitch. pitch Bb is hardly noticedwhen it is added to the ongoing Ab (in measure two of Ex. 5:7),but it functions to prepare the singer's first note. An enraptured, harmonic also dream-like progression appears in this chord become and the ninth of an dominant-ninth octave Ab (D?) [V] spot\342\200\224the newly as the seventh and octave of a Bb dominant-seventh (D7) [V7]. interpreted 5:7
Example
7
7
|iE
^^
It is interestingthat
those
expression are coupled with of suffering that challenges \"von
wildem
s\" DS s
I i].
A
harmonic texts
that
of provide impetus for intensification the most dramatic.Itis not the outcry highly-expressive harmonies. The line,
materials which are not necessarily
Schumannto
find
exotic
and
stressful pain] from whole new world of sound opensup,
Schmerzensdrang\"
t [N5 Vt
Chord Progressions
Dominant-Seventh
2. Non-Functional
als
war
Es
[of wild
Dichterliebe, however,
No. 10 when
requires
only
the text turns
to
introspective sentimentslike\"b leichundherzeblutened\"bpaleaiidhea.rthroken];''vonderFreude weggekehret\" [turning away from all joy]; or when hapless fortune enters the text, asin theline \"du to the death and any solace is meine Welt\" [you, my world], where beauty is wounded C hamisso's text from Was ich unreachable. Schumann's soil sagen? [What should I say?] song is wounded, ist wund, du bistsojung und bistsogesund\" [my heart op.27;No.3,reads\"MeinHerz 237
takes and creates hold of the words \"sojung\" young, strong and happy]. Schumann to taunt the heart-broken singer (see Ex.5:8).Immediately of rapture-filledharmony after the A-major triad, an F dominant-seventh chord appears,followed by a B dominantseventh. All three of these sonorities are connected by the common tone A, which is first the root in the then as the sensitive as stable of the octave presented A-major chord, doubling as the seventh of the B-seventh chord. third of the F-seventh, and finally but
you
are so
a moment
5:8
Example
5=5
i
Herz ist
du
wund,
^
P^tt
bist
so
jung
\342\226\240 \302\245\342\200\242\342\200\224\342\200\242
iSr
t=t
ni
twice in the entire song. All of the harmony, tonic chord is only employed is to tonic tonicization of other scale degreesin D-major. related however, clearly Only through If we take the trouble to define the functional the passage cited in Ex. 5:8is functionally unclear. relationships between these chords,we must also explain why these same chordsdo not sound altered It is conceivablethat F-A-C-D# (if F is interpreted as an chromatically closely related. then sound as dominant. Instead a F#) could resolve [as a Gr6] to E -major, but E-major would the two chords chord of E) follows,making any relationship between (the dominant B-major The
D-major
imperceptible. In his song on Heine's Schumann seems to invent insecurity.However,
the
Wild Sailor], Wait, \"Warte, warie, wilder Schiffmann\" [Wait, tonal of dominant-seventh chords to produce the effect some (see Ex. 5:9). common tones in this progression tend to soften text,
a progression
Example5:9 mich
sahst
bleich
-m
-a-
und
her
P^ blu
tend
\342\226\240 \342\200\242 \342\200\242 m j\342\200\224mw
\342\226\240m m\342\200\224r-T \342\226\240= -minor). (D?)is omitted (formingaB7), and the deceptive sonority (tg5)ismade minor Ex. 5:23,
gethan\"
anexcerptfromFrauenliebe now given me my first
[You have
Example Schumann-.FraMenZ\302\243e&e
5:23 and
Leben,
No. 8
.,6 V4 246
5
.
3]
of the two diminished-seventh Because ofthe parallel construction progressions in Ex. 5:23, is actually that the omitted root at the beginning of the third measure conceivable that I that we the mind when this is heard. For listener's reason, by passage suggest supplied labelthis chord as an abridged dominant-ninth chord (E>?) in G-minor. F# on the downbeatof measure Since the voice part presents 3, it is possible that the right with F# rather than the enharmonicGb. hand of the piano in this passage shouldalsobenotated the piano notation to be correct, since the diminished-seventh we will consider Nevertheless, chord as chord(A-C-Eb -Gb) actually tonicizes Bb -minor. Ifwe considerthis diminished-seventh can it as no an abridged a dominant-function longer regard sonority (Ef) in Bb-minor, we since no implication of the omitted root of the ninth chord (F) is possiblehere. dominant-ninth, F is strongly In of the chord are initially of the fact that the third and fifth withheld, spite
it
seems
a cadential six-four figure as dominant in Bb. through F in the soprano and bass form the outer-voice In measure5 (Ex.5:23),the held-over which resolves to an F-minor framing pitches of a secondary diminished-seventhchord (t\302\256)V) of B-minor) at the same time, like a deceptivecadence(out or a triad. This resolution sounds, double-suspension figure leading to the F-minor tonic (B-C and D-C). Sincethe voice part ends cadence seems to make more sense.Inthis its phrase on the pitch B,the deceptive interpretation F# in it simply functions as a dominant t he the is voice (measure3) case, absolutely correct; part the half-cadence for the singer, but Gb in the piano is no less correct, when we consider the
established
through Bb-minor. our basic out such analytical Working complexities certainly doesnot destroy to of functional but when we try to apply the labeling tools offunctional harmony understanding principles, one conflicting to proceed along more than path at compositional spots like these, it is necessary the sametime. The problem that all sonorities in is that the functional theorist strives to show approaching
resolution
to F-minor
such a pieceare goal-directed; fashion toward certain other
that chords,
is, that whereas
composers
of goal-orientedharmony. to overtly attempting exploreprogressivepossibilities to free
striving
chords
particular
themselves
will
such as These
move
in some
Romantic-era
of functionless
predictable
Schumann were obviously composers
sonorities
in a
were
tonic-free
space. of producing several conflicting analyses ofa passagealsoindicates task are there are that In this way, a listener can chart chords actually unpredictable. time in each step the harmonic ahead of process. Ex. 5:24 contains a further unpredictable resolution of the diminished-seventh
how
The
out
and
many
know
chord (E)T).
of three The first diminished-seventhchord in this excerptprogresses onward by means and one common tone. The seconddiminishedfigures) ascending half-steps (leading-tone one descending wholeseventh chord progresses ahead by means of two ascending half-steps, tone. The functional chord step and one common analysis of the seconddiminished-seventh as an Ab that the the G# enharmonic of [so primary requires pitch leading-tone thinking resolve will be B-C rather than G#-A]. Like Schumann, composers frequently many relationship of smooth voicebecause diminished-seventh chordsto D4 (instead of the root positiondominant)
247
of the D5 do not seem to be bothered by instability they leading considerations.Furthermore, is also resolved in a non-traditional manner chord by sonority. Note that the dominant-seventh a common tone (pedal-point) and means of two ascending half-steps, one ascending whole-step in the bass.
Example5:24 Variations
Schuxaana-Abegg
^ i
^H~lU
m
f
F:
(Ef)
Nvi
(finale)
f if
(Sr)
lg>v
vj]
2
-dom. ped~
and remain on tonic harmony. The horns and 5:25, the low strings, flutes trumpet notes (D# [enharmonically spelled as Eb ] and F#) to the pitches E and G. real change in harmonic function is produced by the melody-line, which is carriedby and the second violins.
In Ex. violas
play
The
only
the
winds
auxiliary
Example 5:25 Schumann-Symphony
3 (Mvt.
No.
-n-j
ppm
II; measures 108-110)
n-i
\302\261J2
\302\243
mm
^=^
sfest
m
m Hms..vkJ
=
\\&
to
\"n
=*
W
that are at the heart chords (transposed by half-step) texture and what came before. the contrast betweenthis harmonic solo is very clever (see Ex. 6:22). In both of the second prisoner's the underlying the prisoner recites ononepitch until diminished-seventh the point line where the chord changes, the melody drops a half-step.
diminished-seventh
four
here, but rather
Beethoven'sharmonization phrases of this melody, chord is changed. At
Example 6:22 be -
rr
lauscht
mit Ohr
Blick
PT
Pr
[we are being oveiiieard
und
and
wir
mt
sind be - lauscht mit
LPT
Ohr
pif
und
Blick
Pr
watched.]
scene The trombones are used in only two scenes in Mozart's Don Giovanni\342\200\224 the cemetery II Commendatore (Act II, recitative after No. 21c) and in the banquet-scene finale 24). (No. as the executor of judgement, respectively. and appears in both spots, as the speakingstatue Theseexcerptsfrom Don Giovanni employ a number of highly expressive diminished-seventh a As is shown in Ex. 6:23, Mozart uses chords, whose resolutions are not predictable. and Classicaland model that is found in works. compositional again Romantic-period again This model consists of a chromatically harmonized bass-line by a repeated three-chord ascending of a diminished-seventh chord, a second-inversionminor triad and a dominantfigure consisting seventh chord.Although the the tonal center is impossible to definein this repeatedprogression, the are all located basic that once has in the same pattern begun, the pitches register.Notice starting
sonority
this progression
is reached again after the progression moves can beenteredor abandoned at any point.
265
through
twelve
chords.
Naturally,
Example 6:23
fc M t
^JzJ$M^&
y\302\273
^
In the secondact
ufLfe\302\243
1^
Giovanni, Mozart succeeds in characterizing the other-worldly even better than make-up,costumeand lighting. At first, the singing of the ghostly II Commendatoreis rather peaceful on one pitch, supported by (a recitation in the at the where II Commendatore makes his finale, changing harmony). However, point counter-invitation to Don Giovanni (see Ex. 6:24),the chromatic and terrifying slowly rising harmonized. The voice part here is not just the melody, but it also voice part is not traditionally as the bass-line at the same time?). Simply put, the functions of the harmonicprogression (both orchestra bass and the voice part move in parallel octaveswith each other. nature
of Don
of II Commendatore
6:24
Example
m Tu
m'in - vi - ta
-
[You invited
sti a
ce
me lo dinner.]
*=* WB
im
kP
^\342\200\224P I ^P
$mwmm
P
T\342\200\2241~
m il
tuo
do - ver
[youare
wa
aware of
m
sa
or
your obligation,]
13 ^mMtt^
igj
266
Example 6:24cont. feS\342\200\224 -
spon
[answer
11J
di
- mi,
Occasionally
Isis
und
m$
di
-
mi,
me,]
*#
i
-\302\273 -\302\273\342\200\242 ^ !>*\342\200\242
*
in operatic arias, the bass voicewill double the upper instruments.Ex.6:25 contains from Mozart's The MagicFlute, where such
line to
Osiris\"
-
spon [answer
#*
melody
-
ri
me,]
frHH
the
&3^
i
iJ
the orchestra an
bass and clearlyleave from Sarastro's
excerpt
a technique
aria
\"O
is employed.
Example 6:25
t~^t
*
stark
mit
Ge
zd
^\342\200\224m\342\200\224
- duld.
sie
[strengthen
very different does not really
It is
with
the
excerpt
Ge
them with patience
-
fahr
in danger]
6:24. Sincethe tessitura of line. Further, there is no real
in Ex.
part is so melodic material shifts as II harmony the
as the bass the (as was the case in Ex. Only Commendatore sings. As it is in the Chinese fable of the spirits, where the vixens in Ex. 6:24, without have no shadow, the very soullessness of the sounds they high,
it
supplied
by
bottom or any
function
6:25).
orchestra
the
earthly
weight,
musically
represent
the other-worldlyexistenceof
voice
recognizethat a real
top and
II
Commendatore.
and sings the excerptin Ex.6:24a number and as the ear becomes of times, It actually materials, this material becomesmoreand more frightening. in seems to abandon the Classical Not until one-hundred style altogether. years later, the music are sonorities treated like this on a regular basis. In Ex.6:24, of Debussy, functional harmony sonorities is literally that do not between harmonic and melodic differentiate replaced by elements. colors which are bordered by the top and bottom Instead, we find only harmonic As
more
pitches
one plays
accustomed
of each
to the
sonority.
267
5. Resolution of Conflict
It is
that
obvious,
the
willfulness
of musically expressed by choices anchored in a specifickey. However, in scenes dealing with expression sonorities
are effortlesslyjuxtaposed,
a suspensionaccording
to traditional
of a
hero or the strength
of a powerful can be intruder and connections between chordsthat are not freedom from tonality can also be an important of agent or resolution of conflict. If tonally deliverance distant or if a voice part gently counteracts the tendency to resolve of resolution, then a door into another world is principles
sonorities
of death. threshold opened\342\200\224music In the final measures of Monteverdi's Combattimento, her. Notice that lover, sings ofthe eternal peacethat awaits on
two measures
the
of Ex. 6:26fails
to
wounded Clorinda, mortally 4-3 the suspensionfigure expressing her deliverance from
perhaps
resolve,
by her in the
last
earthly
existence.
6:26
Example
io
va
- do [I go in peace.]
w
w
m
Near
the
underground
end
tomb
of Verdi's with
her
Aida, we reachthe lover,
Radames.
scene
By 1870,
where
Aida
has
been
when this operawas
sealed in the composed,
the
between sonoritiessuchasthosefound in Ex. 6:27 were no longer consideredunusual. To measure the true impact of this spot,however, we must consider the \" preceding musicalmaterials.Justbefore we reach this excerpt, Radames sings Morir! Sipura \" e bella! (to die is so pure and beautiful!) and Aida begins her cantilena, \"Vedi?Di morte I'angelo.\" in see?: the of Both these are and are sections character (Do you angel death). folksong-like harmonized with simple and functional Classical-periodsonorities.Directly after this straightforward simplicity, its chromatic we hear the spot in Ex. 6:27with third-related triads. chromatic-third
relationships
268
Example 6:27 [Already
1 see
heaven revealed,
where every
sorrow ends.]
\342\226\2400\342\200\224*\342\200\224p\342\200\224* p
fe Gi4 veggo il
dor.
ciel di
-
w schiuder
- si
i - vi o-gni
af - fan -
no
ces - sa,
m
fern
m
\342\200\224}D^
>d\\>
m: ^
\342\226\240a-
OV
TR
B\\>:
[VT*
TG
[HI-*]
6. Dramatic
D: tR [III]
F:
tG
[l-VI]
Climax
Emotional climaxes,suchas the expressionof deep sorrow, entreaty, cursing or hate are are carefully spots planned out ahead of time by the opera librettist. Climax spaced and separated from one another in order to avoid an imbalance of strong emotion and to limit wear and tear on those musical materials that are used as agents of such expressions. Writing an effectiveoperatic climax has always been challenging to composers, and climax sections often a a the outer limits of to conventions. style period's push composer's creativity Two climax spots in Beethoven's Fidelioand two in Verdi's Ai'da employ similar harmonic demonstrate different approaches. Beethoven's completely materials, but the two composers whereas Verdi's parts are more singable.Theproblem voice tend to be highly parts expressive, that with Beethoven's they often nearly overstep approach is that his melodiesaresoexpressive the boundsof what is technically possible. Though Verdi's vocalstyle is eminently more singable, in danger of seeming emotionallyneutral. it is often somewhat anonymous in its beauty and in Beethoven's vocal lineslendthemselves well The technical encountered to difficulties At the beginning certain kinds of climax situations, however. of the second act of Fidelio, In this scene, uses the unaccompanied voice as a medium of strong Beethoven expression. with the Florestan is in jail. His monologue words welch \"Gott Dunkel hier\" begins [God, how it is here]. With his fate in the hands dark Florestan of God. As is sorrow, humbly places great in Ex. 6:28, Beethoven turns to a quasi-atonal texture in order to musically shown the represent features two D-tG [V-bVI] deep sorrow expressed here. The underlying harmony deceptive which are stated one after the other. This harmony becomes extraordinarily cadences, expressive,when we consider the simple harmonic texture that both precedes and follows it.
269
Example 6:28 [I will
not complain
m
^1
WW Teh
mur-re
amount of sorrow; I shall remain steadfast by Thee!]
of the
nicht
das
Lei
MaB der
^
fei
mmm
^w
fc\302\243
S
CftF
te-^jj
3Efc
T=T E:
tG
D
[V E?
^s
*
E;
^Cj steht
den
bei
D-
[V
dir!
-1\342\200\224
tG
V7
1>VI ]
Wiftm*
\302\243
\302\243
is quite different. Near the end of the second act in Aida, to on the have Amonsaro's F-major mercy prisoners. implores king the oblivious to level of harmonic seems melody, however, rising expressioninthe orchestra.The is of the melody derived primarily from the beauty of its melodicconstruction (see Ex. intensity Verdi's
Amonasro
handling
of climax
the Egyptian
6:29).
6:29
Example [But thou; o
Ma
tu,
Re,
tu
king, thou mighty lord]
si
-
gno - re
m^M f*^
^^
270
pos - sen -
m
te
The
orchestra
part,
however employs
style of this from an Fthese sonorities
and the
sonorities,
expressive
highly
and engaging. The harmony surprising, major triad, to an E-major triad and on to a Bb -dominant-seventh of tension below the tonally stable producea largeamount is both
accompaniment
passes
immediately
chord.
Indeed,
The melody pitch F-majormelody. the fifth of a but this F is heard as immediately F, Ab]. The overall harmonic progressionof the
movesdirectly to the octave dominant-seventhchord [G# is enharmonically When on T Ss T[I-Gr can be interpreted as a variation (on fourth scale degree)-I], however. excerpt has not the subdominant heard on the third beat of the second the SlTisfirst measure, pitch (Bb) F is the bass voice [the voicewith disregardedhere] pedal point yet been reachedbythe chromatic and the sonority'sthird (D) is also delayed by a suspended-fourth(E) in the next-highestvoice. voice resolves upward into beat four. The fifth (F) of the Srchord enters only as the top-most E (leading-tone)
4 5
Even
though
on beat
each voice ofthis sonority
three is that
ofa surprisingand
dissonant
E-major
six-four
6\302\273
s 6:33
Example
$
mi'i-Ji
Kt
T^WWW
272
>
-^
jf-V
i=\302\243
*
i\302\243
Jex;
:\302\243
43
*=?
^
^
measures
In
seventh
minor
which
dominant
the raisedroot Bb
-major
X
fes
S=
a
^
&
^
based on tonic (C) in measure 19. A 14-15, D*98 [V232]resolves to a sonority it into a secondary (Bb) is added to this chord of .resolution, however, turning In the following measure (20), does not resolve to its expectedtonic (F-major). of this
is substituted
chord leads toward D-minor, (22). AD-minor chordappearson
seventh
but the
instead,
downbeat
cadence to next measure (23),
a deceptive of the
The chromatic bass line (Fff) leads Gtoward functions as a passing sonority. rising the but a sixth is added to the chord on the downbeat of measure (E) minor, 24,thereby pulling two chords then anticipate D-minor evenmorestrongly harmony toward D-minor. Thefollowing
but
with
it only
the
progression
'S>v
D
[vii\302\2607/V-V].
279
of another to tonic in measure 27 is foiled, however, by means Bb -major chord is made In measure 28, the previous measure's a sixth is added above and again, the bass. This added-sixth sonority functions as S5 [ii 1] minor, in F-minor. The following diminished-seventh chord &l [viil] in F-minor becomesresolved, in D-major as the enharmonic^ were [vii\302\2602] instead, (the Db in theformeris resolvedasthoughit a C#). A seventh (Clj)is addedto the expected on chord the secondbeat of measure 29, D-major however. This dominant-seventh sonority functions as I?? [V/V] in C-major, and is followedin DS 3 [Vt i ]. The resolution ofthe second measures 30 and 32 by two cadential suspension-Figures Dt 3 isfollowed In measure cadence to an Ab-major triad (tG) [bVI] inmeasure33. by adeceptive The dominant the Ab, which changes the sonority to F-minor. below 34, however, a third is added chord in F-minor (measure 34, secondbeat) is, once again, made minor with an added sixth and becomes another s* [ii^s], but this time in G-minor. (measure 35, downbeat), The passagefrom measure 34 to 38 is actually a harmonic of the passage from sequence The
resolution
expected
deceptivecadenceto
Bb -major.
than C[rather unexpected resolution chordin measure38is D-minor in D-minor area is over measure the seven 31]. Though prolonged goal it is made unstable a belowthe in twice tonic measure third (Bb measures, by 39; G# in adding measure 40)and bythe changeto D-major the D-minor triad returns in measure 41. Even though in measure 42, it possesses in a little of its tonic character, sincethe F in the basstakes part chromatic descent. Another minor seventh (G)is added the dominant in above measure pitch (A) a dominant-seventh chord which then abandonsthe key of D by deceptively resolving 44,forming to a dominant-seventhchord [third in the key of E. inversion] with 4b, 3b, 2b, The and first act of Tristan andIsoldecontain introduction key signatures
measure 27 to major,
which
lb, 0b/#, is not measure
1#,
31,
but the
was
the
2#, 3#.
Though the
act beginsin D-minor
The one-flat key signature of recognizable. 1 to measure 65 ofthe third scene.Directly
and the
excerpt after
ends
a controllingtonality (Ex. 7:1)extendsfrom in Ex. 7:1,thereisa short key signature. In the next chord. This Db is then
in C-major,
we discussed the
excerpt
D-major, followed,in measure66,by a one-sharp Db is reached as the goal of an Ab dominant-seventh instant, however, chord... etc. as C#, the third ofa first-inversion enharmonically A-major reinterpreted Ex. 7:1 The cadence and modulatory in are not new. are contained They simply agents were used in development sections, between tonally stable Classical-period techniques which and recapitulations. In the case of Classical-period expositions opera, these devices are common in the recitatives or in the transitional within arias. materials between stableharmonic planes are still in force, the music of Wagner is conceived Though the details of Classical voice-leading in a large, centerless,and tonic-free in the tonal space. (This is the sametendency we observed music of Schumann!\342\200\224see Five.) Chapter and
clear
section in
Exercises:
actually reach cally related to
Check the
rest of
their tonic; b) a central tonic
the
cadences, (so that
Tristan und Isolde for: a) cadences which which deceptively resolve to tonalities that are diatonia broad tonic-area plane can beprolonged and solidified).
third
scene from
280
3. Setting
Ex.
7
from the secondactof girl).
an excerpt
:2 contains
of the flower
disappearance
the Text to Music scene directly
(the
Parsifal
the
following
Example 7:2
Dies
al - les
nannt' ich
Dich
Kundry:
hab' ich
ge - tr&umt?
nun
Rein-er,
tor'-ger
Rie-fest
\"Fal - - par - si\"
So
fal\".
>
r -
Soh
ne
7
melodies actually
in the
im
zu, dener,
to connect same tonal
^
^
Mut-ter schoB ver-schlos-sen,
mit die-sem
Na-men
ster-bend
^
grilfi-te.
rg^i^i^gp^
the words within area. Theconverse
When following
the
consider
orchestra
This marriage of the melodies
because
successful
This pitch
character
dein Va - ter Ga-mu-ret dem
ab'-schem Land er ver- shied,
text
his is also
phrases
by placing
true; changes
them together
of key center in
Wagner's
7:2,
more elusive.
connections
ar-
- si-
seem to be motivatedby changes from one text phrase to the next. InEx. Wagner of short melodic phrases (see joins his text phrases together in a patchwork key-unified
brackets).If we
the
in
J^fti^m
seems
Wagner
als
\"Par
M*tw
^fj^uxuQ-^^)jyi]
frynj!^
(melodically)
rief,
lo-sen?
Na-men
Dich, rein-en To - - ren:
|Jir^if;r
j^f--7!|jiP*C/^]!*'r
4
mich
du
then
tonal
part alone,
are constructed
however,cleartonal
to less tonally
melodies
from
pitches
that
for various
Wagner segments are not separated by rests, the new is often carefully introduced by a leading-tone figure. phrase and help maintain provide a convincing transition betweenkey areas
ambiguity
Wagner's
of the
short
provides melodic
with
melody.
281
room
much
are
implications
centered accompaniments is are harmonically ambiguous. harmonic interpretations. tonal
area
in
Leading-tone
the singable
are shown first words in the secondact of Parsifal Wagner's melodicsettingof Klingsor's motion (see arrows). 7:3. Here, five key areas are introduced by direct leading-tone
in Ex.
Example 7:3 DieZeit
Klingsor
ist
Schon
da.
- es-schla - fe
nr-^
In
order
to better
understand the
construction ofsuchmelodies, compose The
internally.
Wagner's
figures.
imitation\342\200\224a
Ex. 7:4showsa convincing
a far
less
convincing
Creatingyet another
the key implicationchanges
and
that
piece
in this
style
will
simply
employs
leading-tone
as Ex.
changes
and much
more
7:4, but
difficult
motion from
C-major
to
without
leading-tone
motion.
sing.
7:4
&
+-+**\342\226\240
^m
Example 7:5
4r
j'Lfir^
in
to Db-
singable.
Example
+
result
of effort!)
waste
fruitless
melody
major. The voicing here is smooth Ex. 7:5 implies the samekey melody is
in the
connections
leading-tone
lines where
with tonal centers should be accomplished and without the an exercise a of such must be considered (Remember: only study
compositional technique.
just one more Wagner
f^rr^N ._ - ->
^H
of
value
melodic
several
Werk!
between
transition
use of leading-tone
der
halt
Auf denn! Ans
16s-enweiB.
|tHHj^f
U
p
r
P^
der ich den Krampfzu
sie fest,
jauchz-end
r r
r ^ s^
\302\253
Exercises:
kind-isch
^
^ Fluch
Tod
Im
Tor-en, den
y I'T.^v
P^g
ich na - hen sen'.
fern
den
r
-^f-
*=
m
lockt mein Zau-ber-schloB
st^p 282
U
^F
This
4. Wagner's
now discuss
shall
We
will examine
two
excerpts
Free Four-Tone
Functionally
Sonorities
harmonic vocabulary in Wagner'slate works.To accomplish this we und Isolde (1865)and two from Parsifal from Tristan (1882).
Ex. 7:6 is an excerptfrom Tristan the atoning drink).
scene
the
five in
the first act of
und
Tristan
(Isolde hands
Isolde
7:6
Example Isolde: Eh
Dein
-
zu
ge-mahl
sein
So
.
gu
-
ter
Ga
-
den Dank
i
4
31\"\342\200\224In
w
9Sr
W
#
m
7:7 is
*%=5
|B~
$3
*J?iL---
\"Einsam
-
-
4
Ex.
hoi
I'f
r
tfJrElf
14
ben
an excerptfrom scenetwo in derNacht\" and
wachend
second act
in the
her \"Habet
Acht!
7:7
Example den?
en
Tristan:
Doch, *
5t\302\243
1
i
of Tristan undlsolde(between Brangane's Schon weicht dem Tag die Nacht\" ).
V
4
I
i \302\245
r _B_
a m
283
J-
nH
stiir
rl
be
nie
sei
- ne
Example 7:7 cont. Lie
-
be,
wie
-
stiir
T=fe'.
-
Tri
dan
be
I
w
sei
stan
ner
Lie-
h'J# *p-|r.
IV
r
-
sus.
|4
u
^
g^^S
Ex.
7:8
is an
^L
te
excerpt from the
beginning of
fe
act in
second
the
i
Parsifal (Kundiys
first
entrance).
Ach!
t
7:8
Example
Kundry:
] 7*
Ach!
Tie
-
fe
Nacht...
tp
E|=St
^TJ^-rff J \302\245
*
\302\243 3p
EL
^k
^
Oh!
Wahn-sinn...
pW
?^==^r
^
s:
\302\2478
ft
^
6
Jam-mer!
Ach!
Wut...
Schlaf...
Schlaf...
tj.?*
m
S^5
\302\243
SP
284
fe^
s
Schlaf..
>1iJ
IUi>1-lJ. w^^ sus.
w
tie - fer
sus. \302\243^S
4
J\302\273*
sus.
^^
1
I*
7:9
is also
Kundry:
Seh
Ex.
from Parsifal;
a few
later
measures
the excerpt in
than
Ex. 7:8.
Example7:9 )=\302\243=
Seh
nen...
j)
7
1
I
nen!
Ha - ha!
Klingsor:
WTl-m
%
dort
nach den keu-schen
ffTT=t>=^: Mi^
m
E ^^
S\302\273
JO^!
S3'ttJ-J
*
rr
r
^
r-liHli/fer^fEf
E J75
J^JT]
r
^g^
PFf Rit-tem?
Kundry:
r dient' ich
Da.
that occur in Exs. 7:6-9are marked consonant sonorities [major/minor triads] of relatively long duration is the (Konsonante Kldnge). The only consonance A-minor is employed first-inversion triad found in Ex. 7:7. Thistriadic sonority here to provide resolution stability for the dominant chord which occurs in the previous measure. Theother threeclearly defined consonances are maintained for the duration appear in Ex. 7:9,where they of only an eighth-note. In the measure 3 of Ex. 7:9, both consonances come about as a result of motion. These transitional consonances are treatedinthesamemanner that would have passing been traditionally reserved for passing dissonances.Only the consonance on the last triplet in measure 1 of Ex. 7:9 functions as the resolution of previous dissonance. eighth-note In a world of such highly unstable sonorities, the ear must revise its concept of the six-four chord. Exceptwhen employed manner (as in the penultimate of Ex. measure in a traditional as a relatively consonant sonority (see spotsmarked 7:8),' a second-inversiontriad is perceived
I. The few
with
the
in Ex.
[S3
1
Although
symbol K
7:8)
of Ex. 7:8, the
this second-inversion triad actually listener will often hear this sonority
fails to resolve in its traditional fashion as part of a standard cadence formula
285
in the
penultimate
at first.
measure
II. Wagner conspicuouslyavoids the dissonances (minor seconds and major strongest in the four-tone sonorities that have becomehallmark of his style. As is shown in Ex. are constructed structures from stacks ofthirds.Thesethirds will generally 7:10,theseharmonic be minor thirds, however.(Not more than one of the three intervals will be a major third). sevenths)
Example 7:10 sonority number will be used in examples:
The that
the music
12
3
4
S5 6
D7
[ii7]
[V7]
possible
harmonic functions:
=minor =i
l^v
s5
..\302\2737, [vii\302\2607]
r:;0?i [ii 7]
third
=major third
^
9 ^ 7
(7
[vii*7]
[i7]
7
[vii\302\2607]
rS7
s7
[vii07]
[iv7] Tr7
[vi7]
Every four
of these
chromatic
modification (.-') in
Ex. 7:10,leadsfrom
sonority types may also appearin inversion, assuming in this music. Which pitch in chord-groups1,2 and
one
chord that
group to the next. All the concept of inversion
3 actually functions as the root? the chordis notated which tone will serve as root decides usually [since this sonority type is symmetrically constructed from minor but thirds], frequently the chord root cannot be determined until the resolution sonority is reachedand the voice-leading In chord-groups 2 and 3 therecaneven be contradictory with regard analyzed. interpretations to what pitch functions as the root. In fact, three different could serve as the functional pitches in these groups (the pitch B asthe root root of the diminished-minor seventh chord in group 2, or the minor-seventh in group 3; D as the root chord of a si [ii*] in group 2 or Si [iil] in group root of an implied ninth chord in both groups 2 and 3). 3; or G, the omitted Thevoice-leading connections between these four sonority types are dominated by common tones and leading-tone relationships. The voice-leading between these sonorities, relationships charted in Ex. 7:7[seestaff below the example], are representative ofchordconnections that are that it to is generally found in Wagner's music. It shouldbe noted, however, impossible directly connect these sonorities without leading-tone motion. The two pitches inside the interval of a minor third can be reached by leading-tone from of and one the two outside pitches, relationship since these four sonority at most, only one major third, there is only one pitch (in types contain, the middle ofthat interval) that cannot be reached by leading-tonemotion from the two outside pitches. really
In group
applies
1 sonorities,
the way
286
I caution against putting too much faith in either of was strongly attracted to these four-tone and sonorities, his music because of this affinity, became characterized by leading-tone motion (since leadingtones are necessary to connect these sonorities desired to connect his b) Wagner together); with sonorities harmonies four-tone so he chose this of (because they leading-tones, group to connect one another means of smoothly leading-tones). by To
the
avoid
theories:
III.All
a) Wagner
sonorities in Ex. 7:10are borrowedfrom
of the
four
and Romantic
music,
functional
however,
oversimplification,
following
and The
harmony.
are (apart from the consonant changed role that these
of Classical vocabulary the most important carriers sonorities) music can be chords took on in Wagner's the
chord
11
fi
f\\
f\\
0f\\
1] way that they progress and resolve;that is, even whenD'[V'],S5[iii],S5[ii of the four or E) [vii ] resolve, they seldom really disappearfrom the texture. Furthermore, chord provides a definite resolution expectation sonority types, only the dominant-seventh to its tonic]. The resolutions ofthe three other sonorities are much more ambiguous. [resolution the dominant-seventh resolution of the chord has the most definite Although expectation uses its function as a foil for resolution. four often traditional sonority deceptive types, Wagner to summarize cadences are defined differently in various texts, so I will attempt the Deceptive to the
attributed
topic one more time in a systematic way. 1. In its most narrow a deceptive function cadence consists ofa dominant chord definition, or tG which progresses directly to a chord that as tonic substitute functions a (Tr [vi] [VI]). Further, the leading tone must move to tonic in the upper-most voice(seeEx.7:11a). 2.Another definition calls for the same functional progression as in definition 1., but voices to tonic in one of the three lower (see Ex. 7:11b). requires that the leading-tonemove
Example 7:lla-b
D7
G:
[V7
3. A
further
in definition
1.),
Tr
vi]
that
tG
D7
|,VI]
[V7
Tr
vi]
the
D7 [V7
the leading-toneto move chord of resolution may be any
is for
possibility but
D7 [V7
(seeEx. 7:12).
287
Tr
D7
tG
vi]
[V7
|,VI]
to tonic chord
in the that
upper-most voice
includes
the tonic
(as
pitch
Example7:12 most
also possible
frequent
A
ifi
1
*j
*## G:
D7
v(D
r
) sG 3
..07
[V7
IV\"
to tonic variation requires that the leading-tone moves while the harmonic progressionretainsthe samestipulations
4. This
voices,
in one as
of the
lower
three
3.
definition
presents the deceptivecadencein only the broadest sense. These would but no tonic pitch is presentin the chord where progress from the dominant,
5. This definition be
cadences
of resolution
that
(see Ex.
7:13).
Example 7:13
f
TV
(D^tRj
(E^> Sr3 .04 [V7
6. The that
the
of resolution
'11
(see
Sr3
V2/t.n
variation ofdefinition 5. at all, but actually Ex. 7:14).
most remote
leading-tone
r? D'
r
This type of deceptivecadence requires as a common tone in the chord
above.
not resolve
retained
be
Example 7:14
I
i.^4 D7
(D7)
VV. ]
[V7
chordsin definitions 4., although they may surprise the listener,they The resolution
that
provide
the
strongest
substitution
5., and are
for a
Tr
6. are not really substitutesfor
not true
final
288
cadence
the
tonic,
and
deceptive cadences. The progressions occur in definitions 1. and 3. (the
somewhatless convincing). It is musical context that really perceived, and it shouldnot be assumed that every D -T In fact, deceptive cadences can only be considered progressionis a closing gesture. truly deceptive if they are sparingly employed. In Wagner's late the transitory tonic had becomethe norm, and the established works, the In is one in there cadence standard Exs.7:6-9\342\200\224the tonic, exception. fact, only [relatively] D7 occurs in the second and third measures of Ex. 7:7. progression Here, the arrow (-\342\226\272) t3 [Vl-i6] a direct dominant-tonic indicates In there are five relationship. contrast, deceptive strong cadences in the excerpts from definitions 1. and 3. (see Exs.7:6and 7:9; the bent arrow [^> ]indicates that the dominant resolves to a strong tonic All other dominant-seventh resolutions substitute). in Exs. 7:6-9 employ the more broadlyinterpreteddeceptive in definitions 2., cadences (covered 4., 5.,and 6.). The so-called \"deceptive cadence\"(in all of its forms) appears so frequently in the music of that it is hardly deceptive any longer. Furthermore, the four-tone Wagner, sonority constructed from a major triad with an added minor seventh (Ex.7:10;chord-group carries a 4) only rarely true dominant function. For that reason, we should only refer to it as a dominant-seventhchord when it clearly functions in that manner. We must not assume that the later music of Wagner to the same ordered harmonic tradition that we have been studying. In fact, Wagner belongs often took great pains to avoid connectionsthat might his music in harmonically ground traditional key centers. What on the surface appears to be a stringof deceptive resolutions turns out to be an intentional of the avoidance traditional key implicationsassociatedwith functional the avoidance of tonic harmony in late Wagner Therefore, it is best to recognizethat harmony. is not the exception, but the norm. Personally (and here every reader must come to an actually I do not consider any of the resolutionscontainedin Exs.7:6-9to actually independentdecision), in definition
chord
resolution
decideshow
a chord
2. is
progression
will be
cadences.
be deceptive
use of
seventh chord, we will turn 2 of Ex. 7:6,a diminished-seventh chord is formed by half-step motion and then is abandoned motion in a different by half-step voice. A diminished-seventh chord (G#-B-D-F) is also implied in measure8 of Ex. 7:8. In a traditional resolution,the G# would move upward; both the D and F would move downward. D the resolves to the F remains a common tone Here, however, only traditionally (down C#),while andthe G# leads downward to Gl. In measure 10ofEx.7:8,theC# would normally resolve upward, and the Gand Bb downward. G moves Here, the C# resolves traditionally, while upward to G# Now
that
our attention
and the Bb
we have
to the
moves
discussed Wagner's
other four-tone
upward
the
major-minor
In measure
sonorities.
to BN.
When we analyze the progressions lead that 3 sonorities, away from the group 2 or group it can be observedthat the sonority are seldom treated as si [iil], types from these two groups
Si [iis], or E\302\2437[vii*7] chords. Instead, the tendency tones of these standard sonorities led astray. The chordin measure2 of Ex. 7:8 can either be consideredD-F-Ab-C Eb-major), or F-Ab-C-D (ss [iil] in C-major/minor). 289
are (if7
often in
[vii*7]
a further enharmonic spelling ofthis chord (E#-G#-Bmight be possibleto consider this sonority magic and attempt to analyze case, we couldconjure up some functional but do the mental gymnastics involved with in F#-major (Ef [vii\302\2607 ] with a raised fifth), producing a symbol like ^5< [vii \\ ] really this the function sonority? help clarify It also
D).
In this
IV. functional
In earlier properties.
music, these four Wagner,
however,
their
customary
voices no longer follow
pitchesof functional
these
are no
sonorities
sonority
types
resolution
maintained
always
employs them as totally
free
sonorities,
their respective where individual
Furthermore, the dissonant dominant or subdominant poles of
tendencies.
longer representative of
the
harmony.
Generally,
all four
dissonancesareapplied
of these
sonority
types
contain
mild
dissonances.
When stronger
ninths or minor seconds), (i.e., major sevenths, minor with a milder degree of dissonance. they always resolveto intervals and retardation Suspension figures are labeled [sus.]in Exs.7:6-9.In the first measure of Ex. 7:6,the minor ninth the bass part and the voice) is resolved when the Ab G-Ab (between to A^. The following B as a strong ascends continues to after \\ pitch (Bb) entering melody upward to these
sonorities
dissonance against the B4 in the accompaniment. the bass In the fourth measure of Ex. 7:6, the D# and F enteras strong dissonances against pitch E, and both resolve to E. In the five last measures of Ex. 7:8, there are a number of strong dissonances that occur in the top voice of the accompaniment. These dissonances either resolve downward (a major seventh to a minor seventh, or a major ninth ninth to a minor ninth), or upward (a minor to a or major seventh to an octave). major ninth, can still speak of these strongly dissonant suspensions ina traditional We even if the sense, the use of these figures resolution directionno longer abides by the customary rules. Although tends to confuse the underlying harmony, stepwise suspensionresolutionssuggesta traditional of voice le ading. Somewill argue asone that Wagner does not always lessenthe dissonance type that the chord since time of Bach such resolves into the next. Thiscan becountered by argument chord progressions have been employed of seventh chords around the circleof (e.g., sequences On one hand, we can admit that fifths). Wagner's stepwise suspension resolutions are actually of a very old tradition, and on the other, it is clear that these figures are not traditional part suspensions
at all.
V. In the secondmeasureof Ex. 7:6, E andBb (third and seventh of the C dominant-seventh tendencies. of chord) are not resolvedaccordingto their customary First, the most stablepitch the chord, the bass-note C, moves to in a suspension-like fashion Db. Following the this, away E moves to Eb on the last eighth-note of the measure,forming a dominant-seventh chord in third inversion Db is heard as the fundamental bass (Db -Eb -G-Bb). At this point, the dissonantpitch tone of a suspension by a large downward leap, while figure. The Db demonstrates its stability the three consonant tones to the next voices) progress by leading-tone relationships (upper
290
from the last measurein Ex.7:8,the root of the dominant-seventh chord In the first measure ofEx.7:7, F and G#, the G^in the middle between it appears of the bar) sounds likea passingtone,even voice to be the (last quarter-note though root of the G-major triad. It is not totally accurateto say that both consonant and dissonant pitchesof a chord are now Can determine which pitches are consonant are treated alike, however. we actually and which dissonant in such compositions? The previous between the root tone and added distinction like a consonant sonority with in this music. None ofthesechords acts added disappears pitches that is with these are fixed of resolution. Instead, chords characteristics dissonances; Wagnerian unified sonorities constructed from four entitled and treated which are equally equally pitches a no longer connected to root tone. sonority.
In
the
third
resolvesdownward
VI. Traditionally, and the
by step.
dominant-seventh chord eventually to the resolves to the third above the tonic. This createsthe stable of a third. The dissonant second interval of an Si [iif] by the sixth and the fifth produced will remain also resolves traditionally to the interval of a third, but one of the two pitches S5-D or [hi-D] common, while the other will move up or down by second (as in the progressions but they S5-D4 [iit-VS ]). Nearly all of the individual tones in these sonoritiesare active, do not clearly imply the goal of their resolutions. It is only after the resolution has taken place that we can know which pitch of a four-tone was actually intended to function as the leadingsonority with In and tone. cannot certainty Wagner's music,the voice-leading path always be predicted the resolution tendencies ofa sonority until it has progressed to the next cannot be confirmed hears such spots twice. At first, chord. The listener [groundedin traditional actually harmony] the standard function of these sonoritieswill suggest a particular forward resolution, but the that Wagner actually choosesforces to reinterpret (after the fact) the the listener resolutionpath harmonic function of the first chord. In other we cannot engage in an \"active words, synthesis\" of Wagner's music in the same way that we can while to Beethoven.2 listening With sequence figures, the situation As they did in earlier music, is completely changed. a in role In help the sequencesplay major actually Wagner's compositions. fact, sequences listener make sense out of the many complicated harmonic connections. (See the in the minor-third in Ex. 7:8 [compare measures3-4 with 5-6; 7-8], and the descending sequence at the beginning of Ex. 7:9.) descendingperfect-fifth sequence the
leading-tone
tonic pitch
seventh
2 This new der Sachische
listening aestheticis discussed Akademie der Wissenschaften,
resolves
of a
downward
in Heinrich Besseler, \"Das musikalische CIV (1959).
291
HOren der Neazeit,\"Abhandlungen
music with moments of harmonic Sequence figures actually provide Wagner's is also true for passages where a Leitmotif 'is repeated, providing that the repetitions use are not harmonized the a nd of differently. Wagner's sequence the Leitmotif actually returns that these revolutionary harmonic to the listener somesenseof musical predictability Taken connectionstake and the totally confusing, away. separately, Wagner's harmony may appear This predictability.
repetition ofa Leitmotif
may
seem
boring; the
intolerably
motific As
has
between
the
5. The
the
Tristan Chord
seven chapters in Ernst Kurth's extensiveworliRomantische Tristan [Romantic Harmony and its Crisisin Wagner's refer to the initial sonority of Chord.3Numerous other authors of the
One
First
and
complicated
free
in late
repetitions
Krise
former is overly
Taken together, however, harmonic connections and interminable as structural counterbalances to one another. Wagner can be viewed been true, the secret of great always always lies somewhere in the balance artistry too much that is expectedand too much that is unpredictable.
latter too primitive.
in
drama as the Tristan
und
Harmonik
is entitled
Tristan]
Wagners
this
ihre
The music
epoch-making
describe it as yet another harmonic invention ofthe that Kurth's period. belief, analysisof this sonority is best judged by the individual reader in comparison to other views, and therefore, we will devote this sectionto some of the more important and interestingpublished of this colorful harmonic structure. analyses Ex.7:15contains the first three measures of the orchestralintroduction to Tristan andlsolde. and frequently
Chord,
It is my
late-Romantic
Example
7:15
y=i
i^
r=rr
fct
\302\261=tz
We
begin Kurth's
shall
The basicharmonic moving to an chordin
final
chord
E7
this
progression
chord.
Ernst
of the
progression
Therefore,
first cadence in
this cadence
the Preludeconsists
actually concludeson
passage is the dominant-seventhin A-minor is also embellished with several chromatic
tones. Theseare:1)the *
analysis:
alteration
Kurth, Romantische
Harmonik
of the und
of the
fifth
ihre Krise
in
292
B7 chord
Wagners
Tristan
(the
the
key of
of a B7
dominant,
chord
since the
the Prelude). This twoand non-harmonic
alterations
from F# to
FN
(Bern: P. Haupt,
in
order
1920).
to produce
a higher level oftension asthe bass into the E of the final moves 2) the dissonant G# at chord; as an upward-resolving the beginning of the motive in the soprano,which functions suspension to the pitch A; 3) a second upward-resolving suspension on the pitch A#, which appears in the sopranojust before the harmony resolves into the phrase's final E7 chord. (Generally speaking, the voice-leadingin this passage(Ex.7:15) D# also moves by chromatic half-steps. progresses to
Dtj
in the
alto.)
The next analysiswe shall consider is from Harmonielehre [Study of Harmony] by Rudolf Louis and Ludwig Thuille.4 As is shown in Ex. 7:16, Louisand Thuille understood the G# in the top voiceto be an unprepared, chromatically upward-resolving suspension to A. Rather than or the in this of the dominant measure asanaltereddominant (as does Kurth), hearing sonority on the scale seventh even as a chromatically altered diminished-seventh chord degreeof A-minor altered diminished-seventh as a chromatically [vii j ], Louis and Thuille regardthis sonority chord built on the second scale degree [ii \\ ]. In other words, they consider this pre-dominant subdominant
to possess
sonority
function.
dominant
than
rather
function
Example 7:16
,
i
.J\342\200\224J
1
J.
J>i\342\200\224J>
i in
A-minor
not
p
i*|_if
^jy\342\200\224=\342\200\224
Basic
altered ii\302\260 (subaom. function) V altered
Progression:
^p^
ii
V
viiD (dom. function)
of Musical musikalischenHarmonik, [Textbook Harmony], sonority in the Prelude to Tristan actually possesses bitonal properties (the pitch F is diatonic to A-minor and D# is diatonic to E-minor); that is, this harmonic functions event to be an altered chordwhich Mayrbergerconsiders simultaneously in two minor keys.5 Though it may at this altered chord possessesspecific that seem, first, in both A-minor or E-minor,upon it becomes clear that it really has functions closer inspection, of this no pure function in either key. Therefore,Mayrberger postulatesthat the best analysis is one of both that the chord as a simultaneous representative treats sonority keys. In an article from his four-volume treatise, Das Geheimnis der Form beiRichardWagner Secret of Form in Richard Wagner], Alfred to clarify the harmonic Lorenz [The attempts atthebeginning that of the Prelude condenses the twoactually progression by providing a model the measure harmonicsequences into measures (see Ex. 7:17).6 Lorenzfurther simplifies single 12/8. He also removes texture by changing the meter of his study model to 4/4 from the original In
his
4
Rudolf
Louis and
5 Karl Mayrberger, 6
Alfred
Lehrbuch der
treatise
Karl Mayrberger
claimsthat
Ludwig
the
Thuille,
first
Harmonielehre
Lehrbuch der musikalischen
Lorenz, Das
Geheimnis
der Form bei
(Stuttgart: C. Griininger, Harmonik
Richard
Wagner,
293
(Pressburg:
1906).
G. Heckenast,
vol. 2 (Berlin:
1878).
M. Hesse,1924).
and embellishments from the original all of the suspensions so that only the basic harmonic structure remains. The condensed measures in Lorenz's model show each cadence endingon the weak beat of the measure. (This samereduction as I was to discover later, wasalso technique, in his model in the work of Johannes Schreyer.7 Schreyer,however, the barlines used placed in the accent of motific statement the each middle of the measure differently, dynamic showing chord falling on the downbeat of the bar].) the resolution [with Example
JE|E3
r
i*3
7:17
^5
&
y^
^^^
* doch nicht schnell
Bewegterf
VfT
We
,5 jJL-jjjju
-
Wastatich?
he!
Wowarich?
6
Mut
7
g
rrpr
p?i
299
?*
vr ^
r
.a
=tp=
-
ter!
Example7:19cont. -
muS
Sohn
te
dich mor
den! 14
FlJ
P^^
p^#
'lj Belebend
t
mt A
i
rAr^n^h t4
[U
=s
,-3-7 T '
I
r
u
u
J^iJ^if~~4^\302\243\"^
3
3]
Tor!
Blo-der,
15
Wo
tau-mem-der Tor!
irr-testdu
3=E
^ -3-7
ut
hin,
ih
-3\342\200\224, 17
i\342\200\2243 16
W
m
m
w
Th*
i-3-
mHJJlllfo t
^
Oissonance
i *ff.rrrrf
i-3-i
***** 5EEt i=T=\302\273-
i
* SE|E
i-3-i i\342\200\2243\342\200\224i
ges-send
300
k **
k
7:19 cont.
Example Trau
- te,
teu-
\302\253\302\243
^
J
-^
;'
j
/'''i *!'
W
}
JJ
\342\200\224
Jv
j&\342\200\224^
^
r
fremd 24
^\302\243
Jt\"7^ J-
War dir
23
m=k
P^
Mut - ter!
er-ste
22
T
T
[1 g:
D-
[V-
scene, Parsifal experiences guilt
In this
speech; Parsifal sinks down at Kundry's is \"frightfully concerned\" and Parsifal
emotionsin the musical settingof sang
in the
death
of his
mother as Kundry
gives
his
score, the stage directionreadsthat overwhelmed.\" Wagner clearly reflects these The melodic measures. highly expressive
In Wagner's
\"painfully
twenty-two
is very different than the folk-like the Siciliano-like preceding section. Ex. 7:20shows
of the
contour
these
the
over
feet.
solo-voice part
Gr-major
melody
texture
to which
of Kundry's
Kundry
voicepart.
Example7:20
*' a*
mm Ich
sah
das
Kind
\302\273_
an
sei - ner
Mut
-
ter
Brust
and the rhythmic As Kundry's speech continues, the tonality is increasingly expanded 1 with the to an end is intensified. is measures (Ex. 7:19, Nevertheless, speech brought tonal D7 This clear-cut cadential cadence iil V71]. T[vii\302\2607/ii (Ef )Sr^ gesture straightforward
-2)
texture a
at the end of
Kundry's
speech
strongly
contrasts
After many agitated rhythmic changes, changes single shriek. These rhythmic Ex. 7:21 shows the various motive. syncopated affected
emotional outburst. to a Parsifal's line is brought closewith a strongly are actually variations on a recurring two-pitch of this motive in this configurations rhythmic with
excerpt.
301
Parsifal's
subsequent
Example7:21
I* J We Mm
Su
J I*
-
be!
-
ter! Be,
J
TJ|J
JL
-
hoi
de
Mut-ter!
h
jij
j
i*
ih
\302\253.\302\253. mor - ^~\302\253 den
J
jij dei
to
one
-
i*
ner
J
to the
rer ver - bges-send
J
-nu -
dei
The rhythmic figures that are not connected another in similar fashion (see Ex.
n\\n
-
ner
ver-
patterned
ges - send?
variation (Ex.7:21)arerelated
7:22).
Example7:22
WcT
Sohn
mu^\"te
d'ctl mor\"
blod-er
tau-meln-der
}rh\\
Wo
The implied
Someof
the
through
Wagner's
drastic
where the tonality
Tor!
j
irr-test
du
hin,
tonal centersinthe voice
are changed with increasing speedand abandon. part tonal changes that take place toward end of the excerpt are produced the characteristic use of leading-tones. There are even more however, places,
is abruptly
changed,
without the benefit of
Example 7:23
302
leading-tone
motion
(see Ex.
7:23).
The are restated after only appears beginning simple. There are several pitchesthat to which pitches do not sound alike, sincethe chords intervening materials, but these repeated Din the upper voice The tonic-pitch they belong keep changing in the orchestral accompaniment. of the but then is (Ex. 7:19, measure 3) leapsan octave accompaniment reinterpreted as higher, asixteajoutee above the bass-pitch F (measure 4). In the sameway, the Ab in measure 4 functions as a minor third above F, but its appearance in measure5 functions as the diminished-seventh above B, etc. As is shownin Ex. 7:24, Wagner givesthe voice part the same kind of pitch reinterpretation.
Example 7:24
Here,
to an E7 unresolved dissonant sixth ofa 6-5 suspensionapplied is changed to its enharmonic equivalent Db,which functions as C. The pitchD, which is clearlytonic above at the opening cadence in Ex. 7:19(final note of Kundry's texture. speech), becomes suddenly energizedby active (This rhythmic In measure the technique anticipates the twentieth 4, the D can then be considered century.) root of if 3 [viil] in Eb-major or the sixte ajoutee of the S5 [ii*] With this sonority in C-minor. C#
chord. In the a minor ninth
functions
(measure 4), a section (above each of
as the
next measureC#
the
of four-tone
four-tone
sonorities
sonorities,
begins which the group number
cannot
be interpreted
ofthe chord is given
functionally (see
Ex.
7:10).
the domain of functional harmony no later than Wagner's musical materials abandon measure 5 in Ex. 7:19. Thegroup-2sonority in this measure could be consideredeither as as (ii 5) in Eb -minor [the functional-system root of this sixte ajoutee is the subdominant-pitch Ab ]; or as a J9, [vii 5 ] in Gb-major. Further, because the sonority in measure 4 can be consideredan si to view the sonority [ii 5] in C-minor [see discussion in previous paragraph],it is alsopossible in measure 5 as a leading-tone diminished-seventh chord in C-minor (with an unresolved4-3 ass notation would consider this a 7suspensionabove the root, thus: #v \\ [vii 3 \342\200\224 figured-b 6 suspension,sincethe fifth of the chord is in the bass and suspensionsare generally measured above the bass]. Although the sonority inmeasure 5 has possiblefunctions in Eb -minor, Gb -major or C-minor, it resolves instead to E? in measure 6 (the E7 is a dominant-function sonority in Abut it fails to also resolve The at this has little minor, ear, traditionally). choice,but to point, abandon to further a functional follow any attempt path. Chords from sonority-group2 seemto regularly those measures where the voice accompany enters with transient its Neither in measure 6and harmonic structures part syncopatedmotive. 9 belong to a four-tone sonority group, however. Instead, these sonorities possess specific functional implications; the sonority in measure6 appearsto be a D? [V9 ], and the chord in measure
9 sounds,at first,
like
a De-5
[V6-5].
303
Note that
in measures 6 and 9 by moving an unexpected that but rather the root seventh and ninth resolve, from E to D). Though the suspended-sixth in measure 9 does not (it is lead downward (C#) its is to sound this resolution allowed in another B then (B) resolve, simultaneously voice; pitch to Bb in the next measure,thereby resolves downward the dominant-function neutralizing in cadential tendency of the D). A similar occurs in measures 14-15. The sonority process measure 14 can be consideredan s\342\204\242 Iin F-minor. Its functional continuation becomes ] [ii G to Gb in measure 15. Measure15is actually the first impossible because of the descentfrom that continues in measures 16 and 17. step in a descendingharmonic sequence in measure 6 contains a strongly The functional dissonant minor ninth, but this sonority in thirds. The dissonance is made somewhat less intrusive is built by the fact that the sonority sound of the major seventh (E-D#) in measure 9 (part of a five-tone sonority) actually produces a stronger dissonantsound than the minor ninth in measure 6. The dissonance at the end of measure9then leadsto another strongly dissonant five-tone sonority in measure 10. This climax of harmonic tensionis then contrasted by the entrance of the major triad in measure11(IE). The contrast between consonance and dissonanceis made even by the three-tone suspension stronger the that that triad this also contains (note sonority directlyprecedes major three-way suspension the strong dissonantinterval\342\200\224E-F). In measure the the voice part repeats samemotive 10, in measure heard 9 (C#-[enh.Db]-G#), but harmonictension is increased in the by the change To the listener, the voice-partmotive in measure 10 sounds as though it underlying harmony. should be Db-Ab (~>G),but this implied voice-leading is thwarted in measurell (see Ex. 7:25). 9-11 climax. Measures are literally packed full of events that produce the excerpt's harmonic voice.
Wagner
In measure
6, it
the sonorities
resolves
is not
the dissonant
7:25
Example
11-13,the cadenceon the F-major triad is repeated, and then repeatedagain F-minor). Thus, the pitch F actslikea tonic in this area of Ex. 7:19 (notice measures Ex. 7:26 shows the implied 11-12). pedal-point is maintained throughout
In measures (the
second
that
an F
harmonic
time to
progression
in these
three measures.
Example 7:26 9^
9=>
7
7
T
D
T
D
D'
t
T \\>9
[vi
'
\\>9
i
i
vi ton.
ped
304
V^? \342\200\224
I4]
In passages where a tonal basic key center is maintained. measure 13 (see Ex. 7:27).
every chord
is heard,
center
t4
[i4
Only
the
caneasily pass measure,is still
J
J
eS>v65....
1
throughout
in
J 7 6 s5\342\200\224
l&\"
3 Vll..\302\2607.... 6 5
evident
.-\302\2607
Vll/
\342\200\242 7 -06, IV 11 5 J
third quarter-note of the measureimplies a function over this single out-of-key reference. It is that
in D-minor,
clear
the
tonic
and the listener begins the
(F), that
at the end of the bar.) The materials in the following connected passage of the sixte ajoutee on the downbeat of measure 14, and we again enter until measure 20, where a D?-T[V9-!] cadence creates a short tonal region in the minor ninth is found in the orchestral only accompaniment; the pitch D
tonic
the effect
neutralize tonally
J 3
so that the
related
closely
7:27
Example
J
be
will
structure is
of harmonic
kind
This
free
space (Here,
Gb-major.
shouldbe enharmonically The key of Gb-major
considered
as Eb b.)
in measure
The cello part 21, however. function in G, and two measures later the entire orchestrais pulled already implies into G-minor. ninth above Db [the dominant of (The pitch D in measure 21isheardas a minor Gb].D should, therefore, be considered an enharmonic Eb b. In measure 22, however, the D in the voice part clearly belongs to the dominant chordin G!) is
somewhat
questionable
dominant
It appears
that
the
cello part in
measure 21 wascarelessly
notated
with
a C#
rather than
aDb.
Example7:28 Measure
^
Measure
11
SK
jj_^t
21 should read:
^jjppj\342\200\224{jll
T rest The at the end of the cellopart in measures21-22 In measure is very important. 22, D establishesitselfasthe goal pitch and is no longer consideredonly a melodic upper-neighboring of a dominant-ninth tone to Db or the ninth the D in the cello part at the end sonority. Although of measure 22 clearlyfunctions as the dominant in G, the celloDin measure21implies dominant of G above a Gb tonic. This spotis an extraordinary of bitonality. example
305
which employ only Wagner's Exercises: a) Write of sonorities four-tone progressions As in Ex. 7:29, and label each chord to its type (1, 2, 3, or 4 see Ex.7:10). according notate your progressions the connection between sonorities can be easily on a single staff sothat with [/] and all seen. Mark all common tones with [\342\200\224], all leading-tone relationships sonorities
of a
connections
major
second
with
\\_/\\
7:29
Example
b) Extract
a short sectionfrom variation
a harmonic
reduction)
and strive to resolution variation.
disguise
individual
techniques. Pay (See Ex. 7:30 for a
one
of Wagner's
of the original. sonorities
late works
Besure to
and then produce(in single-staff
justify
all non-leading-tone
by applying various suspensionfigures
special attention model.)
to
textual
implications
and
motion delayed-
when creating
your
Example 7:30
o iftri *\\
4^4^|^
i
exercises similar to those in b),but use two-stave systems for your work. At your include functional dominant-seventh or -ninth chords followed by resolution to or minor is limit to a triads. It not necessary to four-voice texture single major yourself A pitch may continue ahead in two directions at the same time, requiring additional throughout. or a voice may rest, requiring fewer etc. It is important to write-out voices, voices, continuing exercises so that they can be playedat the keyboard.Play your everything you write at the piano, c) Produce
own discretion,
so that
you
will
develop
proficiency hearing
the connectionsin this harmonic
306
style.
EIGHT
CHAPTER
1839and 1885(Liszt)
Harmony between
1. Introduction
Bach's greatness
Musical Offering (1747), was dedicatedto the strength, equally manifest in the study of war
and
in music, createswonder and multiple-choirwork(the medium
admiration
in
all.\"
usually
composers
of a monarch \"whose and therefore, especially was no pompous however,
veneration
and peace,
Bach's
employed
work,
to praise
greatness and strength
around the 1600). Instead, Bach honors the king [Frederick by using one ofthe ruler'sown musical themes in a set of compositions that demonstrate the inexhaustible musical possibilities of that theme. The Musical Offering contains two ricercars, a fugue, a and the diverse canons, all of which are based upon sonata, a perpetualcanon eight \"Royal Theme.\" The composer lauds the king for his inventiveness and then further flatters him by in the theme. Bach [the that the Frederick had foreseenallthe musical indicating possibilities humble claims In this servant] possibilities. only to have worked-outand recordedthe various set of pieces, greatness and spiritual are characterized of by the highest level strength until
contrapuntal
Great
of Prussia]
art.
famous Nearly a hundred yearslater(1839), statue, FranzLiszt.inspiredby Michelangelo's This is a kind funeral a of entitled7Z [The Penserosp Thinker]. piece march, composed piano piece whose melody is reduced to the repetition is so little melody in of a single pitch. In fact, there II Penseroso, of that a substance this work there is hardly melody at all. The belongs almost the work, is musicallyexpressed to the realm of harmony. The \"thinker\" who entirely inspired continuous harmonic and reinterpretations ofthe melody-pitch transformations by E, as it is to sonority. passed from sonority Ex. 8:1 containsa short passagefrom II Penseroso reduced to one staff. In this excerpt,the thematic E functions as the minor third aboveC#,the fifth above A, the minor seventh aboveF#, a suspended-sixth above B and the root above G#, the major third above C, a suspended-fourth of an open-fifth E. built on sonority
Example 8:1
iA
\302\253:
m
^
307
mm
of musical texture is repeateda few measures later (see Ex. 8:2). Here, in and minor triads, several augmented triads also take part in the harmonization ofa similar single-pitchmelody line (this time, on G). The
kind
same
to major
addition
Example 8:2
w
1,8
=s=
The materials here have score in order to keep all
t>8
I
l>8^p
been transposed from the original of the chords in the same register
As is shown in Ex. 8:3,Liszt Faust in the in a similar fashionto \"the thinker\" represents first movement ofthe Faust-Symphony The melody, which contains all twelvechromatic (1854). is derived from the tones of four augmented triads. even the firstFurthermore, pitches, triad inversion minor triad (last measure, beat 2) resolvesto an augmented before the directly This seems to characterize whose Faust as a eighth-rests. passage spiritual giant, contemplations cannot be limited to conventional patterns of thought. Example
8:3
m
jirffffi^jj^ Like
the
diminished-seventh
which has no
chord,
sounding root
its minor
because
thirds
since partition the octaveinto four equal parts, the root ofan augmentedtriad is also indefinable, the chord's structure consistsexclusively of major thirds. (Major thirds partition the octave into uses from the tones three equal parts.) In his music, Liszt often that suspension figures emerge of an augmented triad. The six resolutions in Ex. 8:4 are all produced by half-step motion or from the of an triad. downward) pitches augmented (upward
Example
8:4
as
4f
?d Jll'|Pl\302\273ll|)lrll|f-r^rt ?F ?A ?
f \302\273
308
?bl
?
D l
It is
in the
opposite
preparation,
from an augmented triad by stepwise motion in two voices be approached by means of the same smooth voice-leading harmonic Liszt, however, regularly employsaugmentedtriadswithout
possible to progress away
(seeEx.8:5),and
conversely,
direction.
and without
it can
approach by means of
smooth
8:5
Example
Exercises:
Write
out
(on
a single
voice-leading.
staff) various
progressionstoward
and
away
from
augmented triads.
2. Tonality as Reminiscence
It
that changed the soundscape of the musical world, but though same musical Liszt brokethe with unrecognized time, ground important keyboard works sometwenty of is Liszt's use earlier. years widely recognized as Today, revolutionary harmony the work of a great composer, in spite ofhis difficulties with melody writing. Indeed, the casual listenerwill have great difficulty coming to terms with much of Liszt's music, since it requiresmastery of so many, often contradictory, listening skills. On one hand, of a work, and on the other, beable listener must be able to judge the musical effectiveness the to correctly run the and understand a work'smusical connections. Liszt's perceive compositions in easy tonal settings, to harmonies that teeter melodies on gamut from Mozart-likemajor-mode the very brink of atonality. As is shown in Ex. 8:6,Liszt employs four-tone sonorities at the beginning and Wagner-like end of his piano piece Sospiri from ThreeLate Piano Pieces(1879). was
Wagner's
Tristan
at the
Example8:6 beginning
^f77
1
1
l
7
^7
7
7*
^7
ending
309
1
^7 7
*
7^7
Liszt
measure
the tonally free texture of interrupts major-mode melody. This short melodic
straightforward harmonic
TltlT
progression
is also
passage
[I\342\200\224I]. These
seven times with harmonized by a then cells of tonality
sonorities
four-tone
momentary
a three-
resolve
after literal repetition, to the next tonally free passage offour-tone sonorities. Since diversions appear in the keysof Ab -major, Gb -major, Ab -major, Gb -major, E-major, it is impossible to define a main tonal center in this piece. F-minor, and F#-minor, these sections are be all of tonal introduced Furthermore, non-traditionally and cannot a and a of the texture before each tonal is ritardando musical (There thinning-out anticipated. but this process gives no clue as to the specific There section, key area that will be presented.) is a certain beauty and to the Hstener like an about these tonal passages, they come unexpected directly, or these tonal
gift.
Ex.
8:7 shows
several ways that these
tonal areas areintroduced
in Sospiri.
8:7a-d
Example
4
b)
d
ife^1J'
2
1
l^^#P#
PS3
Q
'1$i;'%$
^rnj^^JSa ^m
i
j
j
,71^ m
;M7
ttr.
l
,44 ^fir
If we instead incomplete
,4
ninth-chord
viewed as D-C#).This
in
1^677
Ex.
8:7a in
chord with completed by the following
a dominant-ninth is then
enharmonically
^
4\"~~^
N-
^^^ten
regard the four-tonesonority
of F-Ab-B-D),
-j-^-y
r
'J
spelled
an
310
H\302\273#-
^
.4
4
^
jh-^w^
an enharmonic spelling(E#-G#-B-D root (B?) is produced. This
omitted
melodic
dominant-ninth
minor.
1
half-step
D-Db (enharmonically
produces an
implication of
Ft-
In Ex. 8:7b,the interval Eb -Gb appears in two of the lowervoices before and after the both measure with the rest. This interval implies the samebasicsonority in both spots; that is A-CEb-Gb in the key of Bb-minor. It is obvious, that the Db in the top voiceof 0#v) [vii\302\2607] however, 2 must be considered a passingsuspension-figure measure [accented tone]. Since this passing Gb -major triad, the pitches Eb and Gb can be heard, after the sonority resolves to an unexpected as the third and fifth of the Cb-major triad (subdominant in Gb-major). fact, a progression that does not connect functionally. The initial Ex.8:7ccontains F# -minor triad = E = then to an S5 (enharm. progresses to an S^ (Db subdominant pitch) [ii* in Ab-major]; and finally to an Ab -major It does not make sense subdominant pitch) [ii 5 in D-major]; triad! the third
to interpret
2
chord as an abridgeddominant-ninth
(Bs
) in
D-major (enharm.:
C#-E-G-
B). The
4) would
is impossible
have
which
occurs in
the resolution of
\302\2607
] chord (Ex. 8:7, measures 3The actual voicing ofthis resolution out of the questionin traditional music. because of the parallel fifths between the bass and soprano (see Ex. anticipate
voice-leading
the
l$v [vii
been to
8:8).
Example8:8
?
t'P\342\200\224p
The three measures of major-key tonality in Ex. 8:9 only seem trivial, when observed outside of the larger context of the piece. For that reason, this excerpt cannot reveal its true occur within will lose its most atonal space, the tonality importance. If islandsof tonality such as these, are important characteristic;that is, its strength of stability. Short tonal passages harmonic little morethan nostalgic reminiscences\342\200\224thepain of farewell. It is as if these precious connections (precious now, but simply taken for granted before) are beingheld in the hands one of tonality last time. The materials are indeed precious,but they have meaning only when they can beunderstoodin the context of the overall form. This pain of reminiscence, noticeable at such a high level in the musical materials ofSospiri,needsto be correctly interpreted in performance. a sentimental The insensitive pianist errs who produces expressivo in these passages.
311
Example8:9
^
and
form
Overall
PPPP
details
harmonic
the
follow
The tension provided cadences and the large formal
basic rules.
same
by
local gives meaning to both concerns in a Classical sonata. The diminished-seventh chord and the augmented triad, into harmonic structures which divide the octave equal intervals, presented Liszt with a model for releasing his music from the bounds of Clas sical style at the level of large-scale form and local tonic-dominant
the
key polarity
details. The
worth
song
the keyboard arrangement in this regard. The four verses,
and
studying
E-major and triads
the verse
which
Db-majorindicate the importance
form. Ex. 8:10contains an excerptfrom major
ofLiszt'sSonetto
on
A,
C#,
F and
the
again on A
del Petrarva
the keys of
(1839) are
Db -major,
both
G-major,
relationship in the overall verse. Herein the local detail, of major third) prepare the entrance
minor-third
of the
to the first
introduction (roots
47
are set in
related
by
(Db-major).
Example 8:10
i
V^F
p^^e
r Between
the
subsequent
W*
16^^^
r
m
-p r
r
\302\253r
verses,
the same type of
atonal
Sospiri.
312
m
fields
prevail
that we observedin Liszt's
3.
The
it is possible As we have discussed,
End
of Tonal
to find
Harmony
systematic
relationships are often
relationships
in Wagner's
use of
four-
containing Liszt's to passages, actually defy any attempt producesystematic neither contain uniformly harmonies nor recognizable new Such treated analysis. passages i n exercises). extracted from the texture could be and tested-out (which Rather, sonority types chord resolution must be consideredon its own merits as an existential single case. Liszt every without to their employs regard sonority types and invents harmonicconnectionsbetweenthem materials melodic to these traditional [classical]rank or ordering.Hethen applies Liszt's from one unconventional is not transferable harmonic inspiration piece to the next. backgrounds. ends here. From now on, harmony must be For that reason, systematicstudy of tonal harmony
tone
sonorities
[though these
mostinterestingharmonic
interpretedin the context attempt
to describe
quite
distant].
Passages
however,
of specific
a few of these
applications
In this section,I will appear in the works of
within specific works.
single-caseharmonic
devices
as they
Liszt.
in the final section of Sonetto104delPetrarva times (1839). in measures and chordal form twelve before the end It appears twice in arpeggiation (Ex. 8:11a), in the final measures (Ex. 8:11b). In both cases, the augmented triad is located betweentwo measures of tonic. The root and third (E and G#) of the E-major triad remain common framing tonesin the uppervoices, but the bass leaps downward from the tonic pitch (E) to CM. This bass before it leaps upward again to the tonic leapforms the root of the augmented triad (C-E-G#), in None of the three in the the measure. augmented triad areproduced pitches pitch following in the third-highest voice a functional resolution. Eventhe returning-tone figure by or produce is make this more ( which traditionally (B-CM-B), progression convincing) help might contradicted by the stable change of root provided by the leap in the bass. new method Thus, none of an active sonority's pitches demand resolution\342\200\224a sensational of treating dissonance. Up to this point, we have always been able to trace leading-tone of resolution determine which from the in order to backward point pitches were relationships a non-consonant In this case, however, we have dissonant. sonority placed between two actually tonictriads,where the upper voices carry-through as commontones. Sincethis type of cadence has no functional we must refer to the augmented triad in the middle as a non-tonic equivalent, The augmented
sonority
(T t
triad occurs two
T).
313
Example 8:lla-b a)
b)
OJ
tu
In the previouslydiscussedSonetto finds a completely different solution for a 47, Liszt in Sonetto 47 also contains a contrasting chord placed harmonic situation. A passage between two framing sonorities of the same function (see Ex. 8:12). In this case,the chordin the middle can be functionally classified as a D798 [V3-2]. The chords on both sides ofthis dominantcan be considered T3 [I6],but, as we will soon see, the harmonic motion into and function sonority but traditional. away from the middle sonority is anything similar
Example
8:12 8\"-
T^h-h't* = *
T^h\302\253
1*
t\302\273 ^h*\342\226\240 -Pfe\302\243
j\302\247=\"^
P*
J= =3=\302\243
8:12, measure 1)was heard in the previous measure as an enharmonic entered bass pitch (major third above the root of an E-major triad), but, because ofthe newly F (measure 1), the Gtf is respelled as Ab (a minor third abovethe bassand the fifth of the Db -major It is this latter interpretation of the pitch that seems to be confirmed,considering the triad). dominant-seventh chord in Db -major that appears in measure2. In Ex. 8:12, the top voice ofthe to be centered aroundthis Ab, but a second accompanying voice appears that was continues piano not present before [bottom notes of the right hand]. It is the addition of this new voice, however, that puts traditional harmonic on an uncertain footing. The initial sonority in Ex. 8:12 analysis canbe spelled B$ -D-F-Ab, and this sonority could certainly function as Ef [vii\302\2607 ] in C-minor (if Bb is consideredan upper-neighboringtoneto Ab). It only becomes clear in the secondmeasure, that the chord in measure 1 should be interpreted as however, T3 [I6] in Db-major. (The B-D in the first measure are heardasa double oscillating eighth-notes upward-resolving suspensionfigure to C-Eb in the secondmeasure.) The
pitch
Ab (Ex.
G#
314
to this passage, the more first measure turns into
remarkable it becomes. On one hand, the in measure the goal of resolution 3, after a are direct o f dominant 3-4 measures 1-2). On (measures preparation repetitions a true b ecause the the other hand, we do not actually tonal cadence, only experience top minor third ofthe impliedtonic triad is actually present in measure 3;that is, there is no clear sounding in this tonic chord. Instead of providing the resolution root convincing normally supplied by dominant tonic triad in 3 the implied measure only hints at establishing harmonic harmony, The
longer
we listen
disguisedT3 [F] measureof clear
in the
closure. the first half of measure 5 seems is found in Ex. 8:13. Although of the first half of measure 1 (see Ex. 8:12), the dominant-seventh chord three of measure 5 strongly suggests that the first (in A-major) occurring in the second half of the measure be enharmonically as G#-B-D-F (#v [vii07]. It is also quarter-notes reinterpreted how like D^, f? in A-major [that is, a this entire measure functionally sounds surprising
Measure5 of
to
be another
this
excerpt
repetition
chord with a half-step suspension resolutionin the bass(F-E)and a 6-5 suspension If we consider the latter to actually bethebest analysis, the (C#-B) in the next to highest voice]. 5 will be heard as non-harmonic. (Ab) in the top voiceof measure (G#upper neighboring-tone to A-major, the implied but Liszt Afc|-G# would have been most correct, considering change this as an enharmonic of G#-A#-G#.) AJ>-Bb-At>, presents figure spelling neighboring-tone dominant-seventh
Example
tV^HbJH
8:13
Pn\302\243$*
s
p^prPp
X
0-
X^L
W If
we
analyze
the short
double periodthat forms the introduction triad antecedent (Sr) phrase ends on an F#-minor 1-2).Since D-major triad (see Ex. 8:14,measures
eight-measure
to Sonetto
104in the key of E-major, the [ii] and the the first two consequentphrasebegins on a in construction with the first two measures of the measures of the consequentphraseareparallel tonic that has been coloredby the antecedent, the consequentphrasebeginswith a weakened events. At the same time, however, the new appearance of D-major can alsobe preceding We could even go so far as to consider as the counter-relative considered (tG) [VI] of F#-minor. the counter-relative Near the end of the of the subdominant [VI] in F#-minor. (SrG) D-major a on G-major takes measure rather unbelievable closed cadence 4), consequent phrase (Ex. 8:14, the is as before still heard the subdominant chordin D-major), E-major tonic triad place(G-major of a B7 is established(final measure) chord chord). by means (penultimate 315
Example 8:14
Lalugu.bre with
atonal
an
harmonic
interpretations.
(measure
3, downbeat).
as an
upward-resolving
Gondola], one ofthe last piano Lugubrious pieces by Liszt, begins of Ex. 8:15 shows how the pitch C vacillates between a number The sonority F#-A-C-Eb(measure2) is then followed by F-Ab-C-D
[The
gondola
recitative.
On the third quarter of measure suspension to Db on the fourth
3, the
harmony changes and C is heard measure. On the downbeat
of the
quarter
B-DC is now heard as a downward-resolving suspension to B in the sonority 4 also shows that C couldalso be considered a of measure F-Ab. A second look at the downbeat B would be a passing chord member in the sonority F-Ab -C-D. In this case, the melody'shalf-note the pitch B is considered the leading-tonein the $5 [vii\"3] chord or simply a passing tone. Whether of tonic, it appears as it is confirmedat the endof a single-voice to take over the function tone, line (with a melodiccadenceformula that has been in use for centuries). of measure
4, the
Example8:15
:b
s
^-^n^-TT
r^Tr
m 316
\\*-
^^
As is shown in Ex. 8:16, a passage in the middlesectionof this same remarkable composition contains suspension-figurescreatedfrom the major thirds in both tonic (F#) and subdominant These major thirds then act as downward-resolving and move to [less (B) chords. suspensions It is an interesting reversal of traditional harmonic traditionally stable]minor thirds. figure and when dissonant chords the seek seem to musical and consonant sonorities ground, occupy space to resolve into them. Even the attentive listenermust alter the way he or she actually in hears order to comprehend such passages!
Example8:16
4.
Two
to Atonality
Pathways
Liszt composed Bagatellesans tonalite a Key] in 1885. Though Liszt is without [Bagatelle as an undisputed pioneer of atonal first the fact that this Bagatelle was only space, in 1956 indicates the small impact hisfar-reaching musical achievements had on the published of musical general development style in succeeding generations. The sonoritiesin this can be explained, for the most part, by considering them sets of thirds. as layered composition for the In Bagatelle,Lisztalsoemployed a specific sonority to act as a central harmonic ground entire piece. Thissametechnique would later become an important characteristic in the music of Debussy. Such ground sonorities actually help establishmusical in the same way coherence a centralharmonic that the tonic established focus in more traditional works. Liszt employsan in Bagatelle. triad with an added major second(C# -F-A + B) as the ground sonority augmented now
known
317
Ex. 8:17 showsthree sonority.
passage
Note
that
passagesfrom
the sonority
(D-F#-Bt>+C) and
the third
in transposition
the
second
J iJJi. mm
HSi
f
ground
8:17
mtm
f
that contain this at the end of both
(E-G#-C+D).
passage
Example
If
If
\302\261A%-L4
3)
^
f
^
mp
P^P
In late works, melodic materials often correspondto the harmony in an nonLiszt's traditional manner. The already citedLa ends with a single-voice recitative (see lugubregondola Ex. 8:18),which, since harmony for a few measures, (particularly implies the key of G#-minor in the key ofG# -minor actually precedes the recitative). Five measures before the end, however, in the key of G#, the pitch Gil no longer functions as an enharmonicallyspelledleading-tone (Fx) A the This sinceGis immediately followed (a whole-step higher). brings pieceto an end with by a a sense of suspended is not (It actually very large stepfrom this passage to the viola atonality.
recitativesin Mahler'sTenth
Symphony!)
318
Example
&
m^<
0=*
m
8:18
^ #r ^.
_
p
#o
\\
^
^
\342\200\224ft
fe^
There is a secondpathway that leads to future harmonic developments,however, and the from the musical materials of the distant past. processes of this approach are drawn With this second related sonorities is avoided by the the tradition of functionally pathway, that were employed ca. 1600(seeChapter To the listener, One). adoptionof chord progressions is not so conspicuous,sinceall basic of side-stepping however, this second method tonality are constructed sonorities familiar from traditional triads. Liszt wascertainly with the motets of the late-sixteenthand early seventeenth and it is that his 1839 piano centuries, quite likely this was influenced sacred music from earlier time. piece Sposalizio [Wedding] consciously by isa Ex.8:19acontains a two-measure and 8:19b from Ex. continuation excerpt Sposalizio in a similar of the harmonic manner to that shown in progression which is melodicallyfigured Ex. 8:19a. harmonic
Example8:19a-b
The
those
chord
progressions
used in the
middle sectionof
employed in music around 1600. Note the standard classical cadence formula (TSD7
harmonies
neutralizes
and subdominant
chords
within
the formula
(i.e., TD'S
the
that
relatedto
piece (see Ex. 8:20) are Liszt overcomes and functionally
T) by
simply exchangingthe
dominant
T).
Example8:20
Examine the harmonic piano piece progression at the beginning of Liszt's ca. 1600. Study the use of GuilleaumeTell, and compareit to harmonic practices church mode (which has no leading-tone)in modes in Brahms, especially the use of the Aeolian the third movement of the German mode (major Requiem; al soconsiderthe useof the Mixolydian scale degree) at the beginning of the slow movement in Brahms' mode with a lowered-seventh that the to enrich use of modal materials was intended Fourth Remember, however, Symphony. much as to them in the late-nineteenth standard harmonic as replace century. progressions Exercises:
Chapelle de
320
NINE
CHAPTER
Harmony
between
1900-1918 (Debussy)
1. Slendro and Whole-tone
Scales
far-Eastern countries of Java and Bali have one of the most highly and developed musical cultures. Themusic of these maintained cultures two recognizes separate pitch carefully These systems are calledPelogand Slendro. the octave. systemsfor partitioning are placed in the centerof the gamelan instruments (the orchestra of Java Metallophone and Bali).Thesemetallophones have various sizes of sounding plates and attached resonating is designed to resonate for a specificlength of time, chambers.In fact, every metallophone of the instrument. Certain instruments specializein soft upon the musical function depending (a kind of cantus-firmus technique), whereasothers specializein melodic-ground figuration etc. Because ofthe two different of the octave countermelody, rapid figural passages, partitions The
instruments requiredby gamelan music, each performing ensemble containsa setof Pelog-tuned instruments. and a set of Slendro-tuned but two of the pitches (smallnotes) As is shown in Ex. 9:1, Pelogis a seven-tone structure, with Pelog are somewhat are rarely used. For that reason, the musical intervals associated and major-third). variable(half-step, To our Western ears, East-Indianpiecesbased whole-step based in the Phrygian mode. on Pelog have a certain similarity of sound to pieces
Example 9:1
Slendro divides the octave into five similar, but not exactly equal, parts. intervals are somewhatlargerthan the other three. Every gamelan places are never within the largerintervals the musical texture, but these largerintervals differently found directly one afterthe other. Sinceour ears interpret the smaller Slendro intervals as major On
the
In
other
two
Slendro,
hand,
of the
often equate the pentatonic scale intervals as minor Westerners thirds, are placed Because the largerintervals Sl&idro-tuned instruments. by produced each different individual Slendro ensembles are differently by by compositions played gamelan, in the their scale bases different forms of often perceived,by Western to have ears, pentatonic the sizes of the intervals is much smaller on actual scale. However,the difference between them Ex. Slendro instruments than is implied by the way we notate 9:2). (see seconds to
the
and
the larger
sounds
Example9:2
L,.
-'
\342\200\242
.-^'1
I\342\200\236.
J.
>'\342\200\242'
I
^4^^
\342\200\236.
321
The
basic
between
differences
are easierto
these pentatonic-scale forms
see
in Ex.
9:3.
Example 9:3
It is important without a pitch center, since that we learn to hear Slendro (pentatonic) different Javanese gamelansbuildtheir SMndro sonorities (that is, it will seem to our differently Western ears, that different gamelans will employ forms of the pentatonic scale).For different one pitch of the pentatonic can serve as a pitch as well as any other. this center reason, ClaudeDebussyheardJavanesegamelan music at the Paris World Exhibition of1889,and the this music made on him can be traced in a number of his subsequent impression strong compositions. Typical gamelan-like structures and pitch materialsoccurin Debussy's piano La Mer (1905). piece Pagodes (1903) and his orchestrawork, In addition to the pentatonic the whole-tone scale provides us with another scale, point of contact between Javanese music and Western music. the scale is closer to Though pentatonic than the whole-tone scale (becausethe pentatonic the octave with five pitches), Slendro divides the whole-tone with its six-pitch division of the octave, better to the small scale, corresponds actual difference in the size of Slendro intervals. Slendroand the whole-tone scale are also as a tonal center. scale has no single tone that acts similar, in that the whole-tone A differentiation between consonant in and dissonant musical elementsis not practiced and whole-tone and pentatonic Debussy's gamelan music. For that reason, Javanesemusic compositionshave the following points in common: a) Every
pitch
b) There is no c) Different
of the
scale can soundtogether with
pitch
center.
any
other;
are no dissonances to resolve.
there
simultaneous musical processescanbeconsideredequal
implied hierarchy of
melody
and
in importance;
there
is no
accompaniment.
intervals Western notation does not clearlypresentthe equal-sized of the whole-tone scale. can see in Ex. 9:4a,Debussy takespains to hide the unavoidable diminished-third leap as much as possible (the diminished-third leap into F# on the second sixteenth-note of measure 4 is not very obvious after the long tied-over Ab). In measure 3, Debussy avoids the diminished third the first pitch in the right hand as G#, while notating the secondpitch in the by notating left hand as Ab. The Ab (left hand) is a lower-neighboring tone to Bb, while the G# (right hand) a downward scale passage. In Ex. 9:4b,thereis no necessity to resolve the apparent begins
As
we
dissonancesthat occur and importance.
between
the hands,
since both streams of
322
sonorities
are
of equal weight
Example9:4a-b from
Debussy-Voiles
Book I
Preludes,
SB k *=^
H.
m
s
ITF
f
Ex.9:5a-bareexamples of the throughout only
ideal
work.
the
Ex. 9:5a
E (measure 2, bass) doesnot belong of gamelan technique. The demonstration
the
pitch
bass, and two
separate
texture
pure-pentatonic
shows the beginningof
melodic
groups
work.
the
to the
that enter in a number of places In the second excerpt (Ex.9:5b),
pentatonic
scale. Ex. 9:5bcontains
melodic
fundamental
and arapidly
F
ground
figuredpassage(triplets)
is found in the in the
occur
voices.
Example 9:5a Debu&sy-Pagodes
'
3~
\\l
Vi,,
,
i
'U
\302\261+
*
*
J)
J
F
J\342\200\2243\342\200\224 i i \342\226\240-0 r
'
\342\200\242 *
\342\200\242
1 \342\200\242 \302\273
J -,
p r
-^-TSf-
\302\273 \302\273
1
=
L
^
=
323
an
upper
9:5b
Example
maim
S
t
&
&*-
In Ex. 9:4a, measure is inexcusable. rules, Debussy'svoice leading two hands octaves betweenthe on the pitches Bb parallel 3, there are A)>. In Ex. 9:5a (measure 2, last two parallel perfect beats), rhythmically-displaced that deal with hands. The traditional rules of fifths the two between (C#-G#/F# -C#) voice-leading not valid in this music. Sincethe minor the handling of consonance and dissonanceare simply stable the minor seventh doesnot create and the octave are consideredequally seventh intervals, resolution Ex. an impetus for suspension (see 9:6). of traditional
In terms can
we
see rhythmically-displaced
9:6
Example
ffi
J
f
of are totally does not apply to textures where voices The term independent counterpoint For that each other, but rather, where voices constantly depend upon and reactto one another. to explain or label Debussy's Javanese-like multi-voice by the pieces reason, it is not possible principles of counterpoint.
2. HarmonicTextureinthe Music musical style
Debussy's durability.
considering
several
melodiesworthy a Mozart
section
this
In
of
is likean endlessfabric, we
will
attempt
specific passages from a Mozart in this work, but
to
viola part.
324
We
Debussy
threads of the same texture in his worksby see that there are no princely as materials as musicallytrivial
from
woven
describe
La Mer. neither
of
harmonic will
are there
many
Ex.9:7shows
from La
texture
a melodic-harmonic
Mer, which
from five
is created
pitches
ofthe scale:A-B-C#-F#-G#. 9:7
Example
Debussy-La Mer (2 measuresafter
No.
rehearsal
1 #J-\342\200\224-J
^
|_2J )
y
^\342\200\224j
tJ
m
F=*
ii\342\200\224i\342\200\224t
^
A
H_
4
f
*\302\273-
\342\200\242\342\226\240
Ex. 9:8shows a melodic-harmonic the scale:A-B-C#-D#-F#-G#.
from La
texture
Mer,which
is created
from six
pitches of
9:8
Example
Debussy-La Mer (3 measuresbefore
12 )
No.
rehearsal
*\302\243}UJltFL0
Wr m
The
Debussy
sonority
alternating
Ex. 9:7and
9:8
(A and B
to restrict
7
^^=&
^^S
planes,
based on the
pitches A
also sound simultaneously
the bass line to
the
interval
in
of a
325
both
7
of equal weight in both It is quite typical for excerpts).
and
B, are
major second.
Intraditional
the bass provides of a pitch above each melody note with color. In Schubert, for instance, the pitch C might first appear as an octave above a root-position C-major triad, and then reappear later as the sensitive third (or above Ab-major. With Debussy, however,it does not seem to really matter what tenth) specific bass. Debussy interval the highest voice maintains above the transfers into his music (from a sense of harmonic rootlessness. It is possible to regard Slendro) many of his sonorities only as
heavy
the interval
melodies,
and characteristic
a specific
or light.
The cycleof events which unfolds in Debussy's works often shows a similar indifference to tradition. Classical-periodmelodies, carriedalong by their underlying harmonic rhythms, have and are brought definite to the foreground beginnings endings. However, when melodicevents in Debussy's In such cases, most, if not all ofthe tones music, the situation is completelydifferent. seemto share in a tension-free pitch environment. Hereindividual have neither pitches specific nor direction in Debussy do not really come intention toward a goal. Many structures melody-like to conclusive the background into Instead, they simply recede again by way of a endings.
decrescendo. Ex.9:9contains not belongto
ofthis voice marked sonority
the
another
excerpt
harmonic
underlying
is announced
from La
Mer . The
texture are
pitch Cb (not line is constructed
by the
notes, the melody (Db -Eb -F-Ab -Bb).
a part only
pitches
marked with
of the arrows.
of the underlying of pitches
Mer
si.
P\"'tiUL\302\243f
No. [3] )
(at rehearsal
t^N^f
326
J.
texture). Outside of
from the underlying
Example 9:9 Debussy-La
foreground voice that do Note that the entrance the
pentatonic
Example 9:9(cont.)
m
f#fi
3.
^
in the
Sonorities
Mixture-like
Music of Debussy
as their the pipes that sound in the sameoctave notated pitches are said to to this so-called \"concert-pitch\" register, most eight-foot (8') register. In addition organs also have pipes that also sound an octavelowerthan their notated pitches (16' register); It is possible for an or one or two octaves higher than their notated pitches(4',respectively 2). one or more these to produce to from of registers sounding organist couple together pipes one manual or (while multiple-octavepitch complexes depressing only pedal key). Technically On
the
organ,
to the
belong
this
operation couldbe considered
however, many couple a number of specific higherranks of pipes to a basic sound that the chooses (in the middle ages,up to 22 pitched organist The sounding ranks of pipes in a mixture are ranks of pipes couldbe sounded simultaneously). that not all simple octave multiples, however. Mixture stops often include coupled ranks of pipes a double octave higher.. .etc. sound a fifth higher, an octave higher, an octaveand a fifth higher, ranks used that sound a third higher, a less often, some organ mixtures alsoinclude Though tenth A of four ranks is called a four.etc. mixture simultaneous higher.. consisting sounding mixture rank (Mixture IV). Mutation stops are alsocommon on organs. With a mutation stop, a shorter single-rankof will be to an rank so that a particular overtoneof the lower pipes automatically coupled eight-foot with a numeric integer followedby a labeled rank will be reinforced. These stops are often This indicates the length of the shorter rank (in registralfeet).Thefollowing fraction. number speaking,
simple
octave-coupling
organs have specialmixture
are
common
stops
which
automatically
examples:
327
a mixture,
The Nazard (or PedalQuint
that is the a harmonic interval of a perfecttwelfth; )-22/3'creates harmonic with the third partial [natural series] of the longer pipe (seeEx.9:1Oa). Since the shorter of the two pipeswill only be a third the length ofthe longer pipe, method: 1/3 x 8 = 8/ we can calculate the shorter pipe'slength(inregistralfeet) by the following 3' or 2m [when the fraction is reduced]. l3'5' creates a harmonic interval of two octaves Tierce and a third; that is, the shorter The of In this a with the fifth the case the will unison sound partial longer pipe(seeEx.9:10b). pipe l3'5. will be a the 1/5 x 8= 8/5' or shorter pipe fifth the length of only longer pipe; therefore:
shorter pipe will
sound
a unison
9:10a-b
Example
b)
a)
\302\261
m Nazard (or
way
proceed now
sonority
RealMixture: of harmonic
are not generally used by themselves, Instead these stops are usually perceived.
other with
above a A real
voicesabove
are their
nor
to add
employed
specific special
stops.
of Debussy's
a discussion
works is similar to
of harmony in his
conceives
he
brilliant
l3'5'
and mutations
Mixtures
intervals always directly harmonic brillianceto As we
2\302\253' Terz
Quint)
harmonictechniques,we the
way
an organist
will
see that
constructs a full
the and
single pitch. mixture the
for interval] will be defined as an exact [interval of the lowest voice [parallelspecific intervals
pitches
duplication above the
rare in the music of Debussy. In Ex. voice]. Suchmixtures are exceptionally triad with an addedsixth in the bass [G#] is followed by a real mixture is a scalar descent of seventh chords which created five [third major-minor formation, by In measure 2, another mixture of augmented triads occursabove a double real inversion]. pedal point (tritone).
lowest-sounding
9:11,
the
initial
B-minor
Example 9:11 Debussy-Nocturnes
W:
9EtjE
for
(3 measures
Orchestra
^M
m
d-^$u
328
beforerehearsalNo.
[7j)
W: ^
m
M
In
Ex. 9:14,
parallel second-inversion
triads move
in
tonal-mixture
above a long
held-out
pedal tone.
Example9:14 Debussy-La
Cathedrale
from Preludes,
engloutie
BookI
S
u Ex.
9:15,
pitches in the
contains right
hand
mixture that includesthe diminishedtriad. Note how the texture by providing a kind of compositional complement
a tonal
effect.
Example
Debussy-Brouillardsfrom
330
9:15 Preludes,
Book II
the
free
stereo
The piano
and Lavine contains a juxtaposition of major common tonesbetweenthe chords.The progression at least one triad member that movesby stepto the next sonority by in the same voicein both The roots of not chords). (although the step progression appear may all these triadsarea third apart, however, and each chord in the progressionis only distantly to the previous chord. related Ex.9:16a-b contain two excerpts from the beginning ofGeneral Lavine.
Atonal Mixture:
minor triads in such a way chords is guided between
that
piece
there
General
are few
9:16 a-b
Example
Debussy-Genera/ Lavine from
w
Preludes,
Book II
H\\^
b)
^^
w Iff
*
^S^g
^m
?
Modulating
of maintaining by
without
dissipate
any
Mixture:
Debussy's
mixture
particular sonorities or tonal too much attention to calling mechanical
effect
that
might
techniques areas.
The
must not be considered robotic means of his mixture passages pass
majority
themselves,and their overall expression seem to be presentin the details.
tends to
of Ex. 9:17 belong to the key of E-major, two measures more like a coloration of A-major [A-lydian]. Further, the last measure passage sounds a the We will call this kind of G#, though employs passage sounds generally closeto G-major. a mixture referenceto other keys or tonal centers within passage modulating mixture. Though
all of
the pitches in
the first
this
331
Example9:17 from
Debussy-Minstrels
Priludes,
Book I
measures of Les sonset lesparfums... is worth our attention Framing Mixture: Theopening (see Ex.9:18). Here, only the outer voices proceed in parallel motion. (There are alsolonger that employ this technique in the first movement of Debussy's Children's Corner Suite passages
or in Puccini'sMadame
Butterfly.)
mixtures (measures1-2),Debussy even hints at the imply a progressionin the key of D-minor; six-four is an s\\ [ii*3 ]. In the chord (D5) [Vt ] and th-e second last two measures, seventh Debussy employs mixture sonorities consisting of major-minor related to one another. Notethe singlechange chords, but these sonoritiesare not functionally 3. Perhaps of harmonic mixture in the third chord of measure Debussy freely changed the inversion of this to in the first-inversion order to from overusing second) sonority (from keep F# and A. mixture ofthis been retained and if the the estabhshed had (If here, pitches passage bass voice had remained within the key signature, this sonority would have been spelled FJf-AInside
these
outer-voice parallel-octave
functional harmony. The first first sonority is a clear dominant
two
chords
actually
C-D.)
9:18
Example
sonset Debussy-Les
*
ae
.. from
les parfums.
I.
Uses*
PfYT-fi
4-.
f
f 332
Preludes, Book
I
Example
9.18 cont.
Slendro Mixture: Though it may not be totally appropriate to describe the excerptin Ex. there is a great dealof parallel motion of mixtures, here. All the sonorities except thethird and fourth chords in the secondmeasureand the last three chords are constructedfrom of the four-tone scale Eb-Gb-Bb-Db. This four-tone scale appears to be a pentatonic the pitches With the exception of those chords cited, the voices here with one pitch missing (Ab). scale in parallel motion within four-tone space. proceed
9:19 terms in
Example9:19 Debussy-La
fille
aux cheveux
from Preludes, BookI
in the music of Debussy, we encounter two types of mixtures PolyphonicMixture:Frequently, in the set polyphonically against eachother. A good example of this technique can be observed Book middle section of Debussy's La terrasse...(Preludes, II).
333
4. Harmony
and Compositional Structure asa Unity
of
Invention
works of Debussy,harmony, structure and form are related to each compositional do not harmonize non-traditional ways. Generally,Debussy'schords single of traditional are some this encountered). examples practice occasionally melody pitches(though harmonic sonority. Instead, complete melodies are often accompanied by only one underlying the between and Debussy'sunderstanding of relationship harmony melodyisjust the opposite to an underlying harmonic progression]. of traditional related practice [where melody is directly In Debussy's harmonic sonorities elaboration. music, emerge from the processof melodic Though the pitches ofthe harmony in the melody, are most often the same as thosefound occasionally a harmonicsonority will introduce a contrasting foreign pitch into the texture. For this reason, it is possibleto provide Debussy's of dissonance music with a new definition [non-melodic tones]. Every sonority, or perhaps betterstated,every pitch complex in Debussy's works presents its own phrase structure and orchestrational color. In fact, it is often quite impossible to tell the color or vice vers a. [Traditionally, form and structure whether the phrase structure produces When Debussychanges were considered to be the generatorsof all other musical parameters.] an instrumental structure color or a rhythmic texture, the harmonic frequently changes at the sametime. As compared with earlier music, the harmonic changesthat take place in Debussy are far less frequent, but when are more since harmonic do occur, they easily they remembered, to connected articulations in phrasing and orchestralcolor. important changes are directly sonorities often cannot be separated from their contexts. musical Specific Harmony, phrase structure and orchestration were conceived As a (not invented one after the other). together unified musical texture is produced. result a highly At this point, those readers who wish to further test my harmonic theories on Debussy may at an eighteen-page excerptfrom the score ofLo Mer. As a score-studyaid, Ex.9:20 lookwithme includes sonorities from the score (eachchangeis numbered), numbers extracted page specific and dynamic markings. Thetie-likearchesshow passages where common tones between sonoritiesare maintained the same instrument. Take by special note of the following situations: In the
other
in completely
connection between sonorities (3) and (4)(pp.56rhythm. bar and a tempo change. section a double b) The transitional (pp. 64-5) is concluded with Just before the section change, however, the first violins provide a common-tone connection by means of a trill figure. This figure begins on the pitch G# in (7), is then heard in (8) as an Ab (minor enharmonic in (9) as G# (the third above seventh above Bb), and finally E). again that connection between all of the is maintained c) Above all, notice the common-tone sonority groups by the bass-line G# (pp. 66-74).
a) The harp reinforces
7)through
its
constant
the
common-tone
quadruple-meter
Fixedchorda!sonorities
like
(3), (4),
(7), and
334
(8) alternate with:
a) arpeggiated
chords
(17)
Example 9:20
pp.56-7
h-
^
\\
C)
m
p.59
Mixture
alternation of
pp.63-4
^
triads
PP
(11)
(9) pp.65-6
(12)
pp.68-9
p. 74
ma]or
harmony above
The musical
of
augmented
i~M
(8)
p.63
pp.57-
p.69
(13)
pp.70-1
(I'D
p.72
p. 75
\342\200\224I\342\200\224 \\f
G)l
this harmonic reduction, which is found in the movement entitled: Jeux 4 measures before l38l. See Claude Debussy, 128land ends 4 measures after Three Great Orchestral Works (New York: Dover, 1983)pp. 172-217.
passagefor
de vogues,begins
textural planes(6),(9),(10),(11); between sonorities (1);d) motion c) pendular and real-mixturesonorities(5); e)tonal-mixture sonorities (12), (13), (14), and (16).All sonorities in this excerpt are constructedfrom stacks of thirds. E specially common are seventh-chord for ms chords. There are also a number of augmented some (in various inversions) and ninth triads, and (18);
b) large
with added
sevenths.
335
CHAPTERTEN Selected
Topics
1.Atonal
Harmony
in Harmony
(Scriabin,
(after 1912)
Schonberg)
Between ten and thirty after Debussy, most composers years in practice of employing major-minortonalities and sonoritiesbuilt
(1874-1951),1 and
JosefHauer (1853-1959)2 independently (1895-1963)setforth new principles
methods; Paul Hindemith and
Composition?
Oliver
not yet termed
Although traditional
harmony,
was
had turned thirds.
developed
from
away
Arnold different
of harmony in his
the
Schonberg twelve-tone
Craft ofMusical
Messiaen (1908-) established a new systemof modal classification.4 which was no longer obligated to the processes of atonal, this music, in an arbitrary and illogical fashion. As suspected of being composed choice of sonority composers writing ca. 1915showa surprisingunity as distant shall as see, harmonic analysis of worksby composers
we lookbackat this music, and progression. As we Alexander Scriabin (1872-1915) and
yield
Schonberg
nearly
identical results.
a composer's we theories, treatises or work logsmay prove interesting, Although reading that shall focus our attention on actual music rather than theoretical writings. It is well known, with a composer's declared intentions. (Sometimes musical scores do not alwaysperfectly agree a composer use materials and techniquesthat deviate from an ideal concept, and may consciously Since this book times these alterations musical other intuition.) maybe the result of unconscious as a history of music theory, is not intended we will limit our discussion to those twentiethmaterials and techniques that can be uncovered by score century analysis.
1
did not formally articles on his twelve-tone method after its publish during and directly method is discussedin: Ethan Haimo, Schonberg's Serial long incubation of Schonberg's The Evolutionofhis Twelve-tone Method 1914-1928(Oxford: Clarendon Press, 1990). See also:Arnold Schoenberg, Odyssey: c.l 950), pp. 102-143; \"Delivered \"Composition with twelve tones\" in his Style and Idea (NewYork: Philosophical Library, as a lecture at U.C.L.A., March 26,1941.\" Although
Schonberg
development, the
2
Josef
relatively
Matthias
Universal-Edition,
Hauer,
Vom
3Paul Hindemith, Unterweisung Schott Music Co.,1941;rev.
York:
Melos
zur Pauke
(Vienna:
Universal-Edition,
1925); Zwblftontechnik
(Vienna:
1926). im Tonsatz, 2 vols. 1945).
(1937;1939); transl. as:The
4 Oliver Messiaen, Technique de mon langue musicale (Paris: (Paris: A. Leduc, 1956). My Musical Language
336
1944);transl.
Craft
by John
of Musical
Composition(New
Satterfield as The
Technique
of
Ex. 10:1a-b contains
from
excerpts
one of
Scriabin's last compositions.
Example10:la-b op. 74,
Scriabin-Prelude, M6 number of pitch classes in the sonority:
No. 1 M6
6
lowest intervaJ:
0=
P4
LL
augmented triad
t.i.
M6
M3
number of pitch classes in the sonority: 5
S5>
b)
J~i
hMM \302\243
PP^fr^^f
f tjj\302\243L_Ji
i lOWCSt interval:
leading-tones
by
the
'tt.
t.L
ofthe pitches in
Most
\302\243J^
\302\243Ngj
Ex. 10:1a-b areeithertreatedas leading-tones of intermediate pitches (the most
action
or they convincing
are turned into kind
of melodic
motivation). All never
the
fewer
sonorities than
consideredmembers is highly
unified.
Prelude contain five to eight voices. In addition, there are never greater than six different pitch classes per sonority (octavesare inPreZutie ofthe same pitch class). For that reason, the setofsonority types (It would be interestingto write a history of sonority types and their in Scriabin's
five and
337
in different
employment
from
constructed
three
musical eras. From 1600to pitch classes [triads] with a
the
period, chords are mainly an extra fourth pitch-class his four-tone sonorities. Five and six
early
tendency
Classical to add
of Wagner and [seventh chords] as we approach the time ca. 1915.. etc.) pitch classes per sonority seemto bethe norm either one or two tritones. Every sonority in Ex. 10:1a-b contains also
regularly
employed.
(Although
The augmented triad is
there is no tritone in the augmentedtriad, it
is perceived
to
takes tritone.) The bass pitch in almost every sonority ofa tritone. The bass tritone is actually an alteration [mistuning] of the traditional The of bass, in music ca. 1915, is thereby harmony-defining perfect fifth. deprived its customary role in strongly the chord. In fact, all the voicesin Scriabin'ssonorities defining have the same harmonic weight. In physics,the term equilibrium is used to describe approximately a situation that has no clear top or bottom, where thereis no heavy or light component, and where is either supporting or beingsupported.Since no element the bass voice no longer provides a clear harmonic it is also important to make surethat the top voice of each chordis handled foundation, so that harmonic equilibrium can be maintained the voices. very carefully, among Since many listenerstend to hear sonorities downward from the highest voice to the lowest, the uppermost interval ofa chord is particularly In most traditional sonorities, the important. is interval a third or a it this and consonance that gives the is usually sixth, topmost imperfect its rich of and sweetness. The fourth and sense create a strong, sonority euphony perfect fifth, sound when occur in and andharsh other than minor triads. The sonorities dissonant, they major interval of the in will sonorities Ex. 10:2 not be heard as when consonances at top played the
have a similar harmonic part in the interval
function
to the
keyboard.
Example10:2
^1
All minor
the
ninths
sonorities (major
in Ex. seconds,
i
i i^4
10:1 a-balsocontain strong minor sevenths and major
dissonances ninths
such as
are considered
major seventhsand mild dissonances
in this style). Associations with traditional sonorities are eluded by the processof concealing fifths or them perfect by avoiding altogether. The intervals in Ex. 10:3 (the diagram of the penultimate sonority in Ex. 10:1aare shown from left from the bass to T he of note). lower part this chord is dominated proceeds right upward contains an augmented triad. Though the sonority by two tritone groups, while the top portion
338
three
contains
fifths, the two
perfect
and lowesttones are conjunct the
lower
fifth
and
bottom
the
ambiguous becauseof
their
fifths
(the Db functions
the clearlyaudiblehighest simultaneously as the top pitch of
upperfifth).
two
lines)
(dotted
fifths
perfect
pitch of the
^^
perfect-fifths
presence of
become tonally pitches.
intermediary
10:3
Example r
The
and the
relationship
conjunct
that contain
i r
i
10:1a also demonstrateshow different an octave can sound in this style, underscores the view that the ear Scriabin handles it. This example be allowed must to decide about the propriety of the octave on a case by case basis. (The of octaves here contradicts a number of second-rate twelve-tone employment treatises, which forbid any use ofthis fundamental interval.) The second strongly sonority in Ex. 10:1a contains an octave the bass. Because ofthe tritone-forming Dtf (directly above the leap), leapA-Ain pitch the octave here shares a similarity to the octavethat occurs in the last sonority ofthe example. Inthe final chord of Ex. 10:1a, notice that the uppermostpitch in the left hand is a perfect octave the E in the middlevoice above of this sonority. is a Bb, which Between this interval however, divides the octave of Ex. 10:1 a, interval into two tritones. In both the secondand last sonorities the octaveintervals with pitches a tritone away. are associated In Ex. 10:la-b, the spacing and doubling in the of the octave is handled quite differently is substituted three sonorities marked (9). In thesechords, a major seventh or minor ninth for an octave, while the actual is transposed upward to its next higher registral octave equivalent Two of these sonorities are analyzed in Ex. 10:4. position. to the lowest C in Ex. 10:4, Db seems like a vital new pitch. Furthermore, Compared with this the C also sounds to new Db, starting my ears. Because I hear the octave higher in all three as the pitches I of these sonorities doublings separatepitches,I have re-counted I o f and enteredtheresultinsidethe circle the $ markings. actually perceive strongly urge every to examine these sonoritiesindependently. I am simply reporting what I hear, reader, however, and donot wish to state my opinion as an unquestionablefact. You will need to come to your own conclusionabout how many sounding pitches are actually presentin thesesonorities. The
and
the
excerpt
freedom
in Ex.
with which
10:4
Example \342\204\2421
\\
L-r'
k*-
339
a
~\\
b-*
Exercises:
how
the principles
Using
in this progressions
style.
forward
it continues
to the
we have
of the
Because
discussed
invent
above,
paramount importance of
next, always
each
several
sonority
and
Try out severalpossibilities
instrument.
at an
work
and write-out
hearing
will prevail, if, like between sonorities as much as possible.Betterconnections and then first more voicesmove by step. Either invent the next basicsonority the create the connections first and then invent out the best melodic or connections, sonority. try I have removed the Sprechstimme from Exs. 10:5-6, which are excerpts from voice-part Pierrot Lunaire (certainly,not every reader will approve of this!). 1912 composition, Schonberg's Ex.10:5isa two-staff reduction of the clarinet part, the violin part and the four-voice piano part and
seek
Scriabin,
from
No.
to hear
one or
15.
10:5
Example
6
6
^ 10:6
is an
6
6
5
5
iT*
i
^
Efe
rfrit
r* ittr*^=m; *
)
Ex.
6
^
fpjflp
No. 15
Lunaire,
Schiinberg-Pierrot
excerpt from No. 19,showing
the
s and piano
cello
parts.
Example 10:6 6
4
8
No. 19
Lunaire,
Schonberg-Pierrot
5 5 5
5
6
pizz.
y
i'Ulj'^J11
m
a
3^
f
5*nr
jii
H=t=i w
340
a
t
\\>*
5
6
6
5
cont.
10:6
Example
6
^y^fLg p^ yt-. \302\273 pil
Silg
s
!
^9
?p
, , fg-1
r]
f
f
SEEt
Scriabin excerpts,nearly every sonority in Ex. 10:5-6 contains one those are few sonorities wheretritones absent all contain an Further, nearly s and triads further for use of tritones hereis evidence triad. Schonberg* augmented augmented this in the position (discussed above)that tritones and augmented triads have a similar function the same strong dissonances that we observedin style. The Schonberg excerpts also contain Scriabin.Itisclearfrom the excerpt in Ex. 10:6, that the oldtermpicmo no longer accompaniment As
or
more
we
observed
in the
tritones.
in the piano part that are not applies, since Schonbergalmost always statesspitches in the cello. The pitches of Schonberg* are seldom built in thirds. All sounded s sonorities simultaneously of the harmonies here contain four to eight pitchesand, for the most part, five or six separate pitch in the piano part. classesare present in each sonority. In Ex. 10:6,only a single octave is found in it like an unaccented the bass measure functions here This octaveis formed (F#) 5; by pitch tone. This is evidence another traditional harmonic octave for reversal of passing yet passing earlier dissonances w ere as non-chord but in this In music, tones, regularly justified practice. it is the consonances that require justification. style perfect
341
2. Sonority and Structure(Webern) in the works ofAnton who attempt to analyze harmony von Webern Those or melody [1883to the music, but rather to the questions Webern's results 1945] should not attribute unfortunate music difficulties as I prepared the raises. In this regard, I rememberwell my own analytical Musiklehre.5 A complete for the tenth ofHermann Grabner's edition supplement Allgemeinen discussion of how Webern method andthen twelve-tone invented eventually applied Sehonberg's the serial methods of organizing soundingregistersand dynamic go beyond scopeof markings this text (for more on these aspects of serial music see my supplement to Grabner). At this point, of Webern's we will discuss several aspectsof the structural use of sonority in the first movement here includes only a clarinet, instrumentation bass Symphony, op. 21 (1928).The minimal clarinet, two horns, harp and solo string quartet.
Webern'sSymphony, of its central
based on a twelve-tonerow that shows retrograde symmetry the same intervals, is, the second half of the row presents backwards,asare presentedinthe first half (see Ex. 10 :7). (Also note that the six pitches that comprise the secondhalf of the row are transposed by tritone from the first half.) The op.
on both sides
21 is
axis;
that
row that sets [hexachords] juxtaposition ofthesetwo six-pitch produces a completetwelve-tone is intervallically identical when playedeither forward or backward (original) (retrograde). Since the inversion (I) and the original (O) and retrograde(R) forms are intervallically identical, the order of forms will also same intervals. this inversion have (RI) Therefore, retrograde row has only two actual forms [O and I]. twelve-tone particular
Example10:7
O
There is a doublebar line at the this section to be the exposition.
Ex.10:8,shows
These
row forms
Hermann
tone-row
end of
forms
a row,
while other
measure 25 in the first
that are
are orchestratedin such
several pitches from
5
the
i
>
a way
ed. (Kassel:
342
first
some instruments
will
play
only
We will
movement.
established in the that
instruments
Grabner, Allgemeinen Musiklehre,10th
R
single
consider
fourteen
measures.
will
a group
play
pitches.
Barenreiter-Verlag, 1970).
of
10:8
Example
te
1
^S
U
^
\302\243\302\243=\302\243
^m
s
^
te-
*i
9^^
^
p
*
f\302\243=r
fe^^E^Et^E^ *f
^^
fe-
^
S
f =^
^
^1rf-\302\243E^fe
I
^=r
j=^=r
1R=r
ts-
f
^
^m
*?-
P
w
n
J^i*1
*
IT:
^^
Ex. 10:9a are employed in the first 25 measures ofthe symphony. series of perfect fourths (see Ex. 10 :9b)[black yield two interlocking note heads show the pitches ofone seriesand white note heads show the other series].Standing of both series of fourths for the is the pitch AN, which functions as the axisof symmetry outside entire pitch collection(seeEx.10:9c). Only
Upon
the
analysis,
notes
shown in
these notes
Example10:9a-c
343
Note
chromatic tones are contained but Eb occurs twice. Eb appearsboth
all twelve
that
only once,
appear
in this a tritone
pitch set. above and
Eleven ofthe twelve below the central AN,
same time it is alsothe highestpitch in one series of fourths sixth pitch, counting (the in the and the lowest in the other black-note series sixth (the series) upward pitch counting pitch downward in the white-noteseries).It is necessary to have either both Eb's present or no Eb's and
at the
at all!
set as a singleseriesof perfect fourths (see Ex. octave so that the series will not end in sucha high and below the As (in parentheses), which would lie a perfect fourth above and to the registral center of the pitch set. moved
also possibleto Herethe central 10:10). It is
The
register.
two
series, are combined
see
Eb
thirteen-note drops down one this
Example
If we appraisethis work Webern's
texture
register(measures
only
10:10
to the
according
fails miserably. It is badenough 3-4), but then Bb (measures
that
principles of twelve-tone construction, pitch Ab is directly repeated in the same
5-6)is repeatedtwice.However,
both
these
pitch
not only on the pitches themselves, but also on the central repetitions tend to focusour attention, a specific register ofthe whole set, much like a moving searchlight highlights object for a short time before on. In repeating the Ab and Bb, Webern passing highlights the symmetrical structure contained in the complete on either pitch set by emphasizingthe two closest pitches side ofthe central A. Notice that both twelve-tone rows beginning with the pitch A (Ex. 10:8;top two staves) are rhythmically identical, as are the two rows that start respectively a major third belowand a third above the pitch A (Ex. 10:8; bottom two staves). By this method [doublecanon in major Webern all A will ensures that ofthe above receive the same number of entries inversion], pitches and durational A. Ex. 10:lla-b below contains a chart of emphasis as those pitchesoccurring these symmetries as they occur in the first-movement exposition. 344
10:lla-b
Example
E--
BFt \342\200\242
a)
b)
10-
17*.
10-
16*-
18-
\342\200\24212\342\226\2405
c\302\273-
10-
6 ~ 14\342\200\224
Bt-
10-
17*-
13
14**
Et-
A
-
Gjt-
F -
Et
17*-
\342\200\24210-
146 -
10\342\226\240
5
-
c-
12-
18-
G-
10-
16*\"
D--
10-
17*-
a) showsthe
b) shows the symmetry produced the respective duration of each pitch in quarter-note values
created by symmetry the number of entries of each pitch
by
(grace-notes are indicated
with
*)
Exercises: Listen to a recordingof this exposition a number of times. At first, pay very close attention to the twelve-tonerowsas they occur; practice recognizing and aurally analyzing them. After turn have achieved some success with this, your attention to an aural analysisof you sound of the exposition. individual harmonic sonorities and then to the overall After listen to the rest ofthe composition (you may stop counting-off twelve-tone rows this, as they occur; this means that you Listen to and aurally analyze the harmonic now). changes the sounding register should attention After the to exposition, pay special registral emphasis. here ofthe movement that Webem do not have many instruments moves (the employs upward the third section ofthe movement, which lies in a very lower pitches available!), until we reach the third the in section. Ex. 10:12 shows lowestand (The lower register. highestpitches high the of the because of the repeat Cin cello(measure66a)belongs to the middle section movement,
sign.)
Example 10:12 8\"\302\273-
m 345
of Harmony
3. Classification
extensive
Wagner's
of the
toward
a homogeneous
extension of
shows a further
Schonberg
triad
displacement
indicateda clear tendency
this
by
same
(Hindemith)
four-tone sonorities6 four mildly dissonant and sonority world. The music of Scriabin Scriabin and Schonberg tendency.
sonorities constructed from strong dissonances consistently employed (including either the tritone or the augmented These sonorities present sucha high level of harmonic triad). tension to such a degree,that the contrast of harmonic homogeneity and renouncethe traditional harmonic could not be on to future of composers. style passed generations It was only by this kind of sonority treatment, however,that harmonic styles of the Baroque, be not Classical and Romantic could overcome (and just interestingly extended). It was to take such drastic means to contrast the musical tradition controlled by the harmonic necessary ebb and flow of dominant and tonic. Though in surface textures, the forms ofthe older different which established definite formal goals;this was usually stylesallreliedon harmonic processes worked out by establishing a tonality, to an area of contrasting tonality and (or tonalities) moving then returning again to the original area. avoidance of consonance and the Schonberg's of dissonance stands completely outside of this musical tradition, however. Those emancipation who listen as the end-point in a long evolutionary to rarely Schonberg, do not hear his music is because this often considered dissonant, Instead, every Schonberg process. style simply sounds from the past. trusted sonority is measuredagainst five-
and six-tone
sonorities in his music than Schonberg and minor triads). Indeed, Hindemith's of Bach and Haydn than but nevertheless, it is still Wagner,
far fewer Hindemith actually employs sonorities allow perfect fifths
(Hindemith's has
music
more
perceivedto consonant and considerations new
be
to do with
traditional characteristics of harmonictension and relaxation of Hindemith, these parametersaredefined by the
areas
music
style
major
Even though
dissonant.
dissonant in the
the
intense
and
between
contrast
and between
are
important
composer
in a completely
way.
In this Composition.'7
section we will
Unlike
all earlier
coversall possiblesonority
the main theses of Hindemith's The Craft of Musical studies of chordsdealingonly with selected sonorities, this treatise and organizes then them into six main categories. Hindemith types discuss
various methods of harmonic progression. As Hindemith explains in TheCraft one of the two pitches in every Composition, of Musical all thirds and all sevenths, the interval functions as the root of that interval. With perfect fifths, tone the root, whereas the root of perfect fourths, all sixths and all seconds lower is considered proceeds
6
These
to define
four,
four-tone
sonorities
avoided the
intervals
of a
minor secondormajor
second
(see Chapter
6).
'Paul
Hindemith,
The Craft of
Musical Composition(New 346
York:
Schott Music
Co.,1941;rev.
1945).
Seven;pp.
285-
of more than two pitches, the root is considered to be the root upper tone. With sonorities best interval contained in that sonority.8 As the root of one sonority movesto the next, the will take place when roots moveby step. Hindemith calls the unity greatest amount ofharmonic one sonority root to the next a stepprogression. from process of moving Hindemith made sure that his own music was well-insulated from his theories, however. Hisdistinguished classification of sonorities and his insights about how harmonies should be introduced is certainly significant, but his own compositions tend to disqualify many of these \"a strange Hindemith [chauvinistically] calls one group of sonorities riff-raff, principles. are considered \"the colored and while and minor triads unrefined,\" exaggerated, brightly major what in The noblest of all sonorities.\" Unfortunately, is Craft of Musical Composition emerges a sense that certain sonorities are \"more than others. important\" not matter much if we replaced single\"exaggerated and unrefined\" Though it might with \"noble sonorities and more important\" chords in pieces that have little artistic value, a \"more important\" chord in a successfulwork replacing an alleged \"exaggerated\"sonoritywith where the materials could the musical texture, especiallyin those compositions greatly damage are highly In successful controlled. has equal works, nearly every correctly sonority placed stature [regardlessof its classification]. of Hindemith the composerwaswell aware Naturally, this. For that reason, we will turn away from his textbook theories and examine his worthiest
is the of the
legacy\342\200\224his
music.
Ex. 10:13
shows the first
two
Piano Sonata
of Hindemith's
measure
No. 1 (1934).
10:13 Example
K
8
S[
as that interval The best interval is defined order: perfect fifth, perfect fourth, major
following
seventh,
minor
second,
major seventh.
Sj
S[
S2
W
K
within a sonority which is closest to the beginning of the minor sixth, minor third, major sixth, major second, minor
contained third,
S2
347
in Ex. 10:13. In spite ofa short rest, the melody takes on an arch There are eight sonorities form. Though this phrase opensand closes on a major triad, there are no other triads between three chords are then followed these two. Sonorities2-4 are mildly dissonant. These by two of dissonance. chords that have an increased level The major seventh (A-G#)in the fifth sonority the same major-seventh is somewhat hidden in the inner voices,but the sixth sonority brings interval to the foreground, it occurs between the two upper voices.Thepenultimate since chord, For this reason,it which contains a tritone (A-Di),doesnot contain any strong dissonances. milder and less dissonant than the previous Hindemith uses a tritone sounds chords. frequently to a consonant decrease harmonic tension as he cadence chord. (Note the sonority approaches in the difference between Hindemith'stritone-containing which acts as a sonority, step process of resolution, a and the traditional tritone-containing dominant-seventhchord,which produces large amount of harmonic tension.) A similar kind of harmonic progres sionoccursin the movement Lied from the little played, Stucke but set of pieces entitled Reihe kleiner [Series of Little Pieces]from remarkably charming Ex. 10:14 contains an excerpt from this 1927. movement (the coloratura upper voiceis omitted The harmonic tension curve ofthis excerptis executedin two segments\342\200\224a short [fourhere). sonority] progression followed by a longer and more harmonically intense progression.
Example10:14
R
SL
K
S2
S2
S2
S2
W
R
Sj
Rather than using the composer'sown harmonic classification system, I have found in Hindemith's compositions: symbols are better suitedto sonority analysis
that
the
following
R = Ruheklang;[stablesonority]; K
= Klanggehalt
[chord containing
inversions. This category
Si
=
Spannung
constructed
ersten
major seconds and /or
also
Grades minor
of perfect
fifths or
octaves
and triads and their minor sonority]; dominated by major other important sonorities constructedin thirds.
includes
[first-order tension sevenths
and perfect
348
producingsonority]; fourths.
sonorities
dominated
by
S2=Spannungzweiten
Grades
minor
W
= Klangaufweichung
producing sonority]; sonoritiesdominated
tension
[second-order
sevenths.
and/or major
seconds
by
sonority]; a
[tension-easing
sonority clearly dominated
or
tritone
by
augmented triad. As
10:15, doublesymbolscan alsobeusedto explain element should be written used, the predominant
in Ex.
is shown
doublesymbols
are
',
\" *
t *
KS2
Though
this harmonic
uselessto attempt listenerswill hear
S2
sonority. When
10:15
Example
t
a given first.
\342\200\242
j
ft
*
S2W
T
KW
S2K
classificationsystemis useful,
the system. Even perfecting certain sonorities differently.
with
fe
the
S,W
I wish
possibility
to emphasize that it is quite of double symbols, different
For that reason,specificelementsof
a particular
thus creating the individuals, sonority subjectively weaker or strongerto various of of a possibility dispute over the use particular symbol. Nevertheless,my chord classification is more practical than Hindemith's system. music, system, derived from analysis ofHindemith's will seem
For
Hindemith's
example,
betweenthe two of
the
fact
that
levels
Group of dissonance
Hindemith
III Chords (\"with associated with
treats these
two
levels
seconds
and
those
intervals
of dissonance
sevenths\")
do not distinguish
[major and
minor] in spite
quite differently not take into account
in
his
own
the orderand does Furthermore, his classification system within a of and intervals placement pitches sonority. the way he orders the pitches within Hindemith sonorities in his is very meticulousabout of the fortissimo however. At one climaxes in the Saint compositions, Temptation of Anthony the classicist is satisfied with a mildly from Mathis der Maler, Hindemith dissonant arrangementof the pitches are arranged so that major(see Ex. 10:16a). The pitchesof these sonorities It is possible, however, to reconfigure secondsand perfect-fourths the perfect predominate. in fourths in the penultimate chord of Ex. 1.0:16a so that the pitches appearto be constructed thirds to form quite dissonant (Ex. 10:16b). These samepitchescanthenbefurther reconfigured compositions.
sonorities(Ex.10:16c). sonorities has a fundamentally different tension level was of harmonic to levels show others, my designed multiple system in Ex. 10:16a-c tension and relaxation. In Hindemith's system,all of the structural variations to the classification of the root within the sonority same the belong chord-group (only position would change). Because
than the
each
of these
reconfigured
classification
349
Example10:16a-c
KS
Ex. 10:17a 1922-23
and
WK
'1/2
shows the openingmeasuresto
the introduction section of the last song in the cycleMarienleben[Life of Mary]. Ex. 10:17b shows Hindemith's of the same passage from 1948. The sonoritiesin the earlierversion consist the later of one sonority class (S^,while revised version is a modelof increasing classes. several sonority tension as the phrasepassesthrough sonority
of Hindemith's
version
revised version almost
3 2/1
1(2)
entirely
decreasing
Example10:17a-b tritone! \342\226\240w v-
- *\342\226\240 \342\226\240 w
-w
%
m k. i\302\273
m
t
h
ZEE=^=iE5ZEEE^tEEE^
$
\"1
1
^1
2
*1
1
b)
J)
\302\243TT=r _t-
\302\2473
\302\273 3
K
S,
i
J Si
S^
Si
350
Si
Si
St
a doubt, version, shown in Ex. 10:17b,is,without musically convincing and it and widespread opinion of Hindemith'smusicnow associated with that pernicious in vogue; of Hindemith's namely, that too many phrases were fashioned along the samelines 7%e Craft of Musical Composition appeared. It isalsoclaimed that after Hindemith's fascination with the samebasictension-curve lacksanelementof surprise that might otherwise help hislate worksto be more successful. The criticism is often heard, that one can tell ahead of time how a late work of Hindemith will sound. In the piano introduction to the first version of Maria [The Annunciation], Verkundigung it is curious how unified all the sonorities are (like in the music of Schonberg), and yet how
The revised not be
should
distantly contain of
these
unmistakably modulating
related they actually sound (see Ex. 10:18).All of the chords (except the last one) contain and four of the six sonorities sevenths or minor ninths. In spite tritones, major unified sonorities, however, the outer move in a pattern that is voices Schonberg-like The bass leaps three times by perfect Hindemith. fourth against a carefully tonal
melody.
Example
f =Half P
10:18
step
$
= tritone
Nicht
i
f
r
w
?
Ml
r? S2W
S2W
s2w
S]W S2W
Si
I do not exercises in the style of Hindemith, Though it is possibleto write compositional recommend such assignments. Betweenthe works of Hindemith and his German disciples,there aresomany pieces written this style, that it is an all but worn-out musical approach. It deserves
a well-earnedrest.
4. was
are
Sonority
as
Theme
(Messiaen)
The idea behind Debussy's Tiercesalternees to Thirds] from Preludes, BookII [Alternative of musical materials from intervals other than the third. In addition, there construction a number of piecesin BelaBartok's that share the same series Mikrokosmos piano-pedagogy the
351
and material
of inspiration
kind
to construct
used
element
sonoritiesor elementscan work. Although componentsfrom of the
Aspects
an entire
from
piano work Vingt is interesting movements
Leitmotif
employ the concept
of a combined
other
surface
often
serve
Regards
sur
VEnfant\342\200\224Jesus
because the musical situation single-voice of the
employ
pervadethe musicaltexture likea Wagner Themeof
examples
to the
in
details of a as the basic
composition is constructed.
1944
Several ofthe twenty
movements
are many
which
full-length
particular harmonic In fact, such
a composition.
these
Child\342\200\224Jesus]
ambiguous.
or a
sonority
a particular formal element is transferred elements are not necessarily melodic, they
Messiaen's
Oliver
chordal
A
where
music
twentieth-century
restrictions.
sonorities can bethe central ideabehind be considered thematic. There actually
{Theme
melodic-harmonic
[Twenty is even
more
melodies that thematically
Star and the Cross).Several theme (Theme of God;
Love).
somewhere
Standing
invents the Theme
d'accords
between the [Chord
[large-scale]form
and
the
surface
consists offour,four-
Theme],which
details, Messiaen
voicesonorities(seeEx.
and sonority structure Each of these chords is quite different in terms of its intervallic the Chord Theme, only content. Of the sixteenpitches within the tones F#, G#, Bb [A# ] and Blj once. are used twice. The other tones of the chromatic scale are employedonly eight
10:19).
10:19
Example
*^=
^ii^^f^ ft i:
i/e
iftUe
12
3
4
are treated likethematic material the entire composition. In throughout further without simply appear in a rhythmic setting These same sonoritiesalso provide manipulation materials for other kinds of textures, (see Ex. 10:20a). where the Chord Theme can other chord of the no longer be heard. In movement VI, every is used to material for an texture (Ex. 10:20b). The sonority-theme provide pitch arpeggiated Theme d'accords concentre two of Chord Theme] occursin movement [Concentrated IV, where the sonorities are counterpointed in other movement the two these (Ex. 10:20c); XVII, against other in a sonorities each different counterpointed appear against arrangement (Ex. 10:20d). These
movement
four chords
XTV
these
sonorities
352
Ex.10:21
contains
an
horizontal
This excerpt shows that excerpt from movementXTV. or vertically in the twelve-tone method are quite sonorities partially lie outsideone another in the Chord-Theme
analysis
the processesof setting pitches similar, since the pitchesof the
of an
horizontally
dimension.
Example 10:21
5. Discussionof SelectedTwentieth-Century
Sonorities
first sonority we will examine from the middle section of Hindemith's comes 1 in from drei Pieces (No. [Studies in Three Pieces],1925).In Ubung composition, of the piece, there are long two-voice sixteenth-note this section runs, markedppp. Twelve times, likethe crackof a whip, these soft runs are interrupted by a singlechord marked#(Ex. 10:22). occurs in the music of Hindemith, Bartokand This percussive use ofsinglesonorities frequently 1.) The
KLaviermusik
others. The
use preferential
strong
of the perfect fourth in this sonority foreshadows Hindemith's same interval in the sonoritiesof his later works. This intense sonority,
predominance
this
dissonant My harmonic
component(E-C)
role
in the
of this
(formed by three
intervals
typical of hislater works,
perfect
fourths
a half-step
with
four
apart), would not be
however.
since the third-sixth description, symbol S2K offersonly a negative and does not take an active foreground sonority is hidden in the inner voices
sound of the chord.
Example10:22
2.)
Berg's LyrischeSuite[Lyric Suite] for string quartet (1926), the four instruments their respective double stopsten timesin a unison rhythm 10:23a). atj9f(Ex. repeat This creates an eight-voicesonority which consists of a series of half-stepsinterrupted by only On
one minor
page
third
69 of Alban
(Ex.
10:23b).
Example
10:23
-* I
^^^^^^ 354
JlS5
\302\273t
the aural Many neighboring pitches sounding together in the same registertend to lessen interval within the sonority. In other words,the dissonant impact of the individual qualities effect of such a sonority is weakened. Sincemajor sevenths or minor ninths are the strongest dissonant other pitches to the sonority. (In the intervals, they can only be weakened by adding third scene of the third act in Berg'sWozzeck, where hand becomes covered with blood, Wozzeck's a major seventh drills itself unabated into the ear throughout the entire scene.) is found a few measures later in the LyrischeSuite. This is also sonority spot the a as in This the formed by repeatedrhythm (2) above. time, however, celloplays pitch E twice then to the E it adds a double-stopped G which is also repeated; following the viola alone, this, enters above the on-going with a repeated Db before adding a double-stopped cello double-stop B . . . etc. Ex. 10:24 shows the resultingeight-voice built upward from the bass; the sonority, interval content of this sonority is indicated below the example. This chord has a more intense than the sonority in 2.) above.This holdstruein spite of the fact that this later sonority: impact wider are spread out over a much a) has the same number of pitches;b) its pitches c) the range; interval content is much weaker all the rest of the intervals are is only one perfect fifth; (there thirds and sixths);d) the note-for-note entries of each ascending pitch tends to weaken the available strong dissonances. The listenerwill hear this sonority as radiant and gloriousrather than harsh is pronounced and strong. The impact ofthe third-sixth component as compared to Hindemith's sonority in 1.) above.
3.)Another
10:24
Example
m3
turn 4.) At this point, we will movement actually completedby another. The first ofthesetwo is in Ex. 10:25, the secondclimax trumpets after a passagefeaturing
m6
m6
M3
m3
m6
Symphony. sonority in Gustav Mahler's Tenth two single tutti climaxes, markedff, directly an At -minor triad in a conspicuouslyhigh register. the (measure 4) is brought to completion with
to a
In the
only
Mahler,
follow
one
woodwinds,
horns,
355
strings.
As is entry
shown of the
Example 10:25
1st
The
climax
chord in
+ woodwinds
+ strings
measure 4 isproduced
added
sonority
total chromaticlacksonly
by adding
=
1st trumpet
four thirds
woodwinds. 4 trumpets, strings
(F-D-B-G#)underthe unison
excerpt. In addition three thirds are successively second climax sonority is constructedfrom nine separate
by the strings at the beginning above this A (C-Eb-G).The entire
of the
A played
tones (the
+ 4 trumpets
the
construction in thirds would later
E, F#, and Bb). This type dominatethe musicof Berg. The
of straightforward
pitches
stacked-third
chord
sounds extraordinarily exciting, wild an atonal and threatening, however, and it creates It is especially shockingafter outburst in the midst ofa broadly tonal the previous movement. Ab-minor tutti. Each ofthe sonoritiesin this example takes on a particular character from its it immediately immediate environment. since The third sonority sounds somewhatlessintense, follows the noisy eight-tonesonority the 2). The strong dissonant relationship between (sonority a outer is also In the first sonority, the G# (stoppedvoices factor in the sound intensity here. C in the second sounds the high A, whereas the C# bass sounds against the high horn) against between top and bottom of the sonority. sonority, thereby enlarging the interval 5.) We shall now discuss the sonorities in Berg's operaWozzeck.
effect
of
register
on sonority,
by
looking
at two
chordal
doctor sings the line on page 133 of the er kommt ins Narrenhaus\" [Wozzeck is going to the mad-house] \"Wozzeck, score. of two parts that have no As is shown in Ex. 10:26, this harmonic structure consists with each other in terms ofregisteror articulation. connection It is as though Berg employsthis is repeatedstaccato to loss A dense E-minor triad of reason. and sonority express high against a low and sustained minor the seventh. clarinets an octavelower than the flutes here Placing would have destroyedthe musical effect. The
chord
first
356
appears when the
Example
10:26
2Hns. low
strings
chord is found act. In this scene, Marie at the end of the secondscenein the third is dead and a fleeting bassoon motive is played. As Wozzeck silently drowns himself, empty perfect fifths covering five octaves sound in the orchestra (seeEx. 10:27).Below this stack of fifths, the harp continuesto play its lowest pitch, which has soundedlikea drum beat throughout toward the borders of hearing the entire murder scene.The upward extension of the empty fifths of Wozzeck's is a spiritually musical situation. gesture that expresses the hopelessness precise The second
Example 1st.
10:27
violin
(harmonics)
8\342\204\242-
]4R ~J
2 Tpt(muted)
i 2nd
^
1 2Hns. E'
6.)
An intended
sonority
instrumentation. In orderto will look
at
two
more
passages
effect can either
discuss
Vln.
the relationship
in Wozzeck
=
be clarified
~]
Harp
or
obscured
between sonority
through
and instrumentation
and a passagein anorchestralsong
by
Hans
specific we
Werner
Henze. a spot in the fourth of the first act in Wozzeck Ex. 10:28). First we will discuss scene (see a would be usual for This harmonic the Here, low-register quartal sonority. practice strings play that this uses thirds. reason calls seldom sonorities without but (For Berg sonority Hindemith, to itself.) attention Against this dark empty sound,the four flutes enter witha warm and glowing sound in double tritones. The separation of the two sonority groups is perfectlyunderstandable have appeared in this G in the strings, a major-seventh would spot. Had Berg set the F# against
357
in the top voice of the string and texture, thereby bringing this interval to the foreground flute its Bb with the exchanged intensifying the sonority. On the other hand, had the fourth been weakened. The instrumentation is have viola's G, the effect ofthe doubletritones would explainedby the text: Wozzeck sings, \"Dunkel ist, und nur noch ein roter Scheinim Westen\" [It is dark, but there is yet a red glow in the west].
Example10:28
sustained orchestra sonority after the unaccompanied Lieder from 1957 (see Ex. 10:29). recitative of the singerinNeapolitanische HadHenze exchanged mixed the pitches of the winds and strings, the guitar or instrumentally entrancewould have been obscured (the strings play the pitchesof the open strings of the guitar) and the charming instrumental contrast of tension in the complete would have been lost. sonority Now
.we will
look at
the
way
Henze
the first
orchestrated
Example 10:29 sip
h winds
.
.'.\"
strings
complete
.
* *
pitch
*
inventory
of sonorities. In a subsequent provide a specialintensification first act of Wozzeck, Wozzeck sings \"Es ist, als ginge dieWelt in Feuer auP [It is as though the world has gone up in fire]. Berg sets this text by introducing The instrumental groups oneat a time until an eight-tone chord is established (seeEx.10:30a). the five first instrumental enter but a takes after entrance crescendo place fpp only groups orffp, of the last woodwind this then first after the entry ofthe last woodwind group. However, group in the the minor seconds Ex. (C#-D), entering/, places foreground(see 10:30b). clearly Naturally, this if the oboes and clarinets had intense final entrance would have appeared much weaker, playedpitchesof the sonority that were already sounding (seeEx.10:30c).
Instrumentation
passage in the fourth
can also
scene
of the
358
10:30a-c
Example
Example
10:31
-s
The and fifth
sonority
shown in
and
Ex. 10:31ais a major
and the sonority shown in Ex. tritone. Neither of the two sonorities
tritone,
\302\273 \342\200\224
seventh
10:31bisa minor contains
with ninth
third-sixth
an intermediate with
perfect
an intermediate
fourth
perfect
components. These sonorities anichsteiner School, who base
works ofWebern and composers Kr of the on Webern. these sonorities could be labelled compositional techniques Though S2 W K in a such occurred Hindemith work), looses its meaning when an entire (if they labelling is based on such harmonies. A harmonic composition labelling system can only represent when a variety ofchord typesconnected to one another. something significant It is possibleto usetermssuchas chord-conta tension or strongly dissonant sonorities, ining and stable sonorities with music such as Hindemith, sonorities,weak sonorities by composers tend to employ Berg,Henzeand many younger composers of the present, becausetheseartists a large number of sonority in their works. This is partly the way things have always been, types a return to earlier practices. and partly Before we can accurately we must seek out the sonority discuss single sonorities,however, that is an to individual work. It is the common of harmonies in a work that sets palate palate the boundariesfor the ear and which creates a measuring stickagainst which we can judge single predominate
many
of the
their
sonorities.
359
TableofFunctional
Symbols
The following
is a
T43
functions to I, IV
These lower-case letter stand for the primary harmonic functions and dominant) in minor keys;analogous subdominant, toi, iv, (tonic, and v in the Roman-numeral/flgured-bass system.
s, d
Tl 2
3
78
t3
f
book:
These
l5
D565
used in this
symbols
analytical
harmonic letters stand for the primary upper-case and dominant) in major keys; analogous (tonic, subdominant and V in the Roman-numeral/figured-bass system.
JSP
t?
brief explanation of the
numbers following the
Subscript
chord factors
functional
Superscriptnumbers
indicate
t
Superscriptnumbers
may
the top-most voice.
D7S6 T7 D?D5
also
refer to
the
factor
chord
present in
also indicate added tones numbers in the upper voicesand bass, respectively.
Superscriptand
subscript substitutions
chord-factor
bass.
events in one of the upper
melodic
voices.
T3 D;
which
indicate
symbol
appear in the
tones
non-harmonic
and/or
or
are Small arabic numbers modifiers) (without always stand for chord factors or non-harmonic tones which diatonic to the major or minor of the D , when it appears before t, will key in force. Therefore, the ninth the minor sixth is implied in be a minor ninth; the ninth of a D before T will be a major ninth. Similarly, D4 3 t, and the major sixth in the progression the progression D4 3 T.
The
T)1
symbol ( > ) indicates that one half-step (in this case,
lowered
The symbol
6<
(<
) indicates
raised one half-step (in
this
the
chord
the fifth
that the chord case, the sixth
factor is
of the
chromatically
chord).
dominant
is chromatically
factor
above the
subdominant
chord).
D4
>
3 T
Despitethe above the
The line
Sf 1 5
s
1
major-mode dominant
after
implication is chromatically
a functional
of the
symbol indicatesthat
functionholdsthroughinoneormorevoices(similartoapedaltone).
chord (= s6).
Neapolitan-sixth
361
resolution
chord,
the
sixth
lowered. the
root tone
of that
t> 7
9
j>
5
The slash
chord is not The
\302\243)v
that
symbol indicates in the sonority.
the
through
present
chord
diminished-seventh
Wilhelm Maler's system,
this
the
root-tone
resolves to t appears as D .)
] which
[vii
symbol
Note:$ should Maler's
be numbered: 1,3,5,7 above the leading-tone, chord be considered a dominant-ninth should
Dv
omitted root; therefore its members are numbered dominant. \342\200\242tBv
The
chord
diminished-seventh system this
T (qs D4
Tr
Tr *- (D5)
^) Tr
S,
Parenthesisaround functions tonicize
(In
whereas with an above the
3,5,7,9
symbol appears aslP').
Maler's
(T)7\")
or T.
resolves to Dor d (In
7/V] which
[vii
of the
or symbols secondary
the
indicate that these groups of symbols key area which follows.
Thearrowpointingbackwardsfromafunctionalsymbolinparenthesis is related to the key indicates that this function
of the
previous
function.
The sonority
[Tr]
(D,,)
however,
is substituted The
\302\243^7
the
within
goal of resolution;
S3
for
this
the expected brackets [ ] show the chord below the bracketed
functional sonority
goal.
expected
chord in major [vii ']. diminished-seventh Classical period. (In Maler's system
leading-tone
important chord in the symbol appears as B?.) D7
D? t
and
T
This sonority however, the
and vii
vii ii
*
and ii
^7
in major; in minor
Usefulin
labelling triads
diminished
(especially
Tr; tR
The minor
Tg, Sg
tG
relative tonic
figure
a sonority;
of sequences.Otherwise root-position seventh chords are quite
the middle
and half-diminished
in Baroque-era minor of a
rare
works). tonic
major
triad;
the relative
major of a
triad.
(Gegenklang) counter-relative chords (rare). The
major
minor
of a
counter-relative
tonic
chord
deceptive cadences).
TR
and
chord only in the Romantic era. with an omitted root tone) should 7 (dominant-ninth of music before the nineteenth century. analysis a discrete
latterbecame
The symbol B not be usedfor
as suspension
both
occurs
An this
The
major
relative
of a
major
tr
The minor
relative of a minor
tg
The
counter-relative
minor
362
tonic
chord.
tonic
chord.
of a
minor
tonic
chord
(important
in
Index A
48 D-S3;D,fallowed D-s, 104-5 106-7 D3,d3, S3,s3 S-D rare in Classical period 184 in Liszt 320 T-D-S-T
200-209
Chords
Altered
augmented-sixth functional German-sixth
chords 201-8 analysis of 202 202-3
Italian-sixth 201,203 a dominant-7th changing diminished-7th chord
Chromaticism
ca. 1600
to a 204-5
denned 200 generally motion to next chord leading-tone most important in Classical era producing ambiguous tonal
207 201
Atonality
9
317-20,336-41
inScriabin
tonic or
unison modulations 200 Counter-Relative Sonorities see*. Secondary Triads Chords) Counterpoint in Debussy 324
within
(Counter
B Johann Sebastian 1, 28, 34-5, 38, 43, 45-6, 68, 93, 163, 180, 182-3, 233, 307, 346 Bartdk,Be% 351, 354 Beethoven, Ludwigvan 193-194, 200, 217-218, 221, 223-224, 227-9, 233, 253, 264-5, 269, Bach,
272-4, 291 Berg, Alban
249-50
ulminished-7th
249 chord as goal of 271 double deceptive cadence 249-50, 289 in Wagner, not always deceptive subdominant as goal in Schumann 250
354-9
Bizet, Georges 255, 263 Chords from Minor 176-7 Brahms, Johannes 241, 253, 278, 320 Byrd, William 9 Borrowed
systematically denned 287-9 with dimixiished-7th chords 247 from one diiiunished-7th chord to
C Giovanni 9 Giacomo 9, 111 Emilio de 14, 22 Characteristic Dissonances (Baroque) 58-74 dominant- 7th (leading-tone abridged 67 triad) added-sixth chord 61 distinctive features 58 of origins considerations 60 voicing dominant-seventh chord as a source of melodic invention distinctive features 66 origins 63 64 voicing considerations Marc-Antoine 46 Charpentier, Chord Progressions D-S forbidden 38
Debussy, Claude 28, 239, 267, 317, 321-36, 351 see: Harmony of Debussy Deceptive Cadences 132-4, 269-70, 279-80 created by third relationships 227 D-tG 269-70 '&\"
another
Capello, Carissimi, Cavalieri,
70
250
9 Demantius, Christoph Descending-Fifth Sequences 147-153 harmonic tension 147 counterbalance Diminished-Seventh Chord as secondary dominant 169-75 common-tone resolutions of 246 division of the octave into four equal parts 312 enharmonic 247 spellings rootless symmetrical sonority 206 terminology concerning and traditional symbols 115 resolutions 247, 265 unpredictable Diminished Triad in Sequence 148 ii*1 in minor as s{ 151 see also: villas b7 151 Distler.Hugo 164 Dominant Function 28-42 ea.
1600 21
363
Schumann
242
in four voice configuration 244 possible inversions of 244 no true D? in Classical period 186 Schumann's use of DS 236,240-1
terminology 115-16
229-32 above
doniinant 110 structure 308,312
wide-ranging
model for chromatically ascending bass line 265,272 connections in the fourleading-tone tone sonorities of Wagner 282,286 227-29 leading-tone relationships note-for-note sonority transformation
110-11 Triads in Liszt 308-9,313, as ground sonority 317
symmetrical octave
2
with
relationships
Augmented
338 as suspension figure
in Gesualdo harmony
implications 207
Anerio, Giovanni Francesco
14
chromatic bass lines 106-7 in Bach 160 in development sections 196 descending
term 30 Chords 236, 242-4 abridged dominant-ninth chord (b?) 244-50 in all its functional 245; possibilities see: Wagner's four-tone sonorities as a discrete sonority in dominant-ninth
origin of Dominant-Ninth
Chords abridged (leading-tone triad) 67-68 as passing sonorities ca. 1600 63 free progressions 237-9 functionally in Bach 64-71 in minor (Baroque) 103 in Wagner four-tone sonorities 286 incomplete spellings 65 non-functional dominant-7th Chords 237-9 Rameau doniinant 30 if (v'/V) as dominant function 62 278 Donizetti, Gaetano Doubling and Voice Leading 11-17 seealso:Parallel Motion, NonHarmonic Tones, and Doubling cross relations 14-15 in resolution of Neapolitan-sixth chord 112 in first-inversion triads (Baroque 42-6 and Classical) in leading-tone triads 68 in minor keys, 94-109 in chords-of-the-sixth ca. 1600 26,42 in the Classical period 42-6,178-80 in the Neapolitan-sixth 112 in root-position and first-inversion triads in minor 107 in root-position triads ca. 1600 9 in root-position triads in Bach 37 doubling and voice leading 37 irregular leaps in several parts at the same time Dominant-Seventh
37-8 crossing 11 ranges, spacing between voices 10 with 0\" (leading-tone dim.-7th) 123-5 Dufay, Guillaume 16 278 Dvofcik.Antonui voice voice
Expansion analysis
Tonal Space of sec. key area
of
154-64
with
parenthesis () 157 of the dominant of the dominant dominant- flP 164 dominant of the dominant-- fi* 154, 155-6 substitute for subdominant 156
melodic arch
four-phrase
inthe
leading-tone
154
dominant
154
key
Triads 42-50 nature in time of Bach 43 triad 66-70 than root position 209
First-Inversion transitional leading-tone less stable
Neapolitan-sixth 111-14,209 chord-of-the-sixth
subdominant
in
subdominant may follow dominant one or both are inverted 47 Freedom from Tonic 251-4, 280 brought age of sonata form to end Functional Romantic ambiguity in
if
253
the
era
247
Fundamentals
Functional Harmony to confirm key 29 perfect fifths between of
at least three descending
triads
roots 28 music 30 early employment in secular intermediate key areas related to tonic-ca.l 600 35 major role of primary triads in music 31 froml700-l850 15-17, parallel perfect consonsonaces
38
and tessitura changes 39-40 T-S-D-T (basic progression) 36 three basic functions (T,D,S) spacing
denned
30-2
poles of harmony
as principal
31
G Gallus, Gesualdo, Grabner,
Jacob 15 Don Carlo 2 Hermann 130, 342
H George Frederick 38, 46, 48, 54
Handel,
Harmony in Debussy counterpoint
texture
Pelog tuning
32l
Phrygian mode 321 and whole-tone scales 321-3 321-2 tuning like pentatonic 321 like whole-tone 322 tension-free pitch environment 326 in Liszt 307-20 Harmony central ground sonority 317-18 like S16ndro S16ndro
in
60
major
subdominant chord-of-the-sixth minor 104
332-3 mixtures and mutations 327-8 331 -2 modulating mixtures mixtures 333 polyphonic real mixtures 328-9 Slendro mixtures 333 tonal mixtures 329-30 framing mixtures defined
321 -35 cannot explain musical
324
music 321-24 function of instruments in 321 how Debussy's music is similar to 322-23 no traditional consonances or 322 dissonances 322 strong impression on Debussy
gamelan
harmonic textures 324-35 334 harmony and structure unified interdependency of harmony and structure 334 phrase non-melodic tones 334 interval above bass not as important as in traditional music 326 non-traditional voice leading 324 organ mixture-like sonorities 327-33 atonal mixtures 331
continuous
harmonic transformations 307 end of tonal harmony
313-17
harmony groundbreaking sets of thirds 317 layered melodies containing 12 tones
modal and 319
pre-functional
309
308 materials
subdominant and in progressions 320 of tonality 310 cells momentary voice leading 311 non-traditional role of the diminished-7th chord and augmented triad in transcending 312 tradition 309-12 tonality as reminiscence 311 loses tonality strength of stability two paths to atonality 317-20 in 309 Wagner's four-tone sonorities in Opera 255-77 Harmony ascending harmony chromatically of exchange dominant
256
contrast 265,
of textures 268, 273, 274
climax 269-74 used for impending danger 264-69 uncertainty expressed by passages with augmented triads 255 274-7 large-form disposition of materials 255 repetition overstatment 257 operatic requirements of 255 resolution of conflict 268-69 series of deceptive resolutions 257 stable and unstable harmony in ariasand scenes 258-60 in Scriabin and Schdnberg Harmony 336-42 bass deprived of fundamental role dramatic harmony
338
concealed
uncommon in Schonberg's 341 sonorities use of tritones and augmented triads Thirds
338, 346 and pitch classes per sonority 337 in the Classical Era 178-214 Harmony basic harmonic progressions connect to larger formal elements 183 of style change 179-80 characteristics 183 chord progressions are simple harmonic simplicity is characteristic of 180 style 278 of melody importance 180 a new tempo presto, followed progressions with dominant by subdominant 184 materials 181 of repetition of bass lines 180 simplicity slow introduction sections 210-13 slower harmonic rhythm than in voices
180
Baroque
233-54 Harmony in Schumann 278-306 Harmony in Wagner ambiguity of consonance and 291
dissonance
avoidance of key implication 289 cadences in atonal space 278 281 elusive tonal implications four-tone sonorities 2S3-92,309,313, 346 root tones 286 ambiguous chords of reduced tension 296 common-tone connections between the sonorities 286 hallmark of style 286 in opening of Tristan Prelude 296 interval content 2S6, 290 between leading-tone connections 2S6 the sonorities with changed traditional sonorities roles 287, 290 functional harmony no longer applies 298 of sequence in 291 importance Leitmotif 292 lengthening of time between similar musical events 2 77 lengthy passages in functional harmony
296
model for analysis 298-306 most creative aspect of his style non-recurring progressions 298 290 resolution of dissonances setting of text 281 transitional consonances 285 292 Tristan Chord
unpredictability
292-5 296 analyses of resolution
291-2 where tonality
and atonality
analyses
fifths 338-9 between voices 338 of topmost interval 338
perfect
equilibrium importance role of the octave 339 stands outside of tradition 346 338 dissonances in sonorities strong surprising unity of sonority choice ca. 1915 336
364
summary
297
of of
278
meet
of Scriabin and Schonberg 336-41
Harmony
consonances require justification
341
Hans Leo 9 336 Hauer, Josef Matthias Haydn, Franz Josef 42, 46, 194, 200, 219, 346 94 Helrnholtz, Hermann Henze, Hans Werner 357-9 Paul 16, 336, Hindemith, 346-50 354-5, 357, 359 Hindemith's Sonority Classification
in Baroque 244 in Classical 244 origins 242 two ways of interpreting 244-5 as discrete sonority in Bach 119 as suspension figure resolving to
HaJJler,
leading-tone keys (rf7) 186-7
major in Wagner 286 mixture of dominant
346-51 for traditional and nontraditional sonorities 346
allows
author's revision of system 348 for revision 349 reasons Hindemith's music somewhat insulated from his theories 347 system explained 346-7
best interval 347 347 step progression use oftritone to decrease intensity 348 to traditional use of compared tritone 348 ca. 1600 Homophony 26-7 chord-of-the-sixth cross relations 14-15 forbidden parallel motion 15-17 16 author's explanation two traditional 15-16 explanations hidden parallels 17 linear considerations 13-15 between voices 10 spacing cadence 20-22 suspension triads in first inversion 26-7 triads in general use 9 9 triads in root position vocal ranges and tessitura 10 11 voice crossing voice leading considerations 11-17 278 Englebert Humperdinck,
Jadassohn,
Salomon
295-6
103 Karg-Elert, Sigfrid Kistler, Cyrill 295-6 292-3, 296 Kurth, Ernst
Lasso, Orlando di 10-11, 13-15 Motion 36-7 Leading-tone not always prohibited, 47 doubling in dominant-seventh resolutions 64 D7 with incompletly 65 spelled Italian downward-resolving leadingtone, 261-4 in minor 97-100 in chromatically resolutions non-traditional fashion 106-7 new methods of resolution 246-7 relationships 227, 281-2, 337 Chord 115 Diminished-7th Leading-Tone chord (e?) dominant-ninth abridged 115, 244, 246
118
dominant-7th
Classical-era
no
and
nant 120 true Dom.-9th chord
116
seventh in
subdomi-
in Baroque
116-18 in 9-8 sus. resolution considerations 123-5 Leonhard Lechner, 9-11, 14 Franz 307-20 Liszt, 278, see: Harmony in Liszt 293 Lorenz, Alfred Louie.Rudolph 176, 293, 296 origin
M 253, 274, 318, 355 tonality (Rameau) 28-30 clausulas, closing formulas, cadences,
Mahler, Gustav Major-minor
4-3supension
20-22
of minor 95 problem with derivation Maler, Wilhelm 32, 42, 103, 120, 129, 131, 210, 251 Mayrberger, Karl 293 Ohver 336,351-53 Messiaen, 351 -53 Sonority as Theme Messiaen, thematic musical elements 352 Minor Mode 94-109 dim. 7th as harmonic/melodic axis 97 dominant followed by subdominant
104-5 ease of modulation functional symbols
to rel. maj. 107 for minor triad
103 lowered 6th and 7th scale-degrees in tonicizations of relative major 101 melodic cliches in Baroque 96-7 95 scale forms descending chromatic scale in bass 106 descending minor scale in bass 106 nine-tone complex 95, 97, 176 theories about the minor triad 94-5 triad doublings 107 97-8 typical melodic patterns of subdominant chords 103-4 variety Modal Scales
Aeolian
320
320
Mixolydian
321
Rirygian
Modulation Bach's
progressions employing various intermediate key area 35-6
chromatic
note-for-note
transformation
continuous continuous
sonority
229-32
development modulation
253
365
253 in Schumann
D-t = T-s = four flats downward in circle of fifths; t-D - s-T = four sharps in circle of fifths 220, upward 223-4, 230 l5> toD 154 of all i5\\ (D), (DT) as tonicizing agents
scale-degrees 159 0* leads to other #v 250,265 0\" in major keys, 206 0\" to all scale-degree 169 variation developmental from D', the \302\243v is formed in the bass half-step
253
by ascending 204-5 through freely descending half206 steps in upper voices functionally free diminished-seventh chord progressions one tone remains common 247-8 two tones remain common 246 in Classical era 187-200 227-9 leading-tone relationships, triad reinterpreted major first-inversion as a Neapolitan- sixth (five flats downward in circle of fifths)
197,209 146 key to its dominant minor key easily broken-down by faulty voice leading 101 minor key to its relative major 107, major
146,166,194 model
ofharmonization
chromatically ascending
abovea bass (D'-Ef-tj-D7)
Beethoven, 272 265
Mozart,
modulating passages without a main tonal center 279-280 $to 158 Schubert's modulations around the circle of fifths 223-27 diatonic descending fifths of 202 ST, D7, and '\302\243>', similarity
without
163
see examples, 208-9 T-t (three flats downward in circle of in fifths; t-T three sharps upward circle offifths), 197,211,227,231 third relationships, 215-23 to Seeond theme area in Classical era 189-96 after half-cadence and G.P. 189 application of the dominant of the dominant 190 by unprepared secondary dominant
189
common chords between keys 190-1 within Classical development section 196, 280 abrupt shift of mode 197 199 by way of unison passages reinterpretation of two triad tones 198 Classic-era development typical section 197 unison half-step modulation, 200 268 Monteverdi, Claudio Mozart, Wolfgang Amadeus 42, 183-4, 194-5, 209, 216. 258, 265-6, 309, 324
N
harmonic
traditional
progressions
in
233
Chord 111-114, 209 discrete sonority in Baroque 111
Neapolitan-Sixth
doubling 112
161-2
0 164
Debussy's use
Non-Harmonic Tones 75-94 91-4 anticipations escape tones and appoggiaturas
neighboring tones
89-90
77-9
passing tones 75-6 suspensions 20-22, 82-9 in Bach 82-9 in the six-four figure 52-3 in Wagner 290, 296-7 ca. 1600 (4-3-sus.) 20-23 triad 110 origins of the augmented origins of the dominant-seventh 63 origins of the Neapolitan-sixth 111-
12
and 2-1 suspension
9-8
117
figures
115,
159-61
Secondary Subdominants # (rmgor keys) 158,162-3 jP (minor keys) 165-6 128-46 SecondaryTriads 130 counter-relative chords defined in major and minor counter-relatives
131
O Joachim
von
94
P Giovanni Pierluigi 10, 21 Parallel Motion forbidden parallel motion 15-17 author's explanation 16 two traditional explanations 15-16 hidden parallels 17 Pentatonic Scale 321-2 pure pentatonic texture 323 9 Peri, Jacopo Palestrina,
Perotin
chord as secondary 169-75 172 to any scale degree applied to dominant 169-75 applied resolution in Classical era 173 dominant of the dominant 155-6 in minor most useful 165 smaller role in minor 165 resolutions with brackets substitution [ ] 163,245-6 symbols for secondary dominants diminished-7th dominant
in major keys in minor keys
Oettingen, Arthur
14
Alexander 336-41 346 Scriabin, Dominants 157-75 Secondary backward referencing tonicizations
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