John Vincent - Diatonic Modes in Modern Music
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In which the employment of modes in contemporary music is discussed....
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THE DIATONIC MODES IN
MODERN MUSIC
THE DIATONIC MODES IN
MODERN MUSIC
JOHN VINCENT
UNIVERSITY OF CALIFORNIA PRESS Berkeley and Los Angeles
:
195
f~
/>
University of California Publications in Music Editors
(Los Angeles)
:
L.
A. Petran, R.
Volume 4 Submitted by editors July
pp. xiv 1,
U
Nelson,
•
Publishers: Mills Music, Inc.,
H. Rubsamen
1
1947; issued
Price.
W.
+ — 298 November
15,
1951
J 12. 00
New
York, by arrangement with
the University of California Press, Berkeley and Los Angeles
280*34
Copyright 1951 by Mills Music, Inc., 1619 Broadway, International Copyright Secured.
New York
All Rights Reserved.
.df!
Manufactured by
offset in the
United States of America
To Glareanus (1488-1563) Whose Modal Theories Influenced Four Hundred Years of Music
—
Preface
WHEN
Glareanus
brought out his Dodecacbordon in 1547
and more that the traditional
was
usage. Glareanus' purpose
it
had been apparent for a century
modal theory did not square with the contemporary
ecclesiastical
to reduce the existing practice to a practicable theoretical for-
He could hardly have realized to what degree his work was prophetic of the He could not have anticipated that his system of twelve modes would remain
mulation. period.
hundred
for four
years. It
is
work was not only recognized so penetrating
nomena
tonal (Major-minor) practically unrevised
a tribute to the validity of Glareanus' deductions and conclusions that his as a true interpretation of his
immediate past but also that
his theories
were
and so soundly based on and integrated with the developing and evolving musical phe-
that they remained authoritative for centuries even though musical styles changed radically.
Nevertheless by the beginning of the
last
century there were signs that even so cogent a theory as
Glareanus' must eventually be reexamined. All during the nineteenth century the tonal horizons widened
and with the coming of the twentieth century the process was greatly accelerated. The disparity between and practice was ever greater and the need for a new modal formulation became always more
scale theory acute.
In an attempt to answer this need,
I
have made exhaustive researches into existing practice and have
arrived at a formulation of eight Diatonic Modes. likewise founded
A
A
further theory
on good usage by recognized composers
meaning
codification of practice has
historians, teachers, or students.
what has been done,
it
for future progress. It
A
valid
my
is
Modes
—
is
for all musicians, be they performers, theorists, composers,
new
also provides a solid
the Interchangeability of
of the past century or so.
theory not only explains and promotes understanding of
and substantial observation point for surveying favorable paths
hope that the theories
I
have advanced will have significance for these
important matters.
name George W. Chadwick, who gave me my first instrucwho encouraged me to develop my own modal theories. I wish to record also my indebtedness to Walter Piston, whose penetrating criticisms did much to insure the validity of my ideas during the developing stage; to Dr. Hugo Leichtentritt and to Dr. Otto Kinkeldey for their interest and for reading the manuscript; to Roy Harris, who in many ways helped keep the project alive. I In recording obligations,
tion in
modal
theory, and
it is
a pleasure to
John Powell,
gratefully recall the assistance of the following institutions: the
New York Paris,
Music Library of the Boston Public Library,
Public Library, the Music Division of the Library of Congress, the Bibliotheque Nationale of
and the Staatsbibliothek of Berlin.
My
greatest obligations, however, are to
my
col leagues in the
Music Department
at the University of
California, Los Angeles, Professors Robert U. Nelson,
Walter Rubsamen, and Laurence A. Petran, each of
whom
To Mr. David Brower and
read the text and gave invaluable suggestions.
the University of California Press,
Mills Music, Inc., to Mr. staff, I
thank
owe
Mack
I
owe much
Stark,
other staff
members
for their careful supervision of all technical matters;
Mr. Jack
Ecoff,
Mr.
Norman H. Warembud, and
Lillian
Adams,
for her great help with all
the bibliography and index. Finally,
I
must acknowledge
without the inspiration and assistance of
Los Angeles
December, 1950
my
manner
that the
of correspondence,
of at
the production
a debt of gratitude for their unfaltering cooperation and heart-warming enthusiasm.
my secretary,
and
I
wish to
and for typing
work could never have been
finished
wife, Ruth. J.
V.
/
Acknowledgment
Wish
I
to express here
owners
who gave
my
many
appreciation of the courtesy of the
permission to quote from various publications.
American Library of Musicology,
New
publishers, agents, and copyright
My
thanks are due the following:
York, by permission of the George Grady Press,
Agent, to quote from
Inc.,
A
Theory of Evolving Tonality, by Joseph Yasser Augener & Co., London, for permission to quote from Harmony Simplified or the Theory of the Tonal Functions Chords, by Dr. Hugo Riemann, trans, the Rev. H. Bewerunge. of Breitkopf und Hartel, Leipzig, for permission to quote from J. S. Bach, by J. A. P. Spitta. Schirmet Music Company, Boston, copyright owners, for permission to quote from Principles of Harmonic
E. C.
Analysis, by
Walter
X. Le
F.
Piston.
&
Roux
G. Schirmer,
Cie, for permission to quote
New
Inc.,
from La Musique grecque (Edition Payot), by Theodore Reinach.
York, for permission to quote from Sketch of a
New
Esthetic of Music, by Ferruccio
Busoni, ttanslated by Th. Baker.
Harvard University, Cambridge,
for permission to
and Practice from Rameau to 1900," by V.
Henry Holt and
Co.,
New
quote from
a doctotal thesis,
"The Relation of Harmonic Theory
L. Jones.
York, for permission to quote from Jewish Music in
its
Historical Development, by
A. Z. Idelsohn.
Houghton Mifflin Co., Boston, for petmission to quote from Modern French Music, by Edwatd Burlingame Hill. quote from the Preface to My Ladye Nevells J. Curwen & Sons, Ltd., by petmission of G. Schirmer, Inc., Agent, to Booke (William Byrd), by Hilda Andrews. Journal of the Folk-Song Society, for permission to quote from "Note on the Modal System of Gaelic Tunes," by Annie G. Gilchtist; "Modal Survivals in Folk-Song," by E. F. Jacques. Kistner und Siegel, Leipzig, for petmission to quote ft om Neue Harmonielehre by Alois Haba. La Revue musicale, for permission to quote from "Cours du College de France," by Jules Combarieu; "L'Har.
.
.
,
monie," by Alfredo Casella. Librarie Fischbacher, Paris, for permission to quote
Librarie Renouard, Paris, for permission to quote
Longmans, Green
Tone
from La
Pluralite des
modes
et la theorie
generale de la
mu-
by Xavier Perreau.
sique,
.
.
.
,
by H.
&
L. F.
Macmillan Company,
Modern Music,
from Histoire de
New
mission of H.
&
Co.,
langue musicale, by Maurice Emmanuel.
York, for permission to quote from Grove's Dictionary of Music and Musicians,
for permission to quote
from "Problems of Harmony," by Arnold Schonberg.
Charles Nef, for permission to quote from Histoire de
Novello
la
London, by permission of Abr. Lundquist, copyright owner, to quote from Sensations of von Helmholtz, translated by A. J. Ellis. Co.,
musique
la
(Paris, Payot).
London, for permission to quote from Diatonic Modal Counterpoint, by Ralph Dunstan; by per-
W. Gray
Co., Agents, to quote
from Theory
of
Harmony, by Matthew Shirlaw. New Harmonic Devices, by Horace Alden
Oliver Ditson Co., Boston, for permission to quot? from
Miller,
and
from Seventy Scottish Songs, by Helen Hopekirk.
Oxford University R.
O Morris;
and from
Ptess,
A
London, for permission to quote from Contrapuntal Technique in the 16th Century, by
History of Music in England, by Ernest Walker.
Preston, London, for permission to quote from
A
General Collection of the Ancient
Irish
Music, by Edward
Bunting.
Simpkin
&
Co.,
London, fot permission to quote from English Folk-Song: Some Conclusions by C. .
University of Chicago Ptess, Chicago, for permission to quote from
A
J.
Sharp.
Theory of Modulation, by Thorvald Otter-
strom.
University of Rochester, Rochester, N. Y., for permission to quote from the doctoral thesis, "The Evolution of
Harmonic Consciousness," by Ruth Hannas. Winthrop Rogers, London, by permission of Boosey Counterpoint, by C.
W.
Pearce.
&
Hawkes, copyright owners,
to
quote from Modern Academic
Contents
Introduction
1
THEORY
Book One:
.
.
Part I.
II.
Harmonic
Analysis:
A
5
•
.
.
A
I:
Diatonic Theory of Chromaticism
Brief Critique and a
III.
The Diatonic Modes: The Ordinal and
IV.
Interchangeability of
V. VI. VII. VIII.
IX.
X.
XL XII.
Theory
Extra-major-minor Chords: Tonic Forms
23 38 42
Extra-major-minor Chords: Supertonic Forms
56
Extra-major-minor Chords: Mediant Forms
65
Extra-major-minor Chords: Subdominant Forms
77
Extended Harmonic Resources
Extra-major-minor Chords: Dominant Forms
85
Extra-major-minor Chords: Submediant Forms
,
Extra-major-minor Chords on the Seventh Degree II:
I:
The Diatonic Element in Ancient Greek Music The Ecclesiastical Modes XIX. The Scales of Folk Song XX. Genesis and Growth of the Major-minor System XXI. The Minor Mode
The Use
The Genesis
of the Ecclesiastical
116
Early Systems
XVII.
II:
.108
151
155 163 169 174 178
XVIII.
Part
.
135 140 145 148
A HISTORY OF THE DIATONIC MODES Part
.
Kindred Studies
Pseudo-modality
Book Two:
XXII.
16
Lateral Indices
XIV. The Case for the Locrian Mode XV. The Phrygian as a Minor Mode XVI. Summary and Conclusions
XXIII.
7 12
Mode
Part XIII.
New
Modality and Tonality: Some Distinctions
of the
Harmonic Modes
Modes by Bach and Handel
and the Troisieme Mode
185
Bibliography
193 200 204 209 232 247 260 267 285 289
Index
295
Blainville
XXIV. The Lowest Ebb
of Modality
XXV. Abbe Lesueur, Antiquarian XXVI.
Modality and the French Romanticists
XXVII. Modality and XXVIII. Modality and
XXIX. Other
German
Romanticists
Manifestations of Modality in the Nineteenth Century
XXX. The Modes XXXI.
the
the Russian Nationalists
in the
Recapitulation
Contemporary Period
THE DIATONIC MODES IN
MODERN MUSIC
Introduction
work This nevertheless
divides itself naturally into
The two
A
sufficiently related to
divisions are roughly:
two
be treated
(1) theory,
more or less independent, are under the title The Diatonic Modes in Modern Music. and (2) history. Book One, Theory, has two parts:
parts which, although
Diatonic Theory of Chromaticism and Kindred Studies.
The
interchangeability of scale forms above a single tonic for the enrichment of the melodic and
harmonic means
is
not limited to the juxtaposition of the Major and the Minor modes, but also includes
those diatonic scales which are the
monic
mutual interchangeability
analysis, this
of the relationship
modern counterpart
which
of the ecclesiastical modes.
offers a valid
means
for a simple
When
applied to har-
and diatonic explanation
certain chords (hitherto considered chromatic) bear to the tonic.
These chords have not lacked
logical explanation either
by traditional
analysis,
which
resorts to tem-
porary modulation and the Ausweichung (digression), or by the theories of half -modulation or parenthesis
modulation Piston).
(Piutti), of substitute tones
(Riemann), and of the secondary dominant system (Weidig and
These systems have served too long and too well
disprove them.
The author
aspires only to present a
to be overthrown,
new viewpoint and
and no attempt
is
made
to
thus perhaps add one step to the
progress of music theory.
the
Book Two, A History of the Diatonic Modes, comprises two parts: Early Systems and the Genesis of Harmonic Modes. Although Book Two concerns chiefly the period since the rise of the major-minor
system (1600-1900), a sketch of the previous scale history
included in Part One, for the purpose of
is
orientation as well as to throw into relief the thread of diatony,
which
is
one of the constants of occidental
music.
The common denominator charactistic links the
tovoi
of the scales of
Western
of ancient Greece, the eight
and the two used almost exclusively for the past three lae for tuning,
and the differences
the framework of all our scales latter a fifth or a
civilization
modes of Pope Gregory, the twelve
centuries. Despite divergent
in the theory of the function
an octave divided into
is
their seven-tone diatonism.
is
of Glareanus,
mathematical formu-
and relationship of the component tones, "whole" tones and two "half" tones, the
five
fourth apart depending on the starting point of the reckoning.
(Greek modes, Gregorian modes, Church modes, and so on)
This
all
derive
from
The
several scale systems
this basic scale pattern
and
its
seven octave-species. For purposes of convenience, these basic scales will be called the diatonic modes.
Departures from the basic diatonic forms are but mutations through the use of superimposed "chromatics."
These chromatics (half-tones and sometimes even smaller
to the diatonic scales
intervals)
have always been subservient
and are thus not so much smaller subdivisions of the octave
as they are subdivisions
oi the whole-tones of the diatonic modes. This statement encompasses the "genera" of the accidentals of "Musica Ficta,"
Even
and the chromaticism of major-minor
after the general adoption of the
which for convenience may be
said to
have occurred
the so-called ecclesiastical scales persisting. vival,
and the
The
title
factors involved
chosen for
qualification "diatonic"
is
this
is
major and minor
To
at the
scales
Greek
scale-theory,
practice.
and the practical eclipse of
all others,
beginning of the seventeenth century,
expose their course through
the purpose of the second part of
this period, their
work, The Diatonic Modes in Modern Music,
an arbitrary one. True, there are many other
is
diatonic (the diatonic modes). Proof
great body of folk and art music
now
space of an introduction, the reader
is
lies
find
Book Two.
may
scales
suggest that the limiting
found in music but, notwith-
standing some superficial evidence to the contrary, the scale basis of the musical art of Western tion
we
eventual re-
in the recorded history of the scale structure
civiliza-
and in the
extant. Since these subjects cannot be treated adequately in the small
referred to the later chapters for a full exposition of the evidence.
must not be supposed, however, that there
It
music.
Its functions,
nevertheless, are
is
no natural impulse toward chromaticism in Western
complementary
to the diatonic substructure. Instead of reducing the
seven-tone series to twelve semitones, these smaller subdivisions of the octave, employed as harmonic tones in the
major-minor system, are actually definitive auxiliaries of the Major (or Minor) mode.
Thus, for example, the chromatics in the traditional augmented-sixth chord define the dominant degree):
(fifth
$£* C
Major
and the so-called Neapolitan sixth "leans" on the tonic:
m s J5=fe
3$=
as C
Minor
This will be more fully treated in the chapters on the major-minor system (Book One, pp. 6-15; Book Two, pp. 174-181. It will
be noted that the
existence of twelve
modes
mode names employed follow Glareanus, who is credited with proving the The title page of his Dodecachordon l lists the scales as follows:
instead of eight.
GLAREAN AQA EKAXOP AON I
Authentae
Plagij
A
Hyperdorius
D
Dorius
E
Phrygius
F
Lydius
Hypermixolydius Ptolemaei
B
Hypophrygius Hyperaeolius Mar. Cap.
C
Hypolydius
Hyperphrygius Mar. Cap.
D
G
Hypermixolyd.
Mixolidius
Hyperlydius Mart. Cap.
Hyperiastius vel Hyperionicus Mar. Cap.
E
Hypoaeolius
A
Aeolius
C
Ionicus
Hyperdorius Mart. Capell.
G
Hypoionicus
Porphyrio
B*
F* Hyperphrygius Hyperlydius
The mode on because of
its
where
B, here
diminished
it
Apuleius
&
Mar. Cap.
Hyperaeolius
Politia, sed est errar.
named Hyperaeolius and marked with an
fifth, is
was mainly an academic
it
served disappeared along with the cantus
distinction of melodic ambit.
'Henricus Glareanus, AflAEKAXOPAON (Basle, 1547).
show that it was rejected The whole plagal category has
asterisk to
usually given the designation, Locrian.
been discarded in the modern period, since any useful purpose firmus,
iastius
3
There are several other systems of mode nomenclature but the one chosen has several advantages: a)
It is
well
known and
Germany and
widely used in
systems seem to be current: the traditional
Roman
terminology, and a "white-note" characterization, b)
complete since
It is
qualification
Once
i.e.,
names do not
mode de
fa, etc.)
carry the inextricable preconceptions
is,
of the
and ambiguities which
by numbers.
ecclesiastical classification
i.e.,
in-
(It is clear that
little
it.
The Church mode numbers
are too closely identi-
traditional theoretical dominants, mediants, participants, absolute
regular and conceded modulations, cadences,
has undergone comparatively figurations, that
summary
Greek usage must forever remain nebulous, although everything known of
with certain functions of tones,
etc.)
Although the
essential diatonism of our
music
evolution since the earliest records, the superimposed internal con-
tonal functions and chromaticism, have gone through vicissitudes, and their manifesta-
one era does not necessarily have more than
tion in
mi,
)
accepted, the
the Hellenic period emphasizes the debt music owes to
initials,
mode de
2
certain derails about ancient
fied
re,
encompasses a scale on each of the seven diatonic degrees. (This important
accompany the Greek enumeration or the
evitably
mode de
lacking in the pseudo-Greek listing as given by Koechlin in his admirable
is
rules of counterpoint. c)
it
in English-speaking countries. (In France three
Catholic Church numerical designation, a pseudo-Greek
resemblance to that of another age. In this
superficial
connection compare Greek chromaticism with that of Wagner, or the dominant of Gregorian Chant to that of Cesar Franck.
The
history of music theory
is
a history of the revision of viewpoint in an attempt to meet
the changing relationships of these variables to the constant of diatony. study,
it
has been thought well to divest the diatonic basis of music of
its
To
clear the
way
for the present
overlying complications in order
new point of view. The names Dorian, Phrygian, and so on have a solid historical justification since they have existed present meaning for more than a thousand years. It is true that they result from a misinterpreta-
to gain a
d) in their
tion of their original e)
two
Greek
The terms mode
of
objections. First, they
complexities as
mode
of
D
significance, but the sanction of ten centuries
D
(for Dorian),
have no
on
C
mode
of
historical standing,
(for
—«-
t*
Mode
|U
$
«»
of
and second,
F on A°
would serve very well but
employment would
(for
A -Lydian). b
o D on C
of F on
A
b
This terminology proves very confusing in analyses where the
'Charles Koechlin, Precis des Regies du Contrepoint (Paris, et Cie), p. 132.
their
.. o o ° ° o "
Mode
Heugel
cannot be overlooked.
(for Phrygian), etc.
C-Dorian) and mode of
-a
E5
E
mode changes
frequently:
for
result in such
.
Moussorgsky,
Mode of E on (D = Phrygian)
Mode
of
A
D
.
Mode
A
Night on Bald Mountain.
of
D
on D.
(D = Dorian)
on D.
.
CD- Aeolian)
of G on D Mixolydian)
Mode (D
=
For the foregoing reasons the nomenclature chosen seems the best of the several existing systems. is
certainly not advisable to attempt to invent a
new
It
set of symbols to add to an already confusing array.
BOOK ONE: Part
I:
A
Theory
Diatonic Theory of Chromaticism
"
Chapter
HARMONIC ANALYSIS: CRITIQUE AND A NEW THEORY
A BRIEF
T has long been recognized
I
which normally belongs
I
in
harmonic theory that a tonality
The chord
to another key.
the C-tonality in spite of the fact that
it is
V
7
is
not overthrown by a single chord
i
d-f -a-c in the following
example does not upset
of G.
m ^m m
=8=
3 C
+
Major
In like manner the chord g-b-d-f does not indicate a modulation in the final cadence:
Bach
5
$
t—r
m ^^ A
J
^
J
G Major to
rr u*
Both of these types of harmonic progression are juxtaposed in the following excerpt. This only serves is intended, since the key scheme would then be D-A-G-D, imprac-
emphasize that no real modulation so short a space.
tical in
m
8-
n
£LA
^Mf
if
fMW
IF
t
u
rw
m$
m
+
+
Copyright 1928 by Novello
&
Co., Ltd.
Dream
of Gerontius.
a;.,ru-,^,.n
j.
J
Elgar,
Vied by permission
of
H.
j
P^P i
W. Gray
Co., Agents.
Such apparent violations of key have been given various names which indicated their transient har-
them
monic
significance. Traditional theory treated
of key
was brought about only by a subsequent
as fleeting modulations, considering that a real
full
cadence to affirm the
new
tonality. Piutti
1
change
recognized
the ambiguity of such chords and called the effect "half-modulation" and "parenthesis modulation."
German term Ausweichung
is
quite descriptive of the digressive character.
Riemann
2
The
explains the Aus-
weichung by a system of substitution (the substitute-klang).
1
Carl Piutti, Regel und Erlduterungen zum Studium der Mu( 1883). See also D. G. Mason, "A Neglected Contribution to Harmonic Theory Piutti's Parenthesis Chords,' New Music Review (April, 1908), pp. 299-303. siktheorie
—
"Dr. Hugo Riemann, Harmony Simplified or the Theory of the Tonal functions of Chords, trans, the Rev. H. Bewerunge (London, Augener and Co.).
—
—
Weidig 3 and Piston 4 are modern exponents of the parenthesis-modulation idea. Their system of "secondary dominant formations" recognizes as legitimate all chromatically built chords of the V (7) type placed a perfect
degree of the
preceded by
above every degree of the major and minor scales except the leading tone. "Any
fifth
major or minor, (with the exception of the leading tone, a purely melodic note) may be dominant without disturbing the tonality." B
scale,
its
These secondary dominants are thus related to the
V$, Illit, and VII
(also
lb
triads of the
borrowed from the minor). In minor the
and VII (subtonic). The secondary chords so formed are designated
major mode: V, IV, V, (V
list is
V
(7>
V
of V,
3b
),
"V «J
«-i
°
rt
V——— 4Vs
1
.,
if
^ C Major I
of
V
of
r
r°
6
V
VI,
III,
and nor-
—
»
-**
V
VI, and III
IV of
VI
IV
IV Part of the development in harmonic analysis has
tem previously
in use:
it
come about because of the inadequacy of the
was a clumsy technique which had
the relationship of certain chords.
The
chromatic chords (augmented sixth,
N
fault lay in the 6 ,
to resort to continuous
modulation to explain
narrow concept of key which regarded
etc.) as violations of
harmonic materials forced a progressively broader view of the
the key.
The
sys-
all
but a few
increasing complexity of the
limits of tonality.
With
the wider harmonic
outlook came two significant changes: (1)
More chords could be
related to the tonic.
Under the parenthesis-chord system of Piston and
done by recognizing relationships is once removed. 9 For example, two chords not ordinarily closely associated with the major-minor may become intelligible through an intermediate
Weidig
this
is
chord to which both are in simple relationship.
"Adolph Weidig, Harmonic Material and Clayton
its
Uses (Chicago,
Summy
Co., 1923), chap. xvi. 'Walter Piston. Principles of Harmonic Analysis E. C. Schirmet Co- 1933). h
(Boston,
lbid., p. 1.
"Weidig, op. cit., pp. 344-345. ' Daniel Jelensperger, Die Harmonie in Anfange des neun-
zehnten Jahrhunderts und die Art sie zu erlernen, trans. A. F. Haser (Leipzig, Breitkopf und Hartel, 1833), p. 34. 8 Piston, op cit., p. 45, (IV of IV). Principles of Harmonic Analysis does not mention V (,) of V of V, but the expression is
used in his classroom. The V-of-V-of-V relationship ''
it
twice removed.
.
More extended harmonic
(2)
passages could be accounted for within a single tonality. This change
only recognized in theory a fact long apparent to the ear: an established tonality throw;
persists until
it
another
well-established
is
illustration of this persistence of
and obscures the
first
is
really difficult to over-
Here
in the consciousness.
is
an
a tonic:
1 w
r
s
*
G Major
IV
I
IV
Mixolydian VII [IV of IV]
$ m
^
TT
Tr
"C5"
«
TI~
C Major
I
~n~ ~n~
C Lydian =
Tf~
mr
IV C
II
[V of V]
Although the chords rately. If
we
C
begin with
not satisfactory as a
are identical, there
is
no doubt about the
C
Major, the final chord must be
final. Similarly, to
begin in
G Major
is
tonality of either,
if
considered sepa-
Major: the penultimate chord,
to feel
G
Major,
we
any other close unsatisfactory:
is
can-
not add another chord (C Major) at the end.
The advantages of perspective
of the broader conception of the limits of major-minor tonality are in the directness
and comprehension. In the following example from Beethoven, the entire passage
in relation to the tonic
D. The section containing accidentals may be regarded
only by a kaleidoscopic analysis which misses the point of the music, which
up
in the relationship
middle part
is
which the chromatic section bears
harmonic color projected on the
yet constantly relates the
whole harmonic texture
as a series of
full
modulations
meaning
traditional analysis fails to
show
to the ruling center of gravity
(
D)
Finale.
mm ji
]>
j
v7
P
if
91 V7
this,
account of the chord-by-chord relationships,
Beethoven, Quartet, Op. 18,
if
heard
is bound manner of speaking, the
that the
to the D-tonic. In a
D background. A
while an analysis by the parenthesis-chord system renders
is
is
m^
if
£ VI
(I
if
m %)
v7
3.
10
jpi i-^>-^h
ID)V? oflVIV
I
I
[iv]
IV of IV
v
E minor
-y^ passing
7
tones
II 4
III I
Vof IV
II
Pedal
chromatic
I
7
V of IV
V'of IV
L
v7 V7 of
V7 V
IV
TT 6 II 4
VUO.4
inT
V°
f
of IV
(yoj*
(!)
V'of
of II
II
p^utl
m
Elk
tJlir
'
U-
r?4 1 4
"v^T *
The symbol
which the root
The
older
method of
character of the music gests a diatonic scale
$
is
analysis
is
V
used to designate a chord of dominant function in
omitted.
which uses
transient modulation has at least
recognized in the figured bass.
on a
I
virtue: the diatonic
When a transient modulation
is
indicated,
^=^
~n~
«:
one
related degree:
=*=
-
"C5
E
^ C
v
(# is
DV'
3SZ
G V
7
C V'
it
sug-
11 Its
disadvantages are that, although
it
emphasizes the diatonic element, (1)
it fails
tionship digressions bear to one another and to the established tonality; and (2)
modulation.
The
result
is
it
to recognize the rela-
resorts to too frequent
method recognizes the impor-
a lack of harmonic perspective. Specifically, the
tance of the roles played by the subdominant and dominant chords in determining harmonic progression patterns. It has long
been
known
that the
at the interval of a fourth or a fifth.
What
march
of
harmony
is
strongest between chords
whose
roots are
remained to be recognized was that the chords concerned in
The
such progressions have relationships not unlike those of the true V-I and IV-I.
principles of the
pseudodominant and pseudosubdominant tonal functions, although unformulated, were unconsciously applied by composers, and the theories of
The primary concern
Weidig and Piston grew out
of these theories
is
of a fait accompli.
to account for the progressions involved,
neglecting the relationship which the component chords bear to the tonic.
even
at the risk of
The advantages gained through
a fuller understanding of the progressions are not to be minimized, but certain drawbacks inherent in the
system should be noted: (1) sized. (3)
trariness
The The
is
harmony
essential diatony of the limits to
slighted. (2)
is
which the system may be permitted
probably what Piston has reference to
Although the use of such terms impossible extreme, there are
many
as II of IV, II of
when he
V,
V
to extend
(7)
as a tonal function
seem somewhat
is
overempha-
arbitrary.
This arbi-
says,
would be stretching the bounds of
etc.,
instances to be found in
The
which the expression IV of
V
tonality to perhaps
[sic]
an
seems reasonable. 11
(4) Although easily within the bounds of tonality, the chords designated as secondary by the device
"
= = of
"
are not admitted to have a primary relationship to the center of gravity. Instead, as
earlier in the chapter, the relationship
Where
(5)
the nomenclature
the chords called is
lost,
"V
was shown
only established through an intermediary.
is
of
V"
or "IV of IV" do not proceed ro the
V or IV,
justification for
and these names serve no better than any arbitrary designation.
Faure, Penelope, Act
III,
Scene V.
Final cadence.
^8^
*§_ m* i
=S^ ZKSZ
V7 of V
C Copyright 1913 by Heugel
It is
the object of the present
work
to
show
&
Cie, Paris.
M
3SZ
I
Used by permission.
Through an extended concept of
that: (1)
diatony,
many
chords in the parenthesis-chord system have a direct relationship to the tonic. In other words, certain chromatically conceived chords are actually diatonic. (2) practice
12
A
are well within the confines of tonality. (3)
number of chords not now included in common The complete diatonic system defines the limits
within the bounds of tonality to which the juxtaposition of chords
The "extended conception
of diatony"
is
a tonic and the resulting increase of harmonic will be the object of Chapters III
may be
carried.
a principle which includes the interchange of modes above possibilities.
Substantiation of this theory as an actuality
and IV. Later, every chord of the expanded
list
will be illustrated
from
the music of recognized composers of the past and present.
The establishment
of the theory of interchange of
tonality to each of the diatonic modes.
modes depends on a conception which grants
Such a conception can hardly be controversial but, in an
effort to
avoid any possible misunderstanding about the subject, the following chapter provides a consideration of modality and tonality. 10
cit., p. 45 "IV of V" seems to be a typographical context indicates that IV of IV was intended.
Piston, op.
error.
The
..."An
authoritative list of the chords of common practice given in Piston's Principles of Harmonic Analysis.
is
:
Chapter
II
MODALITY AND TONALITY: SOME DISTINCTIONS
THE
BASIC scale term, mode,
divorced from any consideration of tonal function, means simply
if
a cyclical interval-succession-pattern in sound. In Western European music this Schema
(T
resented graphically as follows
The seven component sounds by a
=
tone, S
= semitone)
in this basic pattern are called tones
may be
rep-
and are represented in notation
and spaces called a
staff. The term tone is also used to indicate the larger of the two kinds of conjunct interval in the pattern, the smaller being a semitone. Major second for the former and
series of lines
minor second for the
The tone).
meaning
latter are better terms: their
basic pattern
is
Although the term diatonic has come
to
The seven
tones of the
Schema
diet
,
across or through, plus xovog
,
be synonymous with the phrase by conjunct staff-degrees,
principally used to denote conformity of a scale to the
it is
not ambiguous.
is
given the qualifying term diatonic (Greek
are designated
Western European Schema.
by by the
the correspondence between the letters and the tones
is
first
seven
an accident of
letters of
the alphabet although
history.
f D i
T A ,F.
7
T T
J^
t
i-
G
Western European Tonal Schema
For the purposes of This
may
serial
enumeration any tone of the Schema
give the result:
may
be chosen as a starting point.
cycle
D-E-F-G-A-BC-D Since the
D was arbitrarily chosen each of the other tones
may
E-F-G-A-B-C-D-E
2
F-G-A-B-C-D-E-F
3
G-A-B-GD-E-F-G
4
A-B-C-D-E-F-G-A
5
B-GD-E-F-G-A-B
6
GD-E-F-G-A-B-C
7
These octave
species,
successively serve as initials.
D-E-F-G-A-B-C-D
1
although not yet assigned musical functions,
may be
called diatonic modes,
since each conforms to a cycle of the Schema.
At least in the West, the most primitive tonal function is the melodic final or tonic. Any tone of the Schema may serve in this capacity. It is impossible, however, to conceive a tonality consisting of but a single tone: at least one auxiliary tone
ments are
at a
minimum
is
is
essential.
only rudimentary: street
After the tonic, the most important function interval of a fifth
Music having a tonic but in which the other tonal
is
cries
and some Pentatonic melodies are
that of the dominant.
above the tonic but, as in the plagals of the
the fourth, or even the third.
Its
functions are:
(
1) to
Most often
ecclesiastical
be conspicuous as
modes,
it
it is
ele-
illustrative.
placed at the
may be
the sixth,
a note in the melody and/or as a
chord in the harmony, and so be definitive of the tonic and (2) to form the principal cadence by the progression (melodic or harmonic), If
but
the dominant
this
is
dominant
to tonic.
a fifth above the tonic, there
cannot be claimed
when
it
is
placed at
may
be a certain physical basis for
some other 12
its
domination,
interval. In the latter case the ruling
and
13 cadential powers of the
dominant
fifth
When become
dominant are wholly conditioned by conventionalized usage, and even with the
must be partly
this
operative.
the tonic and dominant of a
mode have been
and conventionalized
established
assigned their respective roles and these have
to the extent that their
normal employment
is
well understood,
anarchy has been banished from sound and order has taken the place of chaos. The tonal potentialities
have been limited in order that those remaining can be more readily apprehended, and since they are less extensive,
there
from one
that progression tonic
may
is
the
to the other
These are the
final.
we come
a corresponding gain in meaning. Specifically,
is
two most important tones are the
tonal scheme, the
tonic
to understand that in a
and dominant, that they are mutually
cadential (dominant-to-tonic being the stronger),
is
many
although
least conditions of tonality,
definitive,
and that the
other established conventions
contribute.
According to stood that
it is
view,
this
modes have
clear that the ecclesiastical
it is
but
tonality,
must be under-
it
from that of the major-minor system of the past three hundred
a different tonality
years.
Furthermore, owing to the lack of uniformity in the matter of dominants and other tonal conventions,
among
the strength and quality of tonality varied
than some others because of diminished
prominent
its
the several modes. Thus Lydian tonality was weaker
tritone,
and the Locrian was declared defective because of
Since the character of a particular tonality
is
the product of a certain set of formalized tonal usages,
any change in these will produce corresponding mutations in the
its
fifth.
Phrygian mode when
its
dominant was
the metamorphosis by which the
before this point
is
discussed
C-mode
some
shifted
in that character.
from the original b
to
Such a modification occurred c.
Much more
important was
Church theory (the Ionian) became the modern Major; but
of
must be taken of the matter of intonation of the
notice
intervals of
the scales.
Pythagorean tuning was in use until long after the
were of the proportion 8:9, semitones 243:256, and
of polyphony. In this system the
rise
and
thirds
sixths
were classed
whole tones
Under
as dissonant.
the influence of polyphony this tuning began to be questioned and, after the tenth century, the "natural"
came
third (4:5) gradually
Equal temperament
is
a
into use. Zarlino
still later
(1517-1590) completed the process with
his senario theory.
development.
These changes undoubtedly altered the character of the cannot be said automatically to have given
rise to
despite the preeminence of the Major, although
its
scales,
but the adoption of the
the Major. Indeed, the Ionian effect
described,
is
somewhat
mode
new tuning today
still exists
disparagingly, as pseudo-
modal.
The
Ionian
mode
of Glareanus, with
its
dominant on the
fifth of
the scale, and the
have the same diatonic form: T-T-S-T-T-.T-S. Yet the difference between the two the fact that no trained musician cult to put into words.
would mistake the
The divergence between
ventions. Further light will be
thrown on
tions of tonality characteristic of medieval
A lish
it.
1
discusses each thesis
is
one
for the other, the matter has
question later in the chapter by a
polyphony
as contrasted
able and
is
diffi-
summary
of the conven-
despite courageous attempts to estab-
from Rameau's through Riemann's and brings very damaging first
evi-
to formulate a complete theory
2
To him is due the credit for the practical idea that the V 7 contains within major mode key system and so unmistakably defines the key. This is very service-
of the major-minor system.
the limits of the
been
with those of the major-minor system.
dence to bear against their propositions. Rameau, however, was the
itself
modern major
marked. In spite of
based on the dissimilarity of internal tonal con-
on very questionable ground
physical basis of tonality rests
Shirlaw
this
effect of
the two
is
probably the most important single principle of major-minor tonality.
Fetis considered that the necessity of resolving the dissonance of the 3rd
and 7th of the
V
7
deter-
mines the tonality of modern music, and taught that the modern major-minor tonality was the result of Monteverdi's .
.
3
supposed introduction of the use of the
tonality resides in the melodic
.
and harmonic
affinites of the
V He 7
.
also says,
sounds of the
scale,
which determine the successions
and aggregations of these sounds. 'Matthew Shirlaw, Theory and a
of
Harmony (London, Novello
Co., Ltd., 1917?).
Rameau, Traite de I'harmonie (1722); idem, Demondu principle de I'harmonie (1750).
J.-Ph.
stration
S
J.
monie
F.
Fetis,
"Monteverdi," Esquisse de
(Paris, 1830).
I'histoire
de
I'har-
14 .
.
Tonality then,
.
our Major and Minor character,
the order of melodic and harmonic facts which results from the arrangement of sounds in
is
scales; if
and the harmonic
even one of these sounds were to be placed
results
would be quite
.
makes the following statements about
Shir law
differently, tonality
would assume another
4
different
.
.
Fetis' definition:
These remarks have been considered by not a few besides
Fetis to
be very profound and to betray a deep insight
into the nature of music and harmony. In reality they are very superficial. Fetis asks us to believe that
it
which determines harmony and harmonic
knows who
succession, whereas the reverse
is
the truth, as every musician
is
the scale is
acquainted with the history and development of the Church modes. These Modes, quite different as regards the arrange-
ment and proportion of sounds from our modern modes, were, under they assumed the form of our Major and Minor modes. It would be modes out of existence. 5 This final declaration
may be
true
if
we
harmony banished these old
modes" but the whole
correctly interpret the phrase "old
work assumes the present-day
thesii of the present
the influence of harmony, gradually altered until correct to say that
existence of
modes
identical in their diatonism
with
those called "the ecclesiastical modes."
was too
If Fetis
when he
general
specific in assigning tonality
which rendered important
of tonality,
mutual
tion
between
ties.
all results
service to the
chord-successions in a piece achieve a unified their
is
too
says,
has always been the referring of
It [tonality]
only to the major-minor system, Schonberg
to a center, to a fundamental tone, to an emanation point
composer
in matters of form. All the tonal successions, chords,
meaning through
their definite relation to a tonal center
and
also
and
through
6
This statement does not deny tonality to modes other than the major-minor, but different kinds of
earliest Christian period
...
As
modes. Helmholtz
it makes no distincmodes of the Greeks and the
specifically includes the
and emphasizes the importance of the
final to the tonality.
the fundamental principle for the development of the European tonal system the whole mass of tones and
the connection of harmonies must stand in close and always distinctly perceptible relationship to some arbitrarily
and the
selected tonic,
finally return to
which forms the whole composition must be developed from
-mass of tone
The
it.
ancient world developed this principle in
this tonic,
homophonic music: the modern world
in
and must harmonic
music. 7
even more clearly includes the diatonic modes:
Piston's statement about tonality
The presence that the
same
of a center of gravity, or tonic, being the sole requisite for the presence of a tonality,
tonality
may be given
a large
number of
variations in the
makeup of
its scale.
it
will
be seen
8
Recognizing a neglected point in tonality definitions, a distinction between the melodic and harmonic elements, Yasser Tonality tain
number
is
is
does not show the implications of the idea. which organically and tonocentrically unites the melodic and harmonic functions of a
cer-
of systematically arranged sounds as most sirrply represented in a musical scale.
To expand which
still
a principle
this definition
and describe the two fundamental aspects
governed by the above principle,
we may add
in reference to our present (diatonic) system
that the tonal center represents a single note (tonic)
from the
melodic point of view, and a chord of three notes arranged by thirds (tonic triad) from the harmonic point of view. Again, that in the melodic aspect
this
system manifests a characteristic distribution of
its
degrees within an Octave, forming various chains of whole steps and half steps (Modes)
monic viewpoint
this
system divides
nances and dissonances, the
all its
possible tonal combinations into
latter inevitably
two
distinctly
.
seven regular (diatonic) .
.
Finally,
from the
har-
opposed groups of conso-
"requiring" resolution into the former. 8
All the usual definitions of tonality have a certain logic, but there seems to be a general lack of recognition of the differentiations which the
more
must be made between a broad, comprehensive formulation and
particularized, exclusive statements dealing with existing subdivisions of tonality. In the absence
of definitions
which take cognizance of these
General Tonality
is
distinctions, the
which a mental grasp of the musical texture
that principle by
through melodic and/or harmonic conventions relating is
thus the tonal center and ordinarily the
Tonality in Plain Chant
is
following definitions are proposed.
final.
The
all
component tones
conventions
may
Idem, Traite complet de la theorie (Paris, 1844), p. 249.
et
de
la pratique
de
I'har-
monie 5
Shirlaw, op.
cit.,
one of
may
their
is
maintained
number which
not have physical bases.
a system by which a mental grasp of the unaccompanied melodic line
maintained through a system of linear tonal conventions. Conspicuous 1
or
to
p. 337.
"Arnold Schonberg, "Problems of Harmony," Modern Music (May-June, 1934), p. 177.
among them
is
are the final or tonic,
H. L. F. von Helmholtz, Sensations of Tone, trans. A. J. (London, 1885), P. Ill, chap. 13. "Piston, Principles of Harmonic Analysis, p. 60. "Joseph Yasser, A Theory of Evolving Tonality (American
'
Ellis
Library of Musicology,
New
York, 1932), p. 331.
15 the dominant
reciting note, the absolute initials, the mediant,
from the note immediately above.
to the final
It
and the
stylized final cadence: a progression
thus only makes use of the melodic phase of the general
principle of tonality.
Tonality in Renaissance 'Polyphony texture
is
a system by which a mental grasp of the melodic and harmonic
maintained partly through the methods of unaccompanied plain chant which apply mainly to
is
whose function
the cantus firmus, and partly through certain added harmonic conventions
component triad
triads to the triad of the final which has taken the place of the simple final.
must be conspicuous; the progression dominant
usually be perfect, that
member
is,
harmonic
was regarded
melody.
The dual nature
becomes the principal cadence;
scale;
and the
the tonic note in the top voice as well as in the lowest. It
that in spite of these
of the voices
triad to tonic triad
on the important degrees of the
there are other conventional cadences
as a
whole outlook was
results, the
of this tonality should be noted because
it
to relate the
is
The dominant
still
final is
cadence must
important to
re-
horizontal, not vertical: each
was undoubtedly a
factor in the eventual
capitulation to the major-minor system.
Major-Minor Tonality
is
a system by which a mental grasp of the musical texture
is
through a very circumscribed and highly characteristic harmonic (vertical) means of relating
and harmonic elements
to the tonic or
its triad.
Among
maintained all
melodic
the differentiae are:
Cadential conventions:
a)
(1) V-l and IV-V-I are the normal formulae. (2)
The major ing to
(3) (
4)
normally progresses up to the tonic and acts somewhat like a red arrow point-
Restricted are the progressions
b)
one of
V
The seventh of the V has a normal resolution downwards to the The arresting I f is normally used before the V in the cadence.
triads II, III, VI, c)
third of the
it.
II-I,
third of the tonic.
V-IV, VI-V, and any extended employment of the secondary
and VII °.
The chromatic conventions require the normal triads and thus make the
that each chromatic note or chromatic chord lean
on some
relationship clear.
Quite arbitrarily the descriptive term Tonal has been applied to the music written in major-minor
and observing
tonality
Period.
Any
The
three centuries of major-minor music
is
known
as the
Tonal
deviation from the established conventions of this tonality are called extra-tonal or modal.
Pseudo-modal
is
the term used to designate emphasis of the secondary chords
Major mode, which
To
conventions.
its
results in a
weakening of
its
the three subdivisions of General Tonality
II, III,
VI, and VII ° in the
tonal quality. (
tonality in plain chant, tonality in Renaissance Poly-
phony, and major-minor tonality) must be added one other kind: the tonality of the diatonic modes in
contemporary
use.
As
will be
shown
later in
Book Two,
all
the diatonic
modes
music of the present epoch. Their scale types are the modern counterpart of the
are to be found in the ecclesiastical
modes but
there the similarity ceases: the plagal forms have disappeared, the dominants of the Phrygian and Locrian are
no longer placed on the
sixth degree,
and most of the old conventions of harmony and cadences have
been superseded. Certain conventions of the major-minor system have been imposed upon these
dominant
is
always a
above the
fifth
tonic, the texture
is
essentially
harmonic
trapuntal (horizontal), and the dissonances of the seventh and ninth are used freely principles of resolution
which apply
termed Harmonic Modes,
on the diatonic If
scales
10
to such dissonances in Classical
since their tonality
known
is
scales: the
(vertical) instead of con-
(subject to the
harmony). These scales then
same
may be
the result of superimposing Classic harmonic formulae
and Locrian. modes named above without further proof, the matter may be
as Lydian, Mixolydian, Dorian, Aeolian, Phrygian,
one cannot grant tonality
to the
considered as a hypothesis, and agreement reserved until there has been submitted the additional evidence
embodied 10
The
in
Chapters
genesis of the
III
and IV on the principle of interchangeability of modes.
Harmonic Modes
second part of Book Two.
is
the subject of the
Chapter
III
THE DIATONIC MODES: THE ORDINAL AND LATERAL INDICES the ancient Greeks recognized that the interval Even of Since time tuning has been based on a series
their
the fourth, and so
it
became the
first
of a fifth had great significance for music.
fifths.
interval of polyphony.
Organum used the fifth and its The dominants of five of the
inversion, six recog-
nized authentic Church modes were placed on the fifth of the scale, and in the major-minor system the fifth rules
A
supreme.
favorite device for "explaining" the derivation
series of
seven perfect
which may be reduced to
fifths
and ascendancy of the major
C Major
ir
-*y-
scale
scale
is
to refer to a
form:
ir
ti~ "XV
m TT The c,
question which has always been embarrassing for the theory
the second
component of the
sometimes said that the
series
series, instead
final fifth is
nitely."
pletely
diminished and this
3E
is
No
theorist has
is:
Why
does the scale begin on
In order to avoid this stumbling block
f:
said to "close the series in order to prevent it is
clearly
its
an evasion because the
clear
if
we
continuing indefiseries is
not com-
1
fifths.
demonstrated by means of the
series of fifths that the
C-Major
is
complete diatonic scale system. The reason that the major scale begins on the second
becomes
it is
Ol
In spite of the neatness of this explanation
composed of perfect
first?
begins on c and ends on
^ The
of the
reduce the component tones of a series of seven perfect
fifths to
but one scale of a fiftb of
the series
the compass of one
octave and do this seven times by adopting each of the tones in turn as a beginning. There will then be
formed the seven diatonic
scales
known
as Lydian, Major, Mixolydian, Dorian, Aeolian, Phrygian,
Locrian, respectively.
1
Specific citations are not
subject. It
is
given in this brief mention of the a
sufficient to say that the series of perfect fifths as
possible theoretical basis for the relationship of the tones of the
major scale has tempted every theorist from Rameau to Riemann.
16
and
17
F
=
Lydian
C
;
Major
* !:«»
G
-
Mixolydian
~
3SZ
"cy-
If the initials of the initials is is,
of course, the
is
above scales are written
in scale
form beginning on "F", a diatonic
series of
formed. This makes a convenient table of the tonics of the seven modes. Each of these tonics first
notes of
up of the same diatonic duced
m
series.
its
respective
mode, and
all
the seven
modes
in this presentation are
made
Since the initials or tonics themselves are in diatonic order, the table pro-
called the Ordinal Index.
18 Ordinal Index
^ Lydian
m Mixolydian
m
•
• Aeolian
m Locrian
3S Major
^^^
«-
*
»
XI.
Dorian
m Phrygian Initials
m The
~o~ liaison
between the modes of the Ordinal Index
Minor. Thus A-Aeolian
G-Mixolydian
is
is
is
comparable to that of Major and
the relative Aeolian of C-Major, and
its
relative
The
converse of this operation
for the original. This
is
interchange of
those of the Lateral Index, which If
we
relative
shift
from one mode to another
Index there must be a corresponding modulation. In other words, although the component
tones of the musical texture remain the same, the tonal center of gravity these notes.
its
E-Phrygian;
is
the relative Mixolydian of D-Dorian, and so on.
Such relationships, however, involve a change of tonic: in order to in the Ordinal
Phrygian
continue a series of
will be thirteen integrants
is
is
is
moved from one
mode above a
tonic,
2
and the relationships in
this category are
derived as follows:
fifths until
the cycle
complete, that
is
which may be represented
is,
until the first tone recurs, there
thus:
Complete Cycle
in Fifths
3
8-
m- u
to another of
to retain the tonic while substituting another of the scales
-.
*
*
82
See chap, iv for further discussion of the interchange of
mode.
'Note of a
b.
that
g>
is
the enharmonic equivalent (tempered scale)
19
Any group
of seven
middle tone (d in
which
is
the link
4
consecutive tones
this case). If
from
this cycle will
common
taken as the
have one tone which
tonic of the seven possible
the converse of that described in the derivation of the Ordinal
which binds the several derivative
is
common
to all: the
modes (by a process tone d becomes
Index), this center
scales into lateral relationships.
D
=
Lydian
D Major -
D= Mixolydian
.
m- w ^ \>~
D
=
Dorian
D
=
Aeolian
**
D= Phrygian
D By reducing
the
modes
=
Locrian
to their scale forms
posed scales form a convenient table which
and placing them above the common tonic
may be
d,
the juxta-
called the Lateral Index.
Lateral Index Natural Signature
D- Lydian
t±-
m
gfltf
m
^
D Major =
D= Mixolydian
m m ^
D
=
S m
Dorian
m T>-
s
Aeolian
^
D Phrygian =
D= Locrian
ss& This index constitutes the theoretical basis of the principle of Interchangeability of single tonic. Further consideration of the principle
be found in the next chapter. 1
Seven tones are necessary to form a complete diatonic
scale.
and proof of
its
Mode above
a
contemporary existence and use will
20 It
will be noted that
sight, but, in
no mention has been made^f the Minor mode. This omission
not an over-
is
agreement with most writers on the subject, the Minor mode is here considered to be derived scale, the seventh degree of which has been altered to permit the Major
from the Aeolian (or Dorian)
mode dominant-seventh
chord.
(The matter
fully treated in
is
Before concluding the discussion of modal theory point, in spite of the fact that, strictly speaking,
it is
it
Book Two, Chapter xx
seems logical to dispose of one other related
something of a digression.
Simple inversion of theme has been a stock device of composers the fifteenth century; but
at least since the
Ad
it
was a
closely
and Art of the Fugue Bach the two kinds described by Fux
jealous guardians. In his Musical Offering
its
used inversions but these were not of the modal type, being confined to
Gradus
Flemish schools of
there was any early recognition of exact inversion of mode,
if
guarded secret which 'died with
in the
'.)
Parnassum of which the original edition appeared in 1725. made in two ways: by simple contrary motion, and by inverted contrary motion. The simple made when the self-same notes ate merely turned upside-down so that those notes which first
This inversion can be contrary motion
now
ascended,
is
descend. This
done without the
is
slightest attention to the semitones.
For example, see that which has
been'given so often:
Model
Simple contrary motion
* The
^
other kind of inversion
tones remain tones.
The
exact
is
made by turning
manner
in
which
the notes over in such a
this
is
done
is
shown
way
that semitones
remain semitones and
in the following illustration.
6
TT
~n~
(8)
~Tf~
(S)
1
Compare the ascending notes at the left with those desending at the right: When D is F inverted becomes B; G becomes A; etc. This process applied to the
inverted becomes C;
inverted,
original
it
remains D;
model
will
be
E as
follows: 5
Model
#
Inverted contrary motion
SE
Various writers have discussed one phase or another of inversion.
The
subject
is
treated in Rousseau's
Dictionnaire (before 1740) in the article "Systeme" written by Serre and Morambert. credit for being the first to note that the
former
mode "semi-mineur"
Phrygian
mode
Serre
must go
is
the inverse of the Major, although he calls the
because of the minor second and minor third at the bottom of the inversion.
^
C= Major
S
To
6
TI~
t>y»
b
'
T~
C= Phrygian
The subject was not mentioned German theorists. 7
again until a century later
6
Johann Joseph Fux, Salita al Parnasso, trans, into Italian by Alessandro Manfredi (Capri, 1761), p. 181. * Jean Adam Serre, Letter appended to Esiais sur les Principes de I'Harmonie (Paris, Prault Fils, 1753), pp. 143-144. 7 H. L. F. von Helmholtz, Lehre von den Tonempfindigungen
when
it
was recognized by a number of
physiologische Grundlage fur die Theorie der Musik (1863). Artur von Oettingen, Harmoniesystem in dualer Entwickelung (1866). Dr. Hugo Riemann, Vereinfachte Harmonielehre (1893). Hermann Schroder, Die symmetrische Umkehrung in G ( 1902). der Musik, Beiheht 8 der Publikationen de I als
M
21
Bernhard Ziehn of
itself,
s
carried the idea
one step further
in demonstrating that the
the Aeolian inverts to Mixolydian, and the Phrygian
some reason he omits mentioning
is
an inversion
the antithesis of the Ionian or Major. For
that the Lydian and Locrian are inverted forms of each other. Otter-
strom, however, gives the following
When
is
Dorian
list,
which
is
complete.
9
inverted
Ionian
becomes Phrygian.
Dorian
remains
Phrygian
becomes Ionian.
Lydian
becomes Locrian.
Dorian.
Mixolydian becomes Aeolian
He ment.
.
.
attaches ."
composer,
10
no importance
Whether or not
who
Aeolian
becomes Mixolydian.
Locrian
becomes Lydian.
to the fact for
this is true
he adds, "These
may depend on
curiosities
belong to the realm of amuse-
the point of view, but from the standpoint of the
should be aware of and take into consideration every possibility offered for the develop-
ment of thematic material, the statement is misleading. The inversion correspondence between the modes is most simply
illustrated
by the following Spiegel-
bilder (retrograde inversions).
Lydian
MaJ° r
m
^
„
«C"V»
o
Mixolydian
^___^
UEijoav
Dorian "-*
1
-»-2
*:
UEIJOQ
Apparently no one has demonstrated that the whole diatonic system
The Dorian with
its
is
symmetrically invertible.
identical tetrachords
forms the center, since
it
inverts without
modes (those with a major
changing form. The Lydian, the most major of the three major
third) since every scale degree
is
at
its
maximum
distance above the tonic,
is
the mirrored reciprocal of the most minor mode, the Locrian.
The two following diagrams The
first is
illustrate the symmetrical invertibility of the complete diatonic system. concerned with the Ordinal Index, the second with the Lateral Index.
Bernhard Ziehn, Canonical Studies; A New Technic in Composition (Milwaukee, Wm. A. Kaun Music Co., 1912),
p
-
3
'
"Thorvald Otterstrom, A Theory of Modulation University of Chicago Press, 1935), p. 131. "Ibid.
(Chicago,
22
SYMMETRICAL INVERSION OF MODES Ordinal Index
C-Major (Ionian
(UBinoj) JofBj\[
-
o
SYMMETRICAL INVERSION OF MODES Lateral Index
D- Major (Ionian)
m
ubjuoi) Jofej^-Q
Chapter IV
INTERCHANGEABILITY OF MODE Interchangeability of Mode may
be defined
yet maintaining a single tonic. In effect, this
as:
means
the substitution of any diatonic scale for another that any one of the diatonic scales
place of any other above any given tonic. For example, for the Major substituted the tonic Minor, the tonic Aeolian, the tonic Phrygian,
*
Minor (Harmonic or melodic) (b)o
may
take the
on tonic D) may be
*
m „
(say
and so on.
Major
w
mode
#"
^
Aeolian
o
5 bo
«*
^
Dorian
o
"
o
«»
^
o
«»
Phrygian
"
bo
ti
W
t> '
S
Locrian l
ui
b«
Mixolydian
$
"
O
*
tot
Lydian
^^ o
* So
far as the free alteration of
and has long been
the other
serious; is
-O-
M
major and minor are concerned the practice
is
recognized in theory
in use.
Strange, that one should feel major and
now more
«»
"Ti~
They both present the same face, now more joyous, The passage from either to occurs frequently and swiftly, the two begin to shimmer and coalese
minor
and a mere touch of the brush
easy and imperceptible;
when
it
as opposites.
suffices
to turn the one into the other.
indistinguishably. 1
1
Ferruccio Busoni, Sketch of a New Esthetic of Music, trans. Dr. Th. Baker (New York, G. Schirmer, 1911), p. 21.
23
24 It is clear that
adorn
itself
the
with a sharp,
part; minor,
It is
The
it
is
its
upper tetrachord (and thus the
but another form of that principal
lost its individuality; it
scale.
essential elements of its per-
The day
the Dorian consented to
accepted being amphibious: major, and thus modern, in the upper
and antique, in the lower. 2
The Dorian mode minor.
new minor mode, borrowing
from the newly born major,
fect cadence)
[the original minor]
not, morphologically, a species:
.
.
,
it is
is
not even a minor tinged with major,
prevailing idea in recent years with regard to chords in general
between major and minor. Piston
.
.
it is
rather a major tinged with
a variety. 3 is
may be used
that they
interchangeably
.*
makes the following
analysis of
an excerpt from the second movement of Dvorak's Symphony
No. 5: Dvorak, Symphony No.
pm W&\
i§Fp
W*
IF
fc PiM. £ ep^
M^
9
te
i
Dt in
The above example same tonality. The
in the
v 6 ofn
VI
in
IV
furnishes an excellent illustration of the alteration of chords first,
third
5, II.
from the minor and major modes
and sixth chords are derived from the minor mode, whereas the second, fourth, and
seventh chords are associated with the major mode. 5
Rameau
regarded the minor not as an independent scale but as one related
ment from the major. 6 For it,
was
these reasons, one
at liberty to substitute,
the tonic minor for the major. In Lesueur's opera
La Caverne
at the
to,
and deriving
its treat-
where the expression demanded
words "quel
triste" there is a sud-
den change to minor. Lesueur,
£ *=
$
S
-
vez ar
-
des
ra- ches
7
7
P^P
S
pleurs
i
P Vous T
II.
i>
m'a- vez ar
-
ra
?
t
3
G Major
Lf
M m
MMF ^ Mr m O o ^m m
P Vous m'a
La Caverne, Act
.
i ches
7
s^
6
m
?
h
des pleurs
r i
7
quel trist
^ ^
'
^ .
G
-
sort
e
et
qu'il
m'af
-
flige
tjji' &*
^
Minor
3fe
^
Doubtless for similar reasons Brahms^ sometimes adopted the same procedure. 1
Maurice Emmanuel, Historie de
Librairie Renouard, 1911),
II,
la
p. 292.
Langue Musicale
(Paris,
*
Horace Alden Miller,
New Harmonic
Devices
Oliver Ditson Co., 1930), p. 19. 5
'Ibid., II, p. 345. "
Harmonic Analysis, p. 39. Rameau, Traite de I'Harmonie, II, chap. 21. Piston, Principles of
(Boston,
-
25 Brahms, Symphony No.
G Minor
2, III.
G Major
Brahms, Die Trauernde, Op.
^
Lasst
^
P
P
die
drei
Ro
-
sen
stehen,
an
die
m
H
^—
P
P
-m Major
Minor
p
m
Kreuz
-
/-
M Major
g
g
le
bliihn:
-
heut
p
Minor
^^ ihr
das
^5 Mad
-
No.
^
^^
P
1
el
kennt
mm
7,
dem
5.
26 Brahms, Sextet for
Strings,
Op. 36,
I.
G Major
SI
J J J J J J
7TTO
J J J j J j
J J J
JJ
J
r G Major
By
reason of
its
descending form, the Minor
mode
includes the Aeolian and so establishes
its
changeability in traditional harmonic practice.
Lesueur, Ossian, Act IV.
C Aeolian _ or Minor
PNf=r
s
C Minor
M
^
Gretchaninov, Sun and Moon, Op. 16, No.
$
±
T=f
C Minor
C Aeolian
.
.
C Minor
*
2.
inter-
27 Although the ascending melodic form of the minor scale has the major sixth degree, it is not clearly Dorian because of the major seventh degree. Riemann, however, gives more than a hint that he considers it
interchangeable with the Dorian. .
.
.
The major
sixth in the
minor
scale (raised third of the
minor subdominant),
if
used unnecessarily, without
modulation and without melodic rising to the third of the major upper dominant, will always produce turns like those peculiar to the Dorian
mode
of the fifteenth to the seventeenth century.
7 .
.
.
A Minor More
practical evidence that the
the same tonic
Dorian
is
capable of being interchanged with other modes above
given by Brahms.
is
Brahms, Vergangen Op. 62, No.
Andante
3E
w l±LA ^
==T
r p^w
r
^
¥E
r
P* J J
m
ijLo
r
rt
r r .
^m r i-
tr
s
^Ui ^ .
8
1/
T
-Jij
^m^
=8=
Dorian
' Riemann, Harmony Simplified or the Theory of the Tonal Functions of Chords, pp. 92-93.
2XZ
=8=
-F
•=-r
Minor
M
Dorian
s
r
r
^ r
¥
s
J-
r
^
r
.D Minor
$ If
i
mir Gliick und Heil,
i
D Dorian
s
ist
7.
m j i
33=
~1T~
28
It is
a remarkable fact that
the scale [in the three theorists First,
N
6
chord]
who were
is
".
.
.
very few theorists [before 1900] suggest that the lowered second of
probably a remnant of the Phrygian Mode."
9
who
g 10
1
*
1
u
who
^
~r»~
regarded
all
the following as belonging to one key without modulation:
j
J-U. g
j
rj
?^
t, ,
*Eff
^
¥
f
Ne Third, Riemann,
The chord
its
latter
chord
who made
(A minor:
the following observations: b
) is
clear
on
d-f-b
name, of course, but are
known by
the
name
of the Chord of the Neapolitan sixth.
this point, that the introduction of the
second of the minor scale) makes the scale resemble the Phrygian.
(a)
i
least
N°
~m
1§
however, at
r
—w i
*
are,
considered the chord a "half-modulation":
C Minor Second, Tiersch,
There
ahead of their time in their manner of construing the Neopolitan sixth chord:
^
Jelensperger,
8
(b)
& ^^-4
.
.
.
.
.
note characteristic of
.
We leave the it
(the minor
u
S
id)
i=#
P
-O-^ ~T«-
A Minor
8
V. L. Jones, "The Relation of Harmonic Theory and Practice from Rameau to 1900" (Doctorate Thesis, Harvard University, MS., 1934), p. 485. 8 Jelensperger, Die Harmonie im Anfange des neunzehnien ]ahrhunderts und die Art sie zu erlernen. p. 34.
10
Otto
Tiersch,
System
und Method der Harmonielehre
(1868).
n Riemann.
ot>. cit.,
pp. 92-93.
29
.
Contemporary writers, however, have not failed The probability is that this chord (the Neapolitan .
.
second degree in
The
early
this
minor
scale
is
to note this suggestion of the Phrygian. sixth)
was taken over from the Phrygian
one half-tone above the tonic and has a major
form of the Neapolitan Chord was probably from the Phrygian
triad.
scale
scale, since
the
12
where
it
occupies a position a
half step above the initial note. 13
Curiously, complete scale passages in conjunction with the
of the older composers. This times.
is
N
6
chord are not to be found in the works
a development which has taken place only .within comparatively recent
Most composers, unable
to use the leading tone with the chord because of the resulting
augmented
second and diminished third,
$m
7
S c
(a
u6
N6
I*
*s C
=8=
±*P±
and apparently unwilling to use the subtonic
mi
1^ as
i
to correct this, since the scale
9 7 m
~n~
Ittifii Tf~ I
6
would then become Phrygian
~n~
TT
N6
form incompatible with major-minor habits of thought), solved the problem by avoiding either ascend-
ing or descending scale passages at such points. Freed from former hampering viewpoints, contemporary writers unhesitatingly write scales over the
N
8
with the result that interchangeability of
mode
includes
the Phrygian.
Sibelius, Violin Concerto.
D Major 1
Orterstrom,
A
D Phrygian
I
Theory of Modulation,
p.
1.
II
(N 6
)
"Miller,
New
Harmonic Devices,
p. 18.
30
D Major
D Phrygian
I
II
(n6)
8-
m
9
i
i
j
*=fe
i
m
f
m
?
n
D Major The
i
*
a.
±
i
i
I
source of the Phrygian
is
not necessarily the
N
6
it
:
frequently appears melodically or in connec-
tion with other chords.
Rimsky-Korsakov, Scheherazade, No.
III.
26
£
EEE
f
W
s
sg*-^
ST ^ m pg lri
^^S
i==fi
J
=£
5fe
it;
G
G Major
G Phrygian The
scale
I
G Major
VII 7
which most naturally accompanies the
the following form (Locrian)
m
G Major
Phrygian VII 7
is
N
8 is
used in conjunction with
not always
it.
felt to
I
be the Phrygian: quite often
31 Beethoven, Quartet, Op. 131 VII.
Wfi
CjjMinor
Only one tone
The
essential a
b
is
(c) of
Jfejtl!
Locrian
Cjt
the Locrian scale
is
missing in the
first
measure of the following Sibelius excerpt.
quite prominent.
^
Sibelius,
^
fpi f
mw
i
Symphony No.
2, II (coda).
F** V6
"ST
D Minor
D Locrian
I
16
Copyright 1931 *y Breitkopl-H'drtell. By permission of Associated Music Publishers, Inc.,
The d
b
passing tone of the following example makes
n r~n ^m i_u
also indisputably Locrian.
Smetana, Polka Poetique, Op.
i 4 ~cs
p
^m n
it
Aa,e::t.
wm
i
8,
No.
2.
$
V?
G Minor
n^
,
j
V
N6
(G Minor)
I
(Phrygian II or Locrian II) In the "March and
Hymn" from
The accompanying harmonies
Les Troyens by Berlioz the Locrian scale occurs in complete form.
are also Locrian, one chord, the
what the character of a passing chord.
Berlioz, Les Troyens,
E
pg w
P
S£ C Major
I
minor V°? which, however, has some-
te^ >!f
£
"March and Hymn."
**z
ttz
l^r^
i .C Minor
IV
*
32
II
[Minor] Locrian
I
^
.Major
i
El>
i
frf f€ffl
E
»
h .
Finale.
is
i'crcrcttr
^m h^lTl m
i «-i»-t g=g^
m
f
f
'
Dorian
Major Copyright 1932 by ]
&
W
Chester, Ltd.,
London. Used by permission.
V
— *
1
—
•
.
37 Cui, Angelo, Act
^
mm j>m
j
*j :
III.
?
1
j
j
A Aeolian
J.J
J
fi=y=¥
g
7
7
i ^=^
p
^n^
j
i
V
7
^£3=7=
|
j '7
5=. f_
7
7
.Aeolian
Phrygian
(?)
7
r i
-i^h
Minor
2nd
II.
Op. 115,
II.
(?)
Aeolian Faure,
Borodin, Prince Igor, Act
(?)
Quintet, for strings,
Allegro vivo
Et Lydian
3?i=g x
—
=wkf=.
fj£~rt «j
Passing tone
,l
—
r
l>
1
[ajor
?
PI lrygian
—
r
i
p hrygian & i/•
:
« Ik
[ajor
#'
?
i'i
^-Hj Permission for reprint authorized by
Durand
&
Cie, Paris, Prance. Philadelphia, Pa.
Copyright Owners, Elkan-Vogel Co.,
Inc.,
In view of the evidence presented, which consisted of examples from the works of recognized composers, the feasibility of the practice of interchanging
inference ress
js
which only
seems to
modes above a
tonic can hardly be doubted.
The
by their inherent musical feelings, once again blazed a path of progwas recognized in theory. The principle on which the practice of mode substitution
that composers, guided
rest
later
may be
formulated as follows: the eight diatonic modes
tonic without destroying
a The Harmonic Modes,
see
its
function as center of gravity.
Book Two.
l6
are interchangeable above a single
V EXTENDED HARMONIC RESOURCES Chapter
Application
of the principle of interchangeability of
mode not
only gives the possibility of wide
melodic horizons within a given tonality but also of increased harmonic resources within the frame of that tonality, since chords
be found to be
common
may be
on each tone of the scale. Many chords will, of course, example the triad c-e-g is the tonic harmony of
erected
more than one
to
scale; for
C-Major (or Ionian), C-Lydian, and C-Mixolydian.
It is
only
when a chord
includes such characteristic
notes as the Dorian sixth degree, the Mixolydian seventh degree, and so on, that
it
becomes
differentiated
from the usual major-minor inventory.
Here
is
a complete
of the chords possible in the diatonic system including some which are extra-
list
major-minor. Through the broader concept of tonality, the
latter
may be
recognized as having a demon-
Such chords are marked with a cross (+). Chords peculiar to but (+ +). Chords having no marks are found in the Major or Minor
strable direct relationship to the tonic.
one mode are indicated by two crosses
mode.
T
,.
Lydian Tonic
Scale
ir
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^^
Chords
Lydian in I
+ +
+
wm
Lydian
I?
V
IV
III
II
II?
IV7
V7
+ +
+ +
+ +
+ +
i=*
m III 7
VII
VI
VI 7
VII 7
+ +
Mixolydian Tonic
Scale
Chords
§ Mixolydian
b
Q II
I
§
\\
§
»
^
III
IV
V
VI
VII
b
P^P
Mixolydian I 7
mm
III 7
II 7
+ +
+
+
+ + I
"
t>o
*\
IV 7
+ +
H
V7
i
VI 7
+
VII 7
+
Dorian Tonic
Scale
n
IE
~CT~
Chords
j
Dorian
I
1
Dorian •
I
§ II*
h +
ii
*a
"»
^
v
VI
VII
n n
'~n
^
IV*
III
(+)
^
i t
(+)
'
I7
lit*
in 7
IV 7
+
(+)
+
+ +
These chords also occur in the Major and Mixolydian modes but when
used in conjunction with a minor tonic triad possess striking individuality.
38
+
V7 +
+ +
+
VI 7
VII 7
+ +
+ +
39 Aeolian Scale
Tonic
__^
Chords IhorQS
a
j
|
Aeolian Aeolian
b
I'U
b
§ III
II
I
'
„
I
'I t
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g
IV
V
VI
+
1 VII
+
+
g i a a a a
Aeolian
II 7
I?
III 7
+
^
bo
n*
I
V7
IV 7
+
i
VI 7
VII 7
+
+ +
Phrygian Scale
Tonic
^
bo
|,o
moras
*
j j Phrygian Phrygian
+
„
n 1
*»
»»
^
IV
V
VI
VII
II
III
+
+
I
+ +
+
g^^
g m a
j
Phrygian I 7
bo =g=
tt
I
,
ii-u
I
,
II 7
III 7
+
+ +
V7
IV 7
VII 7
VI 7
+ +
+
Locrian Scale
Tonic
Locrian Locrian
^
|X »
|;
I
II
III
+
+
+ +
+
bo
V
IV
bo =g=
Im»
VI
+
+ b
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This particular enharmonic correspondence
ized by composers.
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44
Vincent, String Quartet, IV.
Allegro
Phrygian
Phrygian Locrian
Locrian
Copyright 1942 by Mills Music, Inc.
By adopting an experimental attitude, the Locrian I may be employed as the final chord of a musi2 gives the following cadence formula for the mode "Hypophrygiscb H" (sic) which, cal work. Haba nomenclature, is really Locrian. The diminished chord is frankly the final in this case. despite his +"" + .+ + .
.
B Locrian
I
Another experimental Locrian
close
is
given here. In spite of the fact that the
indisputably Locrian, the inconclusive nature of the diminished fifth
is
last
four measures are
almost evaded by the special
ment. Vincent, String Quartet,
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'Alois Haba, Neue Harmonielebre des diatonischen, chromatischen, Viertel-, Drittel-, Secbstel-, una, Zwolftel-Tonsysterns (Leipzig, Fr. Kistner and C. F. W. Siegel, 1927), p. 60.
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treat-
45 C-Locrian
$n C Locrian
The Locrian chord as
V°
?
of
7
1
N
is
6
naturally
somewhat more
I
1
7
rare than the simple triad. It
tially
6
is
possible to construe the
but curiously enough no examples have been found which illustrate such usage.
Although complicated by unresolved appoggiaturas, the
G-l +
7
followed by G-Locrian
chord of the following excerpt seems essen-
first
7
1
.
Ravel, Trio,
Permission for reprint authorized by
Durand
t
&
Cie, Paris, France. Philadelphia, Pa.
Since this chord
m
are Dorian
7
1
common
I7
must be present
in order to differentiate.
possible by the appearance of a scale or by other chords.
The following examples
is
made
Copyright Owners, Elkan-Vogel Co., Inc.,
I
C Dorian' C Aeolian j C Phrygian'
Distinctions are
I.
because the third
to three modes, other factors
minor and the sixth
is
is
major, these being the characteristics of the
Dorian mode. Faure.Op. 42, No. 2.
ifel
VL
=±
f
W
^m^ E\>
— 8
At Aeolian
I
Major
VII
VI
Dorian I Major I Moussorgsky, Boris Godounov, IV. Introduction
I
V
V
;
The simple forms
of the tonic chord in these
modes hold no
particular interest in connection with the present study since they correspond exactly to the tonic of the Minor mode. The
single exception
countered.
It
is
owes
the Dorian its
+"
which is occasionally enexistence to the Dorian sixth which forms
a majoi sixth with the tonic.
I
^ 46 Rimsky-Korsakov, Snegourotchka, Danse des Bouf fons'.'
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Worth
noting perhaps are instances of the employment of the Dorian Ireland,
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Mixolydian fi
r *5
I
(minor)
Debussy, Six Epigraphs Antiques,
1.
77.
G Dorian
1^
Permission for reprint authorized by
Durand &
Cie, Paris, France. Philadelphia, Pa.
Copyright Owners, Elkan-Vogel Co., Inc.,
Since the minor third and minor sixth are to be found in connection with the following chords, they are identified as Aeolian 1
7 .
The
first
two come about by scalewise motion descending from a simple Malipiero, // finta Arlecchino, Part
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I
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VI
III
III 7 .
II
7
Minor
I
V7 Copyright 1927 by C. C. Birchard
&
Co. Used by permission.
Elgar,
^==^
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£ I
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Pedal
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fej^
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&
Co., Ltd. Reprinted by permission of
H.
W
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Gray Co., Agents.
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3E
V
IV
14
Copyright 1910 by Rouart, Lerolle
el Cie.
By
special permission of Salabert, Inc., of
1
East 57th
St.,
N. Y.
Gesang der
m
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York
22,
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Glazounov, Der Konig der Juden,
as m^t m
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of Associated
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The two examples
T
of
S4 ^
in
^
given are identified with the Phrygian
I
^
si
^= =^
p
^
i
r
r
c
i
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s mode only by
the Phrygian signature
supplied by the composers: the characteristic minor second degree of the scale appears in neither. Both excerpts are final cadences.
Emmanuel, In Memoriam, »
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Rangstrom, Es wollt" das Madchen
frith
aufstebn
(final cadence).
Ftt
Phrygian IV 7
I
7
Copyright by Abr. Lundquist. Reprinted by permission of Abr. Lundquist.
3?"
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50
5
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C Mixolydian
I
7
[V 7 of IV]
The most
frequent employment of this
harmony
as the parenthesis
chord
V
7
of IV. Although examples are to be found in the works of almost every composer, Franck, Brahms, and Faure exhibit an especial predilection for
it.
Brahms, Trio for
pm
jT J
A Major
classical
usually stated,
1
J
t
mm V 7 of IV [Mixolydian
I
employment of the
V
7
IV I7
J
rV (Mixolydian
of
suggests the subdominant key
it
and Piano, Op. 114, rV.
CI., Cello,
¥
gg=i The
is
and imparts
1
7
is
)
either a
in the final cadence where, as
calming influence or a feeling of
lowering harmonic weight.
ppi
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C
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7
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^mm
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1 V 7 of
IV IV [Mixolydian I 7J
I
By permission
of J.
Hamelle
I
et Cie, Paris.
Brahms, Op. 33, No. 15.
Eb Major
It is also
I
V'of IV IV [Mixolydian I 7]
II
1
held that a cadence involving some such progression as the following
of the tonic, since
is
perfectly definitive
suggests the keys a fifth above and a fifth below.
it
P
*
TS-
r
S
f
s
TF C
V
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V7
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of
V
\V 7 of IV
VI
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IV
Suggested tonics and signatures:
m
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No
one would hold that these are real modulations since they are not
"fixed," yet the
upper and
lower dominants are truly implied: hence the term parenthesis modulation.
Without denying
this
method of explaining the definitive powers of a progression which includes dominant and subdominant, some notice should be taken of another view-
parenthesis modulations to the
The
point.
tonality of the
whole cadence
C-Lydian, and C-tonality with b sions into the
two contiguous
4
b
is
is
C
despite the /
:
and b
b
accidentals. C-tonality
mode
C-Mixolydian. Thus the Major
is
defined by
with
momentary
/ ' is
excur-
modes:
C-Major: C-Lydian: C-Major: C-Mixolydian: C-Major.
Although
in traditional cadential practice the
resolves to IV), this
is
the relevancy of the lydian
7
1
chords
(
not
name
its
V
sole use: the chord 1
of
IV becomes
marked with an
asterisk)
actually untenable,
*
is
.
I
TV and
acci-
is
the true
V
T
of IV,
(i.e.,
when
it
resolve to several other harmonies. In the latter case
questionable. In the
not unassailable.
Contiguous modes are those which differ by but one See the Lateral Index above, p. 19
dental.
may
be construed as
VI) would have pivotal significance as VI of
T
Mixolydian
V
/// of
1
two following examples
of IV, the chords
IV
respectively
—an
if
the Mixo-
which follow
(
analysis which,
II if
and not
52 Brahms, Variationen und Fuge uber ein
Thema von
rm Lr~ j^ n
j^ —
*
»
-T
^
* Mixolydian
f"
Mixolydian
l\(\)
[v 7 ofIV
V7
VI
[v 7 of IV]
VI of IV]
Saint-Saens,vLe
^
a
^
f£f P
*
o
P
-
o
P
^
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reprint authorized by
evidence the conclusion
ing a stereotyped classical
which
carries
with
it
The Mixolydian
no
^
VI III
Durand
P
is
I
&
Elkan-Vogel Co.,
Cie. Paris, France. Copyright owners. Philadelphia, Pa.
may be drawn
that
V
7
of
IV
is
Inc.,
a legitimate specific term imply7 is
a
name
for the
same chord
sometimes used in the midst of an otherwise major passage:
Op. 42, Introduction.
Mixolydian
I
Permission for reprint authorized by
Durand
is
_
Major I
&
Cie, Paris, France. Copyright owners, Philadelphia, Pa.
most frequently occurs in the elaboration of the
cancelled leading tone.
3fc
of IV]
I7
following final cadences
o
harmonic progression, whereas Mixolydian 1
C Major
it
=?=5= Mixolydian I 7 [V 7 of IV]
I
Saint-Saens, Coeli Enarrant,
but perhaps
o
implicit enchainements.
7
1
i¥
3fc
=§=
[V 7 of IV
this
P
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o
Celeste.
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?:
Permission for
Feu
g
7^
i+6
I
3
IV
7
I
Bt
Handel, Op. 24.
regarded as Mixolydian
it
Elkan-Vogel Co.,
final cadence.
would seem that the
Inc.,
Unless the
tonality
is
mode
of the
threatened by the
—
-
53
wmm m
Brahms, Sonata, Op.
1,
Andante. /7\
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ii
[V of V]
'
5
59 Ravel, String Quartet, First movement.
*Tj I —T
i
J
.
m F Major
fci=*
*
lJ^
Lydian Lydi
pizz.
I
Permission for reprint authorized by
Il9
Durand &
Cie. Paris, France, Copyright owners, Elkan-Vogel Co., Inc Philadelphia, Pa.
Janacek, Concertino for Clavier. A A
a^^
^
/CTf:
i
#
m
A
i A
*
*
A
A
P P m m
rC>
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^ A
Lydian
A
/T\
Minor
II
I
Copyright 1935 by Hudebni Malice Vmelecke Besedy, Prague, Czechoslovakia. Used by permission.
Gretchaninov, Liturgia Domestica, Op. 79-
$S
*
^
i=J= s
^p C Lydian
3
I
II
By permission
II
I
of Copyright
Owner, Boosey
&
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p I
Hawkes, Inc.
Moussorgskyj Boris Godounov, Act
C Lydian
I
III,
Scene
II.
3
60 It is
a remarkable fact that considerable personal research has failed to reveal other established uses
for the Lydian II
(V
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