Aspects of Plural Function in Chromatic Music

Society for Music Theory

When Functions Collide: Aspects of Plural Function in Chromatic Music Author(s): Kevin J. Swinden Source: Music Theory Spectrum, Vol. 27, No. 2 (Autumn, 2005), pp. 249-282 Published by: University of California Press on behalf of the Society for Music Theory Stable URL: http://www.jstor.org/stable/4499838 Accessed: 15/11/2009 22:56 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=ucal. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].

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When Functions Collide:Aspects of Plural Function in ChromaticMusic KEVIN J. SWINDEN

Daniel

Harrison's

1994 study, Harmonic Function

in Chromatic Music, questions

the traditional

mapping of chords onto function, and instead suggests that scale steps embody the source of harmonic function. His reformulation creates a new one-to-one mapping of scale steps onto harmonic function, which may be, at times, problematic. This article examines aspects of Harrison's theory

and advancesa differentmechanismforthe evaluationof harmonicfunctionbasedon the Tonnetz. It examinesa particularset of chromaticharmoniesthat displaypluralfunction,which may be organizedaccordingto a genusand speciesmode of classification.

tionship between G4 minor and E minor at once suspends tonality, and yet the passage somehow holds together. At the end of the passage cited, the phrase comes to rest on B major, recasting E minor as the new tonic of the modulat-

INTRODUCTION

The study of nineteenth century harmony abounds with rich chords and striking relationships. Sadly, many of these elude clear understanding. Our existing theories, though elegant and expressive, have not penetrated the moments in chromatic music about which we most care. The best-known theories give a tidy and systematic picture of diatonic harmony, but often finesse so many of these wonderful chords as exceptions to their harmonic principles, or simply fail to explore fully the functional effect of these chords. Such treatment, however, highlights shortcomings of theories that cannot explain such configurations within their systems of rules and structures. We would be well served to search for a mode of understanding that values these moments for what they are, rather than for being warped versions of something else. Consider Wagner's "Tarnhelm" motive from scene three of Das Rheingold, shown in Example 1(a). The repetition of the G#-minor triad invites us to hear this chord as a temporary tonic, alternating with an E-minor triad whose relationship to this tonic is far from clear. The chromatic-third rela-

ing phrase.1 What is so spectacular about the alternation of E minor and G# minor? Such an uncommon progression may well attract attention, but if we want to know how it works, the answer lies in the particular contrapuntal and functional association between the chromatically-related G#-minor and E-minor triads. The essential counterpoint that governs the G# minor/ E minor alternation is fairly straightforward. The upper

I The passagecited follows a fermataover a rest that was precededby a

half-cadencein C major.The mysteryof the "Tarnhelm" motive is cerintensified the of the triad G#-minor tainly by relationship following so closely on the heels of V of C major,and a fullerstudy of the passage would need to considerthe harmonicrelationshipin this largercontext. For presentpurposes,I am concernedwith the verylocal tonicity of G# minor within the key scheme of descending major thirds (from C, throughG# minor,to E at the end of the passagecited).

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250

(a) Wagner,Der Ring des Nibelungen, "Tarnhelm"motive.

(b) Wagner,Der Ring des Nibelungen, "Tarnhelm"voice leading. EXAMPLE I

2

3

linear phenomenon embellishing G# minor, there would be no need to add an emphasizing bass note E? to the Klang. There is something more to be said about this progression. Functionally, there are competing elements within the progression. If one overlooks the E? in the bass for a moment, the counterpoint might suggest that G? is a clever disguise for Fx, the leading tone. In this situation, the contrapuntal motion would be governed by a tonic 1 and 5 expanding outward to a Dominant-functioning 7 and b6. The BTwould be an inner-voice pedal tone, stabilizing the function of the passage in the orbit of G# minor, as shown in Example 1(b). This interpretation grows out of the condition already agreed upon that E minor is a chord that is subordiminor. With renate to-and in some way prolongs-G# spect to the presumed Tonic, 7 and kb are dissonant neighbors. But there is that slippery k6 in the bass. A lesser composer might well have left us this hypothetical version with 7 in the bass, or perhaps have put 5 in the bass to emphasize the Dominant function of the middle chord. Wagner, instead, created an ambiguity by placing E? in the bass, leaving a plagal bass line to support an otherwise authentic counterpoint, and changing the effect of the har-

voice, 5, is embellished with an upper neighbor, ?b; the lower voice begins on G# (i) and moves in chromatic contrary motion through a lower neighbor G?.2 Against this counterpoint, a stationary B? stabilizes the progression. Finally, E? is added to the bass, presumably to add color and emphasis, thus harmonizing the first inversion triad with its own root. While this explanation delineates the contrapuntal association of the two chords, it does not adequately address their functional relationship.3 If the E-minor triad were merely a

mony altogether. What I find fascinating is the existence of an entire family of chords in the literature that have common elements and functional behaviors, lending themselves to a genusand-species mode of organization. In this paper, I provide a way of thinking that groups many of these chords into a larger network of relations. This essay explores collisions of

As modal mixture is a fundamental principle of chromatic harmony, throughout the article all scale-step numbers and Roman numerals are based on a fixed notation in relation to the tonic pitch, regardless of modality. That is, in relation to A major-minor, F and an F-major triad are notated as k6 and VI respectively. The modality of a local key area may be inferred by the quality of the tonic chord (I or i) should the reader wish to take special note of instances of mixture. Other authors have considered this passage from the perspective of transformational theories (Lewin 1992) and mediant relations in the

context of a theory based on common-tone voice leading (Kopp 2002, 182f). Harmony texts typically describe this relationship as a chromatic mediant relation or "Coloristic Chord Succession" (Kostka and Payne 1995) without further comment on the harmonic function that may be present in the progression. Indeed, Kostka and Payne 1995, 439-40 go so far as to advise the student to abandon any attempt at interpretive analysis altogether in favor of simply labeling the chords with a letter-name root and chord quality.

ASPECTS OF PLURAL FUNCTION

FUNCTION AND PROLONGATION

Many theorists have struggled with the difference between diatonic and chromatic tonality, with varying degrees of success. Most Schenkerians address music of the late nineteenth century with little apology, while Schenker's detractors cite his own inability to deal adequately with the repertoire.4 My initial position is that Schenker's contribuit is essential to adtions are more than valuable-indeed, dress his contributions regarding the interaction of harmony and counterpoint. By the same token, however, Schenker's system inadequately addresses the slippery issues of harmonic function in the music of the late-nineteenth century. To rehearse these arguments at this late date would serve little use. Further, under the nouveau regime of functional analysis initiated by Harrison 1994, a critique of Schenker on these grounds becomes inappropriate. However, I believe it is neither necessary nor appropriate to discard many of Schenker's most important contributions. My intent is not to

5 4

Daniel Harrison writes: "Schenker's failure to deal with Reger's op. 81 is emblematic of a general failure to understand the harmonic structures and procedures of chromatic music, or at least to understand them with the same sensitivity that can be brought to the analysis of commonpractice and atonal musics. [...] We cannot repay this debt with Schenker's coin or with coins stamped from his bullion; Schenker's own experience is warning enough that his currency is not convertible" (Harrison 1994, 5). In a similar spirit, David Kopp writes: "Most of our prevailing analytic models and methods, predicated on eighteenthcentury practice, have traditionally explained chromatic music as the elaboration of diatonic structures. The music's frequent lack of conformity with these models has often been interpreted as a sign of weakness or inferiority in the music itself, rather than due to any inappropriateness of the model" (Kopp 2002, 1).

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revise, rewrite, or extend Schenker'stheory,5but only to investigate harmonic function in chromatic music with sensitivity to his ideas. Some authors propose that the nineteenth century represents a second harmonic practice, governed not so much by traditional rules of diatonic harmony and counterpoint, but by interactions and amalgams of scales (including the possibility that a chromatic scale might serve the role once occupied by diatonic scales), symmetric divisions of the octave, models of directional tonality, or dual-tonic structures.6 These bipartite divisions imply that chromatic music cannot be considered an extension of diatonic, but rather, must be wholly separate. By extension, theories and methodologies appropriateto the earlier first practice need to be retooled or replacedto address this new way of composing. Theories of harmonic function, on the other hand, hold that diatonic and chromatic harmony may display different idioms and customs, but are bound together by a common functional basis. Some of the most important work in this areahas come from theories of CharlesJ. Smith (Smith 1981 and 1986) and Daniel Harrison (Harrison 1994 and 1995), both of whom rely to some extent on Riemannian notions informed by a host of other historical contemporaries. Both

Subdominant and Dominant functional elements. Part I develops a theoretical apparatus; Part II considers specific instances of this phenomenon in various guises. I. THEORIES OF HARMONIC

IN CHROMATIC

6

Blasius 1996 providesan excellentbackgroundto understandingwhy such a courseis ill advised. GregoryProctorwrites:"thereis not a single 'commonpractice'extending from the early seventeenthcenturythrough the end of the nineteenth century.Rather,the era can be dividedinto two large, overlapping style systems,herein referredto as: classicaldiatonic tonality, and nineteenth centurychromatictonality."(Proctor1978, iii). The essential featurethat distinguishesthese two tonal languagesis the underlying scale on which each is based:the diatoniclanguage is grounded in the traditionalmajor-minorsystem,while the chromatic/enharmonic language is based on the 12-note, equal-temperedchromatic scale. Other representativeexamplesof these approachesto the nineteenth century as a second practice may be found, among other places, in Benjamin 1975, Krebs 1981 and 1991, Stein 1985, Kinderman and Krebs,1996.

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Hugo Riemann and Arnold Schoenberg believed that the differentiation between diatonic and chromatic music was a matter of style, rather than substance; neither recognized a strict division between the two styles. Unfortunately,neither Schoenberg nor Riemann developed an analytic methodology sophisticated enough to present detailed analyticalpictures of both vertical and linear dimensions. Without a system that allows the linear representation of harmony, any analytical theory is impractical,and ignores what is perhaps Schenker's most significant contribution.7 In an effort to capture the powerful syntactic model of a theory of harmonic function while also capturing the linear-harmonic musical aspects as afforded by a Stufentheorie,I adopt a Riemannian theoretical model: a harmonicfunction/bass-line system following lines developed by Charles J. Smith, and further informed by Harrison's renewal of harmonic function. The analytic system holds to the tenet that just as surface voice-leading events may prolong a harmony (in the Schenkerian sense of the term), linear events may also be brought into the service of harmonic function. The Smith/Harrison distinction regardsthe nature of harmonic function itself. Smith's function is more akin to 7

As an analytical system, it is on this point where Harrison 1994 may fall short. Harrison's three methods of analysis (segmental, linking, and accumulative) generalize functional moments and points of functional discharge according to segmentations based on the perception of an imaginative listener. What Harrison gains in analytic flexibility, he sacrifices in analytic rigor and the more scientific notions of experimental repeatability. Harrison never claims to provide a sophisticated system of analysis; rather, he values the simplicity of his analytic notation (Harrison 1994, 127). As a replacement for traditional models of counterpoint, Harrison's new counterpoint weighs the functional discharge of several individual melodic lines; these lines don't so much interact as compete for functional presence. From the outset, he denies both the applicability of Schenker's system to this music as well as attempts at revisionism (see note 1, above). For arguments that critique Harrison from a Schenkerian perspective, see Whittall 1995. Despite this shortfall, however, Harrison casts a gauntlet that no scholar of harmonic function can afford to ignore.

Schenker's harmony--it is a property of a chord, part of what a chord is. Harrison'sfunction is an action-it is something that a chord does.Thus we are not speaking of functional prolongation, per se, but rather, of functional persistence, despite intervening voice leading activity.Thus, the analytic notation employed is designed to draw attention to functional connections between chords and acrosspassages. The analytic notation used modifies Smith's approach (Smith 1981 and 1986). It is a hierarchicalnotation designed to privilege the prolongation of harmonic function rather than a specific harmony per se. At the layer closest to the musical surface open noteheads indicate chord tones; filled-in noteheads indicate non-chord tones; and barlines separate discrete harmonies (often trivial harmonies). The structuralouter-voice counterpoint is identified with stems, while slurs relate the voice leading of non-chord tones to the chord tones they embellish. Subsequent layers re-interpret harmonies as embellishing chords that prolong or connect regions governedby a particularharmonic function, showing the interactionof harmony and counterpoint. On deeperlayers, barlines separate functional regions rather than chords; the deeper one goes into the hierarchy, the closer one approachesa Schenkerianbackground, showing a very large expanse of Tonic prolongation. While a more orthodox Schenkerian notation could be used for this purpose, it would not sufficiently highlight the aspects of harmonic function that I discuss. In the interest of keeping the examples as compact as possible, I have compressed the analytic layers closest to the foreground to functional symbols applied to the music itself, and presented a reasonablemiddleground linear analysisto support the discussion. DETERMINING

HARMONIC

FUNCTION

Small-scale and large-scale harmonic structuresare classified by harmonic function and bass line context. Categories of harmonic function identify chords in terms of their relationships within familiar diatonic contexts, and provide the

ASPECTS OF PLURALFUNCTION IN CHROMATIC MUSIC

basis for a harmonic syntax.8 Principally,authentic progressions involve directed motion from Tonic (T) to Dominant (D) regions and typically return to Tonic; these categories should requirelittle defense at this point. The third significant category betrays the fact that harmonic function cannot be defined by pitch-class identity alone, even in the simplest diatonic contexts. While some authors prefer to consider all IV chords as Dominant-Preparation (DP), others preferthe label Subdominant (S). The former betrays a bias for authentic models of harmonic progression, relegating plagal models as distinctly secondary;this seems to follow Classical diatonic practice, and is closely aligned with Schenkerianassumptions. The latter implies that plagal progressionslie on equal ground with authentic systems as understood in a Riemannian dualist model.10In this study,context shall differentiate DP function from S function; when speaking in general terms about the sonorities involved, I shall use the term "Subdominant." In addition to reckoning the relationship of a Klang to a tonic pitch, the second principal functional determinantis a chord's context. If we privilege the status of bass scale steps, we can categorize chords according to their linear configurations.11 Following Harrison's bold lead (Harrison 1994), I shall abandon Roman numeral designations for all but the most straightforward harmonies.12The occasional Roman numerals that are mentioned are provided only to aid the 8

9 io ii

12

All functionalcategoriesarecapitalized,to distinguishthe termDominant (the functionalcategory)from dominant(the V triad),andTonic (the category)from tonic (the chord),etc. Other functionaldescriptors that do not sharetheir name with a chord are likewisecapitalizedfor the sakeof consistency. The termDominant-Preparation was firstused in Forte1979;the term Predominantwould serveequallywell in this regard. This positionis well defendedin Harrison1994. The importanceof bass scale steps when reckoningharmonicfunction is too often undervaluedin treatiseson functionalharmony,with Smith 1981 and 1986 and Harrison1994 providingnotableexceptions. Smith 2003 also presentsthis challenge,but does offeran alternative.

253

reader;they are neither meant to convey functional meaning, nor to suggest a privileged status for the indicated root. Inescapably,Roman numerals remain the linguafranca of our discipline, even if through them we retain biases that may need to be discarded when considering highly chromatic music. Defining a single functional affiliation for each of the diatonic chords is often problematic, enough so to prompt Harrison to abandon the effort altogether. In a traditional conception of harmonic function, we needed to rely on definitions of harmonicfunction ascribedto a predefined, "acceptable"pitch-class collection (Akkord).In contrast, Harrison thoroughly works out a theory in which the individual scale steps themselves bear the burden of expressing functionality (Harrison 1994). This theory is most promising, and indeed renews the notion of harmonicfunction in a powerful way. For readersnot well versed with Harrison'stheory, a brief synopsis is provided in the appendix to this article.13 Because harmonic function resides in the constituents of chords, we are given a tool with which to deconstruct any sonority (Klang) and to reckon its harmonic function carefully. The argument is predicated on the proposition that each primary scale step (with its own orbit of governance) stands in a unique relation to its Tonic. More recently, however, conclusions in Harrison 2002 seem to challenge this position. Harrison 2002 builds a case to support the "unconformed Tonnetz"as a model for key relations-a Tonnetz that is not conceived as a closed system in equal temperament (as on a torus), but rather one that may extend infinitely in every direction, conceived in just intonation.14 13

14

Rifkin 2004 applied Harrison's theory in a promising way. Rifkin heeds the call of Burkhart 1978, that a recurrence of a structural motive must be presented in a similar or parallel functional context, but reckons that function according to Harrison's theory. In this manner, Rifkin presents a compelling theory of motivic/functional analysis in the music of Sergei Prokofiev. It is widely accepted that the elements of the Tonnetz may stand for pitch relations or key relations. Pragmatically, of course, one does not

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Harrison 2002 concludes that when a composer takes a journey through keys on the grid, let us say, moves from one C on the grid to a different C on the grid, these two Cs are not the same.That is to say,the composer has ended in a different place; enharmonically equivalent pitches on the grid, or indeed any recurrencesof the same pitch class, do not have the same meaning. In a way, Harrison broadens the scope of directional tonality; now, a piece may begin and end in the same key,yet still have directionalproperties. Harrison 2002 tacitly contains the correction to what I see as the basic errorof Harrison 1994. On the unconformed Tonnetz (Example 2, centered on a C major tonic triad), the 4 primitive for S function is not the same 4 that extends the Dominant triad to a seventh chord. These two degrees stand in a different relation to the original Tonic, contrary to the suggestion in Harrison 1994, which asserts that there is only a single 4 in relation to the Tonic, and that it is a primitive of S function. The unconformed Tonnetzreconciles the perceptual difficulty I have with Harrison's formulation of harmonic function. Sometimes 4 expresses Subdominant function, and sometimes it expresses Dominant function. The same point can be made about 2: sometimes 2 is an amplifier for the Dominant and sometimes 2 comes about through an extension in the Subdominant direction. Likewise the submediants: to my ear, k6 is perceived differently when it appears in iv and when it appearsas the seventh of vii . This begs a new question. How do we know which 4 we are looking at on the score?Allow me to present a reading of the major-minor system on the unconformed Tonnetz that remains faithful to a dualist mode of theorizing. For ease of reading, I shall work with the C major-minor complex. In Example 3, the shaded area representsthe composite scale of the major-minor system as generated by the primary triads. In this figure, motions toward the West represent moves

meander into the realm of theoretic key signatures and expect that the music shall not be adjusted for sensibility's sake.

toward the Subdominant side (T to S, D to T) and motions toward the East represent moves toward the Dominant side (S to T, T to D). The shaded area (the major-minor system) is sufficient to account for the three primary triads and the functionally slippery mediants and submediants as contiguous lozenges on the Tonnetz. Each triad quality has a distinctive shape: an upward pointing triangle is a major triad and a downward pointing triangle is a minor triad. Less common, mixed structures are observed on the diagonals (Ak-C-E, A-C-EB, Ek-G-B, and E-G-Bk). The main East-West axis contains the bases and associatesof the three primary functions, and in the offset rows to its North and South, we find the functional agents. This region forms the main province of the key. The rows that are twice removed from the main East-West axis contain the elements of more distant modulations, and the strong tendency for a key to dissolve.The pitches located in these regions point to Tonics on a differentEast-West axis than our home key, even if they point to a different location of the same tonic (a different C). Likewise, should one stray too far East or West, one might easily get caught in another tonal gravity.However, the flexibility along the main East-West axis is somewhat greater, allowing for D ofD and S of S regions to maintain an affiliation (if more remote) to the original key. As essential seventh chords became fundamental harmonies, we may look to this Tonnetz to stretch the basic major-minor system. The first stretching element would be to consider the seventh of V7. Projected from the dominant triad, we stretch the system to include the F found on the Dominant side of C. If we were to mirrorthis action on the Tonnetz,we would stretch the system Westward, invoking the Riemannian practice of generating a minor triad downward from its dual root (its fifth, in traditional terms).Thus, we gain access to a supertonic triad that is fully on the Subdominant side of Tonic and a leading tone triad that is fully on the Dominant side of Tonic. Since nineteenth century harmonic practice typically permits dominant ninths and leading tone sevenths, it is easy to allow for a hyper-

ASPECTS OF PLURAL FUNCTION IN CHROMATIC MUSIC

A

F

E

B

G

C

D

Ab

E6

B6

A

a

B C

Cl

F

A

AB

EXAMPLE 2.

D#

G#

E

El

A#

Fl

B,

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GI

C#

C

Gt

DI

A

E

EG Db

G6

D6

A6

E6B6

B

Tonnetzand 4. Unconformed

extension of the basic chromatic complex to include the A and Ak lozenges toward the East. A balancing Westwardextension toward B and B1 is also possible; strictly from a theoretical point of view, there is nothing that would prohibit this move, and it seems to sustain an equivalentjustification as a duality.It must be noted, however,that a hyperextension in either direction results in the leading tone or subtonic seventh chord. The harmonic function of the former is at times slippery; that of the latter has a nebulous function that rarelyhas an unmediated associationwith the home key. It is often read as either Dominant of lIII or Subdominantof IV. Example4 outlines this largerregion. A comment is warrantedregardingthe functional status of the hyper-extendedelementsjust proposed.Notably,these pitches are located far from the originalTonic on the Tonnetz. Significantly,two of them they are found in the parallel row, two steps removed from the main East-West axis. As suggested, the axes that lie two steps above and below the main tonal axis of the key bring scale steps that may be drawnto the gravityof anothertonic. Specifically,these two axes above and below representmoves towardthe sharpside of the key and the flat side of the key respectively. As

Harrisonpoints out, a move toward the sharp side is a generalizationof Dominant motion, and a move toward the flat side, of Subdominant (Harrison 1994, 27). Thus, although the hyper-extended7 is achievedby a Westward (Subdominant) extension, it crosses a Northern tonal field boundary. The newly acquired7 is once again Dominant, but a Dominant caught in the tonal gravity of a different 1-the one found to its Southwest.The parallelargumentalso standsfor the hyper-extended b6 that extends into the flat-side axis, and its recovery of Subdominant function. Therefore,pace Harrison and Erpf, the vii' chord becomes the first diatonic harmonythat is functionallymixed by nature. Adjacent to the outlined areain Example 4, we can recognize some basic chromaticchordsthat include F# (stretching furthertowardD ofD function) and the Neapolitan degree, 62, extending further toward the West. If we stretch furtherWestward,we reachthe realmof S ofS. These traditional diatonic harmonies of the complex major-minorsystem form the experientialbasis for an understandingof harmonicfunction in more complex Kliinge. I suggest that our understanding of harmonic function is based on pitch-class groupings, according to two guiding

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A

E

c

F1

G

AM

Fa

EXAMPLE 3.

Ct

BR

A#

D#

G

C

CG

G

D6

G

Ab

B

E C

F

F6

Et

A

Da

G

E6,

B6

UnconformedTonnetz and major-minor system.

principles.The first principleis functionalparsimony.Given a choice, it is more naturalto group together pitch classes in closer geographicproximity.Thus, in a D-F-A complex, functional parsimonywould dictate that the D results from stretching the system toward the Subdominant side. It would be decidedly unparsimonious to take the F-A from the Subdominantside, and to pick up the D from the Dominant side of our home Tonic. One would need strong contextual justification to locate a D-F-A complex completelyon the Dominant side of Tonic, where it might be considered a modally unusualvariantof D ofD function.15 Alternatively, in a Dominant-sided D-F-A complex, the A might be perceivedas a non-chordal pitch class against a more stable harmony--in which case the argument for an independent function begins to dissolve. (I shall returnto this in the discussion of linear chords and Example 34.) The second principle is a left-privilegedinterpretation,which allowsthe leftmost element on the Tonnetzto overshadowthe harmonic 15

G

1CF

B

Gb

GC

Fb

Cl

D

E6Bb

Ab

A

B

This argument assumes sympathy with the discussion of the minor Dominant in Harrison 1994,passim, especially 53-54.

function of elements on the central East-West axis, where the context is appropriate.When notes are added to a Klang in an Eastwarddirection,it is easy to imagine these as added factors to a tertian sonority: fifths, sevenths and ninths. Added notes in a Westwarddirectioncould representadded sixths (which might not disrupt the prevailingfunction of the Klang),or new bases,which redefinethe originalnotes as agents and associates.Such a redefinitionis bound to change the functionalorientationof the sonority.While the A-C-E complex might sustainTonic function by virtue of the powerful C-E Tonic elements, the left-privilege suggests that this complex may lean towardSubdominantfunction. The topography of the Tonnetzprovides a structurein which to rethinkthe primitivesof harmonicfunction. However,our reckoningof harmonicfunction is incompletewithout consideringour expectationsof tonal syntaxand the linear patternsof the bass line. The paradigmatic authentic harmonic progression is a succession of chords T-DP-D-T (with DP optional). Any contiguous segment of the paradigm is considered an authentic harmonicprogression;any element that disruptsthe

ASPECTS OF PLURAL FUNCTION IN CHROMATIC MUSIC

E

A

F CO

B

%

c

F

G

A

AB

D

E

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D0 I

GG

A

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AA

O

ES

B

G#

C#

D

DD F

E#

%

E

A

A

DO

Bb

EB

BG

Gcl

I

%

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E

B

BF

V EXAMPLE 4. UnconformedTonnetz and extended major-minor system.

paradigm is considered non-functional with respect to the progression.The paradigmaticplagalprogressionis a succession of chords T-S-T.16 A categoryof linear chordsis essentialto an investigation of harmonicfunction.These chords are often functional,but they do not participatein typical paradigms.Examples include passing or neighborchords (for example,a passingIV6 chord between V and V6), chords that result from linear processes(such as the 5-6 motion abovetonic that generates a vi6 chord without a strong sense of Dominant-Preparation or Subdominant function), and many of the standard 4-chord techniques and sequences. The notion of a linear chord allows us to assess chords by their voice-leading and metriccontexts,where a blind applicationof functionaccording to identity is unmusicaland unconvincing.Linearchords 16

In laternineteenthcenturypractice,HarrisonfollowsRiemannin postulatingthe possibilityof a dual paradigm,T-D-S-T. As this is the most problematicparadigm,I shall leaveit unconsideredfor the time being.While I am sympatheticto the model, its considerationis not germaneto my purposeat the moment.

suggest a hierarchy,despite any sense of harmonic function dischargedin the process. A roster of typical bass lines, catalogued by their linear shape, is a useful accompanimentto the abstractfunctional paradigm.Such standardbass-line progressionsare common among harmony textbooks, although they are normally found amidst discussions pertaining to individual chords, rather than organized according to chords that share the same function and are built over the same bass scale step.17 In this way, characteristicbass-line patterns and functional progressionsbecome inextricablyintertwinedin this system, each informing and guiding the functionalinterpretationof the other. 17

For example,Aldwelland Schachter2003 addressthe behaviorof IV, ii6, IV7, and ii as they move to variouskinds of cadentialand noncadentialDominant chords,but these discussionsare well dispersed throughoutthe text.Certainly,when these discussionsareconcatenated accordingto bass-linemotion,thereis a dangerthat some subtletyregardingeach particularDP(4) chord might be lost, but this is at the expenseof the clearpresentationand importanceof bass-linecohesion in functionalharmony.

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valuable,because the motion from Tonic is generally unrestricted. Example 7 catalogs the bass lines that are eliminated on the grounds that they do not characterizea particular functional disposition; Examples 8 and 9 provide the resulting lists of characterizing authentic and plagal bass lines respectively. Examples 8(a) and 8(b) tell us that a 5-i bass line is, in itself, strongly suggestive of authentic D-T harmony:there is no legitimate plagal succession with such a bass line.19Likewise, Example 9 shows that a bass line that moves from 4 to I stronglyindicates plagal harmony for the same reason. It is not surprisingthat the resulting rostersinclude only motions from the paradigmatic S and D agents and bases. When Dominant or Subdominant agents are placed in the lowest voice and move to the Tonic Base, that condition alone is sufficientto support a strong paradigmaticfunctional articulation. Having postulated the tonal focusing power of bass lines, we must still consider the implications of the upper voices. Any single upper-voice pitch may be a constituent of several different diatonic triads or seventh chords-an obvious point with an important ramification. Since any pitch may imply one of several possible chords, a single pitch within a Klang cannot represent a single chord. The unconformed Tonnetzdiscussed above adds depth to this observation.In a major-minortonal context, there may be different attitudes availablefor many different scale steps. That is to say, there are two distinct kinds of 4 in this system: one is found due West of the Tonic (a strong Subdominant location) and the other is an off-axis extension of the Dominant in the stretched system. The principles of functional parsimony suggested above argue that we should look at the companion scale steps in the Klang to help us determine which 4 we have before us. Example 4, in its extended version, shows us that we have only one 1 and one 5 in the system. If one of these is the left-

COLLIDING FUNCTIONS

Progressions are classified according to their bass lines. Within an unembellished harmonic paradigm, nine Dominant-Preparation to Dominant possibilities and six Dominant to Tonic possibilities comprise the common authentic progressions. While there are only a few common Classic era bass lines for plagal progressions, nineteenthcentury practice greatly expanded the possibilities. These bass-line rosters, given in Examples 5 and 6, can be confirmed in most standard theory texts by concatenating the discussions of appropriate chords and their typical resolutions. Exceptions to these practices may constitute "marked" musical events, but certainly are not so prevalent as to invalidate the theory as a whole.18 Examples 5(a) and 5(b) present rosters of authentic bass lines according to their functional disposition; Example 6 presents the comparable roster for the nine plagal bass lines found in nineteenth-century music. Using these figures, we see bass lines that may representmore than one type of progression (authentic or plagal). Any bass lines found in both authentic and plagal contexts are considered functionally ambiguous, and therefore should be eliminated from a new list of bass lines that characterizeone particular functional disposition. For example, since a 4-3 bass line might reasonably support either D-T or S-T progressions, 4-3 is eliminated as a characterizing bass line. On the other hand, it is reasonable to declare that a 4-I bass line is emblematic of a plagal progression, since the only typical context for a 4-1 bass line is S-T. Similarly, bass lines that could reasonably arpeggiate a single harmonic function (such as 4-2, which can potentially support either DP-D or DP-DP) and bass lines that might commonly support T-D or T-S are also eliminated, since they do not characterize any single functional disposition. Rosters that summarize the possible common-practice motions of T-D or T-S are not terribly 18

The term "marked"is used in this context following Hatten 1994.

19

See also Harrison 1994, 48, Example 2.1, which confirms this finding.

ASPECTS OF PLURAL FUNCTION

D

DP

D

-

T

2

4

-

-

(b)3

IN CHROMATIC

MUSIC

T-S

Bass Line T-D

i-i 1i-

DP-D

x

x

2-i

259

D-T

S-T

Other

x

x

x

x

A 2

2

4

i

-

i

7

4

-

(~~3

4-(2

4-2

-

T

i

-

i 1

-

((03 (-)

S-S X

X EXAMPLE

basslines. of.authentic

2

x X

5. Roster

S

D-D

X

4_7

(b) EXAMPLE

(6)3-2

D-D

7. Non-characterizingbasslines.

DP

D

4

5

(06)5

T-T

x

x

x

4-4

7• -

X

X

()3-i

D

-

-

7

T i

(b)

(a)

EXAMPLE8. Characterizing bass lines: authentic.

(b)3 EXAMPLE

6. Rosterofplagal basslines.

S

-

T

4

-

i

(0)3 most element of the Klang, then it will likely subsume the function of the Klang to its purpose. If we find ourselvesat a different 1, then the music has undertaken a noteworthy journey to a new place.20There is also only one pair of Tonic agents (3, b3), and two pairs of Subdominant agents (6, b6) 20

Cf Harrison 2002.

EXAMPLE

9. Characterizing bass lines.:plagal.

and Dominant agents (7, b). Regarding the two Subdominant and Dominant pairs, one is found close to the Tonic whereas the other is in the hyper-extended tonal field. In

MUSIC THEORY SPECTRUM 27 (2005)

260

either case, invoking the more remote agent will require an extraordinary circumstance.21The viif chord is striking in that it invokes a remote agent, attesting to the slippery nature of this symmetricalharmony and accounting for its ability to slip so easily into a new tonal field. This observation supports Harrison's position regarding the devotion of the functional agents to a single tonic, even if it turns out to be a different manifestation of the same tonic pitch. Regarding Dominant agency, the last case suggested (a Dominant with ?7 agency) is ratherextraordinary.In most cases, left-privilege suggests that the Klang which contains k7 will function as either T or D of S. In a more extreme case, the context might suggest that k7is found off the Western edge of the majorminor complex, and that ?7 reaches toward S of S function. However, two versions of 2 and 4 can be aligned with either strong S or weak D. The closest chromatic scale steps to the major-minor tonal field are #4, availablein close proximityas the first step towardD ofD function, and availablein close v2, proximity on the subdominant side. II. SUBDOMINANT-DOMINANT

COLLISIONS

The criteria above constitute a new instrument for observing harmonic function. When evaluating harmonic function, two elements must be observed-the bass line, and the component scale steps of the chord in their relation to Tonic on the Tonnetz.Characterizing bass-line patterns are the primary determinants of harmonic function. In traditional harmonic language, the function of the upper voices (the sonority) typically agrees with the function of the bassline pattern. Occasionally,however, these two elements con21

One might also locate 6 due East of the Dominant associate 2 (three fifths to the East of Tonic). If that 6 is used, then we are getting remote, but we are still along the main East-West axis, and are perhaps engaged in "Dominant Accumulation?" (D of D of D) as per Harrison 1994, 153 f Note that the remote version of b6 is further removed in the Southern direction, and is much more prone to behave as Subdominant of a new tonal center.

tradict each other. For example, the bass line 1-4-i characterizes the plagal paradigm T-S-T; however, if the chord above 4 contains a leading tone that resolves correctly to tonic with the change of bass (i.e., it behaves as an authentic leading tone), then there is an inherent contradiction between the presence and resolution of the leading tone (the agent of Dominant function) and the motion of the bass (one of the bass lines that characterizesa plagal paradigm). If such phenomena were rare and confined to the musical surface,it would suffice to comment on the curious effect of the progression,and to explain the processes that brought it about. Such contradictoryprogressions appearwith surprisingly regularity in the music of the nineteenth century. Given that they appearso frequently on both the surfaceand deeper levels of structure, it makes sense to investigate the family of chords that contain collisions of Subdominantand Dominant functions.22 22

A comment regarding Harrison 1994 and his discussion of Mixed Function (a concept he credits to Riemann and Erpf) is necessary at this point to clarify the difference between our discussions. Harrison uses this term to describe chords of inherently mixed function: "Since secondary triads contain scale degrees associated with different functions, they arefunctionally mixed structures, able to communicate more than one function" (Harrison 1994, 60). That is to say, since 2 is associated with D harmony, while 4 and 6 are associated with DP harmony, a supertonic triad is functionally mixed. Of course, it is quite a different matter to claim that a chord has the capability to express more than one function (Harrison, after Erpf) versus the claim that a chord expresses two functions simultaneously,as I shall argue below. In the application of Harrison's version of mixed function, conflicting and ambiguous functions are weighed to give a harmony a three-dimensional functional vector. My reformulation of function-finding obviates the majority of diatonic chords that have this property, with the exception of viio7. The kind of functional mixture I speak of here is the very particular mixture found when a characterizing functional bass line conflicts with upper voices that characterize a different function. In Harrison's use of the term, mixed function chords are common diatonic phenomena. While the Kldnge I explore are, by comparison, less common they are nevertheless important and worthy of consideration.

ASPECTS OF PLURAL FUNCTION

There are two distinct ways for Subdominantand Dominant functions to collide. The first type is defined as a chord whose bass scale step participatesin a context that characterizes a Dominant-Preparation or Subdominant chord, but which also contains the Dominant agent in an upper-voice. These chords shall be designated by their primary(bass context) function with a superscript'D' indicating the element of Dominant function in the upper voice. Thus, the two paradigmatic contexts for this first type are T-SD-T and T-DpD-D-T. As with any structural paradigm, the basic forms of these possible progressions may be decorated through various non-functional chords or successions of chords that share the same function. Example 10 presents the basic structural contexts that contain SD and DPD chords. It is noteworthy that the mixed-function chords in these two paradigms have markedly different effects. In the first instance, the Dominant element in the SD chord appearsbetween two manifestations of Tonic; in the second instance, the Dominant element in the DPD chord anticipates the arrival of the stronger, authentic Dominant. Nevertheless, even though the two contexts representdifferent manifestations of a chord containing a functional collision, the collision is the common element that allows us to draw a similaritybetween them. The second type of collision occurs when a bass scale step contextually characterizesDominant function, but its essential harmonic characteris imbued with Subdominantfunction, according to the function-finding techniques discussed above. This type shall be indicated in the same manner as above,with roles reversed:Ds. A Ds chord cannot, by definition, exist in the context of a plagal succession-it may only appear over a characteristicallyauthentic bass. On the other hand, in the context of an authentic progression,a Ds chord may stand in place of an expected Dominant chord in the same fashion as a SD chord. The theoretic contexts of progressions involving Ds chords are given in Example 11. We shall return to Ds structureslater, after exploringthe SD and DPD categories in greaterdepth.

IN CHROMATIC

MUSIC

261

SD chordsin plagalparadigms In theory, the basic form of the plagal succession T-SD-T may appear over any characteristically plagal bass line, as defined in Example 9, above. Interesting examples of SD progressions appear over (b)6-1 or 4-1 bass lines, where the leading tone is occasionally spelled enharmonically as bi.23 Note that while Kb is proximate to the Tonic on the Tonnetz, it is twice removed from the main East-West axis in relation to the Tonic. An authentic (hypothetical) bi seriously challenges the nature of a tonal system, perhaps in a way that cannot be sustained. Most importantly,spelling such a pitch as b1 and treating it contrapuntallyas such are very different things. In every case I've found, b1 appearsto be spelled as such to form a tertian sonority that is easy to read, yet it is contrapuntally treated as a leading tone. (Refer to Example 1, where b1 (G?) was treated as a leading tone (Fx) in the key of G# minor.) Therefore, on functional grounds, I find it more compelling to challenge the spelling of the note and to understand it as the Dominant agent, thinly disguised, thus occupying a different (disjunct) location on the Tonnetz.In these situations, Kiis a proxy for 7. Because the SD chord classification is inherently ambiguous in a traditionalsense, an obvious choice for the label and notation of each chord is likewise unclear. SD chords could be reasonably shown as altered, or non-standard Dominant chords, or conversely, as altered Subdominant sonorities.24 23

24

While I do not discountthe possibilitythat the characterizingbass line the weakest of the characterizingbass (b)6-(b)3(although admittedly lines) may supportsuch structures,I have yet to find convincing examples to demonstratethis pattern. Having attemptedto reduce all chordswith colliding functions to expressionsof single Romannumeralswith appropriatealterations,I have discoveredthat thereis simply not a single tidy symbol that will satisfy all cases and conditions.I am gratefulto Daniel Harrison for warning me (both in his book, and in reading an early draft of this paper) againstfetishizingRomannumeralsymbologyat the expense of a clear

MUSIC THEORY SPECTRUM 27 (2005)

262

AuthenticBass

Plagal Bass T-SD-T T-S-SD-T EXAMPLE

presented to draw attention to this equivalency in the context of a Roman numeral interpretation. By definition, all SD chords are assumed to resolve to a T(i). In an authentic paradigm, this roster would also suffice for DPD chords resolving to D(5) chords. This list is not exhaustive, but it provides insight into the nature of the chords and their possible spellings in the literature.

T-DPD-D-T T-DP-DPD-D-T IO. Possible contextsfor SD andDPD chords.

Authentic Bass T-DS-T T-DS-D-T T-D-DS-T T-DP-DS-T EXAMPLE II.

SD(4) and SD(6) SD(4) chords appear as embellishments of plagal cadences in some liturgical pieces such as the traditional hymn-tune Caithness, given as Example 13. Although the SD(4) chord sounds innocuous due to its embellishing context in a succession, its features are nonetheless T(i)-S(4)-SD(4)-T(i) evident. First, the function of the succession is unaffected by the decoration because it is governed, at the deepest level, by a diatonic plagal cadence; that is, its resolution denies the Dominant function often afforded to an unqualified vii 4 in favor of recognizing the chord's Subdominant potential. Second, the insertion of the leading tone before the resolution to tonic strengthens and directs the progression more forcefully than the unadorned plagal close. For these reasons, vii3j behaves as SD(4) rather than D(4). On the Tonnetz, this manifestation of vii' is achieved in the hyper-extended field to the North-West of Tonic. The chord is principally S(4), which has been stretched to include a Dominant agent. An example of a similar sonority in a non-liturgical context is found in Robert Schumann's Kreisleriana, no. 5, shown in Example 14.25 Here, the leading tone, F#, embell-

Possiblecontextsfor Ds chords.

As the purpose of this article is to explicate the functional behavior of certain Kldnge, the analytic label for SD chords simply appends the bass scale step to the functional designation. (While this symbol does not discriminate between all of the possible sonorities for the category,the accompanying discussion shall make those differences clear.) A healthy roster of SD chords may be derived by placing familiar diatonic and chromatic vii' or vii' chords over either a bass 4 or (6)6. Example 12 provides such a roster of possiand SD(b6) chords with their scale steps; it also inble SD(,) cludes misleading Roman numerals that might be recognized through common enharmonic spelling. The most common enharmonic spelling substitutes 1 for 7, such as the G? in the 6vi chord of Example 1. 7 by proxy produces a comfortable triadic spelling, despite the linear behavior of G as a lower neighbor, Fx. The last column on Example 12 is representationof harmonicfunction.It is certainlypossible to examine these harmonies as Roman numeralswith complex figured bass appendages,but such symbolstend to obscureand complicatethe discussion of harmonicfunction.

25

This piece is also discussed in Agmon 1995, 210, Aldwell and Schachter 1989, 392 and 2003, 418. Agmon exhibits the passage to support his case for the weak Subdominant function potential of VII7. However, the strength of Agmon's argument is undermined by the privileged status given to chordal roots in his theory. It must be stressed that it is only in its second inversion (over the bass scale degree 4) that any Subdominant function may be realized. Although the first edition of Aldwell and Schachter 1989 does not acknowledge the implied mixed function of this progression, the 2003 edition makes this explicit.

ASPECTS

Genus

Quality dmd

OF PLURAL

Structure 4 vii.. 2

FUNCTION

IN CHROMATIC

MUSIC

RN (?) O

ia

S

sD)(4 )

dm1,no 3rd

b 2 ^4

viil, (iv6?)

Fr 3

4 1 #2i

IVo0 6)

,30

(26

dm

4-b a ivL, 5 7 i iv"4# 4

m•

2#V

Mmi

EXAMPLE 12.

16

'V6 (vii/IV)

E:

T(i)

S(6/4)

IV

sD(4)

I

vii112

b 4

dm+6

E:

vii1, (iv??)

d6

A"gm4

sD(,7)

vii"4

.... ..................................

6 4b

dd7

sD(4)

4

...

d

263

b87 2

(D)

T(i)

ivo6 V+4 EXAMPLE

vi b3II,

RosterofSD chords.

ishes a plagal progression, resulting in a SD(4) chord that is approached from its diatonic subdominant and resolves to a root-position Tonic chord. While Aldwell and Schachter (2003) point out that such treatment of a diminishedseventh sonority built on the subdominant is not rare,I am especially interested in the germinal properties of this progression, and in the fact that many more complex examples might be related back to this simpler context in a largertaxonomy of chromatic chords that are not so easily explained. Example 15 (Schubert's Phantasie, op. 15, mm. 28-29) provides an interesting context for a SD(44)structure.The passage is situated between an opening section in C major and a structural cadence in the dominant; it can be read as the pivot region between these two keys. In measure 28,

13.

Caithness.

Schubert embellishes a V3 chord in an approach to I6 in C that is expanded with 6/10 voice-exchange between the outer voices, moving to a G-major dominant triad. The figure repeats before continuing to a cadence in the key of the dominant. The pivot harmony is thus the C-major triad in m. 29: Tonic becomes IV of G. The modulating dominant, however, is a SD(4) chord in the key of G. Rather than moving to a traditional root-position C-major triad in the 6/10 voice-exchange, Schubert includes inner-voice motion that transformsthe C-major triad into a secondary vii4j of G that resolves to G over a S-T (4-1) bass line relative to the new key.This is a decidedly weak modulating dominant that easily allows the ear to remain anchored to the key of C for a repetition of the two-measure figure, before continuing and confirming the new key. A noteworthy feature of this example is the inclusion of the secondary 6 in the SD(4) chord ratherthan b6, which is by far more common. The examples to this point have looked at SD(44)chords that function as embellishmentsof diatonic S-T progressions. Examples of the SD(4) are more convincing when they are

MUSIC THEORY SPECTRUM 27 (2005)

264

sehrlebhaft

,6 a G:

G:

,I -l iv

S(4)

EXAMPLE 14.

C 117

SD(4)

(D)

4 3V3

6

G: IV6,6"

T(i)

Schumann, Kriesleriana, op. 16, no. 5, mm. 51-53.

freed from a decorative role. An instance of an independent SD chord resolving directly to a root-position tonic triad is found in the opening to Brahms's Academic Festival Overture, op. 80, given as Example 16. Here, the leading tone B? is superimposed over a repeating 1-4-1 bass line in C minor, creating a conflict between a plagal bass and an authentically rethe category solving leading tone in the top voice-precisely SD as defined. A SD(4) chord of a different variety may be found in the final measures of Richard Strauss's Till Eulenspiegels lustige Streiche, op. 28. The chord in the second measure of Example 17 (sometimes called the "Till Sixth," Bb-Db-E?-G#) is an augmented sixth chord whose characteristic augmented sixth (Bk-G#) resolves to 3 (A?) of the following F major tonic triad, over a structural 4 to 1 bass-a sonority that has strong Dominant associations (by virtue of the leading tone, E0) resolving to tonic. The Till Sixth thus combines the Subdominant and Dominant elements necessary to qualify as a SD(4) chord. Two measures later, Strauss uses a similar chord

C: D(2)

T(3/1i) G: S(6/4)

SD

[V] I

[V] T(i)

EXAMPLE 15. Schubert,Phantasie, op. 15, mm. 28-29.

with two small differences. As the upper voice arpeggiates through the tonic triad over the final four measures, another SD(4) supports 5 in the soprano, with 6 appearing in an inner voice rather than b6 as used in the earlier Till Sixth, above. In this case, the resulting SD(4) chord might appear to be an embellished third-inversion V+9 resolving to tonic over a 4 to i bass line, but such a Roman numeral analysis seems grossly misleading. The final embellishing chord of the piece is a plagally-resolving German augmented-sixth chord. Hypothetically, Strauss could have spelled the Till Sixth by proxy (with bi and kb), and used a contiguous segment of the Tonnetz to do so (see Example 18). But this spelling would have obscured the linear behavior of the chord, and hence its function. The representation in Example 18 shows the functional behavior of the individual elements of this chord and demonstrates its resolution to Tonic from both the Subdominant and Dominant sides. On this figure, the nature of the functional discharge is explicit. The 4-1 motion

ASPECTS OF PLURAL FUNCTION

,r

pp

sepre

?

e sotto voce

SD(4) EXAMPLE

i

SD(4)

I6. Brahms, Academic Festival Overture, op. 80, mm.

1-2.

is due East, representing base-to-base, S to T motion. b6-5 is S to T, agent-to-associate motion; the 7-1 motion is exactly symmetrical to b6-5 with a Dominant agent to Tonic base discharge. The last motion, #2-3 accompanies 7-i in parallel motion, and thus has a latent D-T of 3 functional discharge; upon the arrival of 3, it is subsumed by the Tonic base, and thus #2-3 is a kind of synchronized (as opposed to successive) dominant accumulation, reconciled in the strength of the 1-3-5 Tonic Klang. In short, S and D functions are equally balanced in the discharge to T. The opening seven measures of the Adagio of Bruckner's Ninth Symphony present a passage that defies traditional Roman numeral analysis, but which can be illuminated functionally. The passage is given as Example 19(a). The movement is in the key of E, and the opening phrase ends on an Emajor triad; as no other clear position-finding elements are available, this information will suffice to provide a startingpoint for the analysis. This accepted, the opening unharmonized Bhfunctions as 5 of E, whose promise to move to tonic is fulfilled by a substitute Tonic chord with the E# in the bass of m. 2. The upper voices of this chord, however, complicate such a simplistic opening gambit. A page from Harrison 1994 supports this interpretation: the chord built on E# contains the bass and agent of the Tonic triad, displacing the associate by the two semitones on either side of it, A# and

IN CHROMATIC

MUSIC

265

C#. Certainly,the 5-i bass line provides sufficient grounding for this interpretation.But it is what follows that is especially intriguing. The E# chord initiates an elaborate tonicization of A, shown in Example 19(b). The leading tone of A is delayed through a stepwise chromatic ascent in the upper voices, against which the bass moves to D# (4 of A). D# is harmonized with a transposition of the Till Sixth chord before leaping down a fourth to A#. The 5-4-1 bass-line motive, together with the SD(4') chord, is then cleverly used as a structuralmotive to tonicize A. Immediately following, this same motive is used to effect a tonicization of D major, which arriveson the downbeat of m. 5. When the bass leaps to A# on the third beat of m. 3, Bruckner resolves the SD(4) chord deceptively by flatting the fifth of the goal chord (the A major triad), which then serves as a chromatic dominant of D (V65), and initiates the subsequent tonicization. (See Example 19(c).) The chromatic dominant passes through a bass G# on the way to G#, filling in the 5-4 motivic bass line with a passing #4 that supports an enharmonicallyrespelled viiW/V.4 then supports another SD(4), similar to the "Till Sixth" but for the substitution of 6 for b6. Thus, the bass line and the functional motive used to tonicize A in m. 3 is elided into an embellished version of the same progression(adding a passing chord and slightly altering the color of the SD(4)), which tonicizes the key of D.

The remainderof the passage is much clearer;Bruckner uses the D major triad as a diatonic pivot chord, from which he moves to a half-cadence in the key of A, closing the phrase on the first E major triad of the movement in the famous quotation of the Dresden Amen. In summary,plagally resolving SD(4) chords seem to be found in only a few specific contexts. Not surprisingly, the most common approach chord to a plagally-resolving SD(4) is either a diatonic Subdominant chord with 4 in the bass (SD(4)), or a move directly from tonic. Approaching SD(4) chords from S(6) is uncommon; an approach from an altered Dominant (as in Bruckner's Symphony no. 9 "Adagio") is

266

MUSIC THEORY SPECTRUM 27 (2005)

i

I

16F

SD(4)

i

I

D(4)

I

44n

Gr

T

-,

T(i) EXAMPLE

17.

R. Strauss, TillEulenspiegels lustige Streiche, op. 28, last six measures.

clearly extraordinary.Only occasionally does 6 appear as part of the SD(4) chord at all; there is a clear preference for b6 in this context. When 6 is found, the chord resolves to a majormode tonic.

is in this context that the chosen notation "SD" sidesteps the problems encountered when forcing a Roman numeral to fit the circumstance. The symbol Mvifundamentally misrepresents the linear behavior of the leading tone, whether or not it is spelled with the common enharmonic notation of bi. Likewise, the linear behavior of #2 is belied by the common spelling as b6.26However misleading the context may appear, the fact remains that bk is, for all purposes, a functional leading tone, despite the plagal bass line. The spelling of #2 as g3

Plagal bass:SD( 6)-T(J) While 6 in a major key may theoretically support a SD(6) structure, I have yet to find examples that are convincing. On the other hand, SD(I6) chords are among the most common manifestations of SD structuresin the literature.

In the minor-modeprogression,T(i)-SD( 6)-T(i), b is

often held as a common tone, while I and 5 expand outward to 7 and L6 respectively, creating an enharmonically spelled 6vi chord. This voice-leading paradigmis precisely illustrated in Example 1, the "Tarnhelm"motive from Wagner'sRing. It

26

The interchangeable spellingof #2 andb3is commonplacein both chromatic DP and chromaticD chords,dependingon the modalityof the tonic that follows.For example,when a Gr5 resolvesto a majormode tonic (or cadential-6) b3 is usually notated with #2, and yet alternate symbolsarerarelyproposedfor such substitutions.

ASPECTS OF PLURAL FUNCTION IN CHROMATIC MUSIC

*

EXAMPLE I8.

**

0

267

A

"Till Sixth"resolutionon the Tonnetz.

(a) Bruckner,Symphonyno. 9, iii, A4dagio,"mm. 1-7 (score). EXAMPLE 19

268

MUSIC THEORY SPECTRUM 27 (2005)

Ti A: D()

sD

A: D(5)

SDk(T)

analysis respells the appropriate notes to demonstrate their linear, rather than their purely harmonic behavior. In the Overture-Fantasy to Romeo andJuliet, mm. 32-36, Tchaikovsky provides a similar context for the SD('6) chord as above, but includes 4 in a T()-SD( )-T(i) progression. The passage, omitting the Harp part, which arpeggiates the framing tonic chords, is given as Example 21. In this example, the leading tone E# is part of an arpeggiation in the Flute part, clarifying its chord-tone status; 5 moves to a neighbor note b6 while K3 is retained as a common tone through the progression. All this appears over a 14-6-1 bass line. While the upper-voice 7-b3 diminished fourth (in the Flute) appears anomalous with respect to normal Dominantto-Tonic voice leading, the authentic resolution of the leading tone (7-1) is present in the English Horn and French Horn II. A remarkable manifestation of a SD(I6) formation appears in the famous aria "Nessun dorma" in the third act of Puccini's Turandot.27As shown in Example 22, Puccini presents a context in G major, where the bass note b6 (Ek) supports a V' triad with an added seventh. In the first presentation, 5 (D#) is held across the upper voice of the progression, stabilizing the progression. In subsequent presentations, the voice moves to the seventh, 4, which resolves to 3 in the following tonic chord, while the accompaniment parts maintain 5 as an essential element of the harmony. Thus, acknowledging the well-known difficulty of finding a satisfactory Roman numeral for what might appear to be a Dominantninth chord in fourth inversion, this instantly recognizable chord is better left with the generalized analysis of SD(I6). Furthermore, it would clearly be a stretch of the imagination to think that the bass tone b6 is any kind of ninth. As in the previous examples, this bass tone is operating independently of the whole sonority, although in this case, the situation is more extreme.

(b) Bruckner, Symphony no. 9, iii, Adagio, "mm. 2-3.

A

i

ITI U

A: "T(1)" D: D(5)

(P2)

sD(4)

T(i)

no.9, iii, Aldagio, (c) Bruckner, "mm.3-5. Symphony EXAMPLE19. [continued]

is then simply a maneuverto show the chord in the music as a tertian triad, avoiding the harmonic doubly-augmented second from b1to #2, preferringinstead the major third, bi to b3. Furthermore, there are instances when 4 is added to this basic sonority (as we shall see below) and the same unusual spellings appear. A passage from Franck'sPiano Quintet in F minor, shown in Example 20, demonstrates the same SD( 6) chord as Wagner's "Tarnhelm"motive, but one that resolves to a major mode tonic. In this passage,Franckalso simplifies the spelling of the chord to appearas a 6vi triad in the music. The linear

27

I am grateful to John Cuciurean for bringing this example to my attention.

ASPECTS OF PLURAL FUNCTION

IN CHROMATIC

MUSIC

269

Allegro

C#: I

sD6)

I

C#: I EXAMPLE 20.

Franck,Piano Quintet (F minor), i, mm. 90-93.

Authentic paradigms: DPD (4-D(5) When placed in an authentic context, where DPD chords resolve to traditional Dominant chords, the nature of the leading tone in the mixed-function chord subtly changes. Rather than bearing the entire weight of the functional discharge from Dominant to Tonic, the leading tone in this context anticipates the Dominant proper, blurring the functional boundary between the intermediate DominantPreparation chord and the Dominant that follows. The bass line 4 to 5 is clearly laden with the functional rhetoric of DP-to-D, but Pablo de Sarasate complicates this progression in his Zigeunerweisen for Violin and Piano, op. 20, given as Example 23. In this example, the leading tone, B?, arrives prematurely above the bass 4 in m. 14; thus, the resulting chord progression intensifies the Dominant-Preparation with Dominant function and thereby anticipates the Dominant of the passage atop a DP bass. Strikingly, in this con-

text, the arrival of the cadential- provides the resolution of 7 in the DPD chord, but this "resolution" is also an anticipation of the authentic resolution in the ultimate tonic. Example 24 shows a similar progression in Schubert's Moment Musical, D. 78, no. 3.28 In mm. 34-38, Schubert 28

This example is also used in Agmon 1995, 210, and Aldwell and Schachter1989, 534 and2003, 572. Again, in Agmon's analysisit is not the VII Stufethat definesthe subdominantfunction,but ratherthe bass line. Schubert'sjuxtapositionof a chord that contains a functional leading tone againsta 4 to 5 bass line createsthe functional tension. Also, the earliereditions of Aldwell and Schachterdo not acknowledge the mixed functionalpotential of this chord, but in the 2003 edition, the authorshave reinterpretedthe progressionto be a diminished-_ chord that standsin for a ii56 chord,the chord-tonesof which (not present in the music) are "elided"into the neighbor tone embellishments. However,these analysesaddressthe voice leadingorigins of the passage, and do not purportto clarifyits harmonicfunction. If the leading tone is

MUSIC THEORY SPECTRUM 27 (2005)

270

Fl.

duces Dominant function into the chord by superimposing the leading tone, E?, on the bass 4. The result is a DPD(4) chord that is prolonged through a non-functional, passing secondary dominant of V on the way to V7 in m. 37.29

1

11 I, II

Cl. I, II Eng. Hn. Bsn. I, II

6.

|

61:,

Authentic bass.DPD(B6)-D(5)

..

It is apparent from the literature that when SD( 6) chords are used plagally, they are not normally embellished; rather, they normally embellish Tonic chords. This is not the case when DPD( 6) chords are used in an authentic paradigm. A common manifestation of DPD('6) is the viio4 chord. By definition, a Dominant functioning chord with b6 in the bass cannot resolve functionally to tonic-b6 in the bass must resolve down to 5, over which a functional Tonic chord is extraordinary. Rather, viio4 normally dissolves into the dominant as an embellishing chord, functioning instead in a weak pre-Dominant role, while already containing the leading tone. An oft-cited example of this progression is found at the beginning of the development section in Beethoven's "Pathetique" sonata, op. 13, given as Example 25. In this example, Beethoven uses the fully-diminished seventh chord as an enharmonic pivot between the keys of G minor and E minor, where viio4 in G is reinterpreted as viio, in E, which subsequently resolves to a V7 chord of E. V7 of E is then prolonged until the Allegro molto e con brio. Although the notation viio4 correctly identifies the pitch content of the harmony, it does little to engage the subtle element of DP function in the progression. However one chooses to label the sonority, DPD(b6) remains a helpful mode of classification. Furthermore, this notation acknowledges that the pivot undergoes more than an enharmonic

and Cb. F: i

sD(

i ,)

ii

F: i 21. Tchaikovsky, Romeo and Juliet, FantasyOverture, mm. 28-33.

EXAMPLE

presents a bass line that proceeds from i-4_#4-5-i, clearly implying a plain functional paradigm [T(i)-DP(4i)-D(5)T(i)], into which a secondary dominant to V has been inserted. However, instead of the traditional DP(4) chord that would be expected in m. 35, Schubert prematurely intro-

indeed standing in for 1, does it bear the function of i (not present) or does it retain the function of the leading tone that is actually heard? Aldwell and Schachter's analysis suggests that we attribute supertonic function to the chord while the leading tone is, in concept at least, a dissonant neighbor. My analysis claims that both functions are present and are in conflict, intensifying our experience of the moment. For more on "elision"in Schenkerian analytic practice, see Laufer 1997 and Cadwallader and Gagne 1998.

29

Laufer 1997, 218, note 9 shows an example from Mozart's Piano Concerto, K. 481, that is exactly parallel to this circumstance. He argues that the origin of the voice leading is found in the Schenkerian concept of "Elision." Through elision, Laufer demonstrates that the DPD(4) chord has its origin in a diatonic DP(4), with which the composer has elided a neighbor-tone 7.

ASPECTS OF PLURAL FUNCTION

IN CHROMATIC

MUSIC

271

Andantesostenuto THE PRINCE

p

Nes-sun dor- ma! ...

Nes-sun dorma!...

X i4

G: I

SD(I)

I

SD(

G: I EXAMPLE

22.

Puccini, Turandot,Act IIL/1, "Nessundorma."

reinterpretation.It also undergoes a subtle functional transformation,where the Dominant functioning chord in the old key mutates into a chord with Dominant-Preparationfunction in the bass. This new interpretationof an old problem adds to our understanding of this aspect of many enharmonic modulations by recasting the functional behavior of the pivot chord in the context of the new key, where it preparesthe modulating dominant proper. An example where a DPD(I6) governs a deeper level of structureis found in measures1-4 of Liszt'sAnnetesdepdeerinageII, S. 191, no. 2, "I1penseroso,"given in Example 26. Here, Liszt prolongs a DPD(6) chord by arpeggiating down to a DPD(4) structurebefore arrivingon a V7 chord

on the final beat of m. 3. Liszt spells 7 as bi through the mixed-function chords, but restores the correct spelling of the leading tone with the arrival of V09; while he uses C (bi in the key of C# minor) in the upper voices of both the DPD(6) and the DPD(4) chords, he enharmonically reinterprets C? as B# when the Dominant proper arrives. While the "Vorspiel" to Wagner's Tristan und Isolde is one of tonal music's most discussed passages, a mixed-function interpretation has been implicit in analytic writings for quite some time. The opening to the "Vorspiel" is shown in Example 27. Many analysts have commented on the G#-B voice-exchange between the soprano and tenor in the opening measures, which suggests a sense of shared harmonic

MUSIC THEORY SPECTRUM 27 (2005)

272

ll.

Lento

1: ral

f

trispassion

rall.

po

C: i

DpD5(4) V4

i

C: i8-7 EXAMPLE

23. Sarasate, Zigeunerweisen, op. 20, mm. 12-15.

function between the Tristan chord and its resolution.30The bass line from ?6 to 5 of the Tristan progression (one of the characterizing bass lines associated with DP to D function) is coupled with the prolonged leading tone (in this case, through a voice-exchange), which gives the Tristan succession so much of its character.The addition of the inner voice #4to 4 between these two harmonies is an additional complication. The tendency of #4to move to 5 (D of D to D) is thwarted; #4 instead moves to the weaker Dominant factor, 4. Represented on the Tonnetz,the resolution of the Tristan chord has a remarkableelegance.The 2/7 voice-exchangerepresents the D functionalpersistence.b6 to 5 is a functionaldischarge from the Subdominant agent to the Dominant base; 30

This interpretation of the Tristan progression was explored in Smith 1986, 136-39 and later in Harrison 1994, 156-57.

this motion precisely mirrors the expected resolution of the Dominant-of-the-Dominant agent to the Dominant base (#4 to 5). Instead of this resolution,the polarityof the Dominantof-the-Dominant agent changes from major to minor (#4to 84), at which point 4 becomes a factor of the Dominant. Unlike the other DPD chords discussed thus far, the Tristan chord is not a tidy chromatic Dominant placed atop a bass line that suggests DP function, owing to the presence of #4. However, I believe that the association of this chord with other similarDPD(b6) chords is a useful correlation. FUNCTIONAL

COLLISIONS OF TYPE Ds

Authenticbass:Ds (5)-T() DS(5) chords in general are closely related both to Dominant chords with added dissonance, and to dominant pedal

IN CHROMATIC

ASPECTS OF PLURAL FUNCTION

MUSIC

273

Allegro moderato

!

I

F: i

V4-3

(v/

DPD(4)

F: T(i)

D(5)

T(i)

EXAMPLE 24. Schubert,Moment Musical, D. 78, no. 3, mm. 34-38.

TI

,

,•T-

f

fp

2" ,' i

-

G:

.

.

f"[•

.

"1 1

"1

I

D(4)

r

I

T(63)

D(4) E: DpD(6)

EXAMPLE

_

D(5)

25. Beethoven, Sonata, op. 13, "Pathetique,"i, mm. 134-37.

T(i)

MUSIC THEORY SPECTRUM27 (2005)

274

i

C#:

C#: EXAMPLE

T()

D(5)

T(i)

26. Liszt, Annees depe'lerinage II, S. 191, no. 2, "Ilpenseroso,"mm. 1-4.

tones. From the former, a DS(5) chord is distinct in that it often refers to Dominant Elevenths and Thirteenths, the so-called "tall-chords,"31 whose upper, dissonant elements behave as real chord tones rather than unresolved embellishments. Dominant pedal tones, on the other hand, typically support Subdominant or Tonic chords in a non-functional context-that is, they resolve to the diatonic dominant before the change of the bass. A DS(5) chord is different from these because it bears the entire Dominant function of the passage, where there is no resolution of the upper-voice Subdominant elements. As with SD chords, the notation of Ds chords is similarly fraught with problems. Thus, rather than contriving a complex Roman numeral to account for the many possible configurations, the notation will be simplified to a straight31

9-8

V95

DPD(6/)

Kostka and Payne 1995 use the term "Tall chord" in this manner.

g2 A: i DPD(6g)

A: T(i)

V7

D(5)

EXAMPLE "mm. 1-3. 27. Wagner,Tristan undlsolde, "Vorspiel,

ASPECTS OF PLURAL FUNCTION

IN CHROMATIC

MUSIC

275

forward account of the chord's function. From a practical perspective, DS(5) chords may be thought of as complete Subdominant chords built atop 5 in the bass, normally placed in a texture where the two functional halves, and their behaviors, are clearly separate. A roster of DS(5) chords (such as ii7 built atop 5, IV7 built atop 5, etc.) is easily imagined, and an enumeration of all possible permutationsyields little direct benefit. The opening of the first movement of Schumann'sFan-

suspension. The metric context and the emphasis of the arpeggiated ii7 (Gm7) chord reinforce this interpretation across the sixteenth-note figuration.The metric emphasis of the G minor-seventh chord suggests that the real uppervoice voice leading prolongs a G through a downward arpeggiation from G5 to G4, resolving into the suspended ninth above the Tonic chord in m. 3. At the deepest level, the Dominant chord remains privilegedby convention.

tasy, op. 17, given as Example 28, contains a striking DS( formation that is subsequently undermined at a deeper structurallayer. In what is apparentlya conscious effort to blur together Subdominant and Dominant function, Schumann superimposes a ii7 chord over 5 in the bass. The resolution of the DS(5) to D(5) across mm. 7-9 blurs the harmonic function, as the right hand resolves to Dominant harmonywhile the left hand continues to outline the supertonic triad in m. 7. On a deeper level, the Ds(5) chord is realized as non-chord-tone motion, embellishing a structural V7 chord. In this case, the nature of the prolongation of these non-chord-tones preserves a surface-level independence of the harmony. In the opening to the "Rigaudon"from Le Tombeaude Couperin(Example 29), Ravel blurs the Dominant function in the second measure by superimposingan arpeggiationof a complete ii9 chord over an authentic bass. Unlike the Schumann example above, Ravel does not decorate a diachord tonic Dominant with a DS(5) chord; rather,the DS(5) stands alone and resolves directly to Tonic in a DP(4i/2)Ds ()-T(i) progression. In the first few measures of Debussy's "Prelude"to the Suite Bergamasque,given as Example 30, Debussy strongly emphasizes a ii7 chord built atop a bass 5 for all but the final sixteenth note of m. 2, which introduces the leading tone and so fleetingly turns the harmonytoward an explicit,traditional Dominant. Once again, the surface-layer analysis holds the DS(5) as a recognizable and significant aspect of the composition; the second layer revealsDebussy's elaborate

Authenticbass:T(i)-DS(7)-T(i) From a theoretical perspective, the neighbor bass 1-7-i holds some of the most intriguing mixed-function situations. This bass line is also the most problematic from a notational perspective and the most sensitive to the modality of the Tonic chords. The examples that follow all hinge upon the spelling of a Dominant chord that is alteredwith #2. A vii` chord inherently presents a conflict between the bass note, which is emblematic of Dominant function, with the upper-voice scalesteps #2 and b6.These scale steps are disjunct on the Tonnetz, and thus naturally divide the chord's allegiance to a Tonic. When #2 resolves to 3 in a major mode Tonic, there is a clear sense that it functions as #2; when #2 resolves to a minormode Tonic, it is normally spelled as b3, and, more importantly,soundslike b3resolving by common tone. Chopin presents a #2 alteration of a viiOchord in his Bb minor Sonata, op. 35.32 As Example 31 shows, the opening measures tonicize F, as the dominant of Bb minor, implying a secondary viiO/V, from which an implied 2 of F moves through #2 on the way to 3 of F (V of Bb) in an extended structuralanacrusis.In this context, the chromatic scale-step #2 clearly moves to 3 in a Dominant-to-Tonic impulse; imagining this resolution as K3to 3 is not productive, and seems to cloud the issue more than it clarifies.

32

This interpretationmaybe found in Smith 1986, 122-24.

MUSIC THEORY SPECTRUM 27 (2005)

276

Durchausfantastischundleidenschaftlichvorzutragen %

-W

EXAMPLE 28.

Schumann, Fantasy, op. 17, mm. 1-9.

ASPECTS OF PLURAL FUNCTION

IN CHROMATIC MUSIC

277

Moderato

C:

IV7

iil

C: DP(/)

V13

F: I

D>

7

19

T(i) -

Tii EXAMPLE

29.

Ravel, Le Tombeaude Couperin,"Rigaudon,"

F: T()

D(5)? Ds(5)

T()

mm.1-2. EXAMPLE

Example 32 presents a contrast to Example 31. The opening measures of "Salome'sTanz,"from Strauss'sSalome, embellish the tonic with a surface-level plagal succession i-bV16-i, which establishes the key and mood of the dance. After the first phrase closes with a half-cadence, the second phrase begins in the same fashion, but as the expected WVI chord embellishes tonic in the upper voices, the bass moves to the lower neighbor bi,apparentlysubstitutingbvi6for WVI6. However, we have seen this respelling before, in the context of SD chords, where the pair Kiand 0i are proxy spellings of pitches that have a linear function of 7 and #2 respectively. When appearingin the bass like this, the second phrasethus begins with an authenticstatement to contrast the opening plagal gesture, resulting in a Ds(7) chord. The essential plagal aspect of the progression is embodied in the "resolution" of #2 to b3 in Tonic, exhibiting the linear behavior of a common-tone b3alongside the Subdominant ~6resolving to 5. Careful analyses of this behavior must separatethe appar-

30.

Debussy, Suite Bergamasque, "Prelude," mm. 1-3.

ent vertical spelling and acknowledgment of a triadic sonority from the linear behavior and clear authentic functional discharge that characterizes the sense of double-function afforded this striking progression. Rimsky-Korsakov, in the second movement of the Capriccio Espagnol, op. 34 (see Example 33) uses Ds chords rather than straightforward Dominants in both the initial compound basic idea and the continuation phrase of the second variation. The DS(7) chord in m. 43 is identical to the one found in Example 32, above. The passage concludes with a strikingly rich cadence that superimposes a Neapolitan triad above a bass 5 in m. 47. While this cadential dominant might also be interpreted as an altered V7 (with a lowered 2) the texture and spacing of the chord suggests a DS(5) interpretation, where the Neapolitan chord is heard superimposed over the lower-voice Dominant harmony.

MUSIC THEORY SPECTRUM 27 (2005)

278

Doppiomovimento

Grave

L

f-

Bb: (viio/V) F: vii'

Bb:

"I"

[DS(7)/V]

EXAMPLE 31.

CONCLUDING

V6-5

DSO()

V7

Chopin, Sonata in Bbminor, op. 35, i, mm. 1-6.

most ples in an effort to explain the "big moments"-the interesting and striking events in the compositions at hand. Hatten 1994 develops a theory of markedness for the interpretation of music.33 There is tremendous opportunity to assimilate the present study with Hatten's interpretive strategies. In this context, plural-functioned harmonies constitute one half of the equipollent opposition (Plural-function vs. Singular-function) where Plural-functionality is clearly the marked term in the opposition. I argue that the presence of a functional collision in a harmony constitutes a stylistic type, within which the variants I've explored above represent a range of musical tokens. This approach can lead us to make

REMARKS

The Kldnge I have discussed in this article are related in that they all involve a collision of Subdominant and Dominant functional elements. While in practice bi frequently appears instead of 7, the linear nature of the progression is evident. It is so strong, in fact, that the authentic functional discharge embodied in 7-1 must be acknowledged as the guiding element of the progression, granting some degree of Dominant function to the chord so that the result is a true functional hybrid. Scholars of the nineteenth century speak often of the Romantic penchant to blur boundaries in art and in music. The Kldnge I have discussed blur the boundaries of harmonic function on the musical surface. This blurring, rather than creating ambiguity, suggests a conflict that draws our attention to functionally hybrid chords. I have chosen my exam-

33

This theory is adaptedfrom the field of linguistic semiotics;Hatten credits the work of Michael Shapiro (1968) as his source for these ideas.

ASPECTS OF PLURAL FUNCTION

IN CHROMATIC

MUSIC

279

m.7 m.073

Lm

C6:

i

6VI6

6i

i

1vi6?

DS(7) a

t~

_

7

~~

__4__ ___L

c :

_

_

___

_

__

_

__

_

___

_

_

__

_

__

_

__

_

___

_

__

_

_

_

_

__

T(i)

T(i)

EXAMPLE 32. R. Strauss, Salome, "Salome'sTanz," mm. 1-3, 7-9. Andante con moto dolce

r--- 3

>

r---

3

-4o

D: F: I

i vi

D:

T()

Ds(7)

iII

Cad6

DS

EXAMPLE

33. Rimsky-Korsakov, Capriccio espagnol, op. 34, ii, mm. 41-48.

D

Ds(5)

T(i)

_

_

280

MUSIC THEORY SPECTRUM 27 (2005)

informed interpretive decisions where these harmonies are found. But there is yet much work to be done; this study is only a first step toward a fuller understanding of these fascinating harmonies. Further avenues for study might attempt to draw intertextual connections between plural-functioned harmonies; to define a tradition for their use; to make generalizations about their location; and to come to grips with issues of stylistic evolution. It is my hope that this investigation might prove a useful point of departurefor such studies.

APPENDIX: A BRIEF SYNOPSIS OF DANIEL HARRISON S THEORY

Harrison's approach is a mature dualist formulation whose nineteenth-century origin may be traced to Hauptmann. Using a dialectic apparatus,34 Hauptmann was concerned not with building a dualist tonal system, but rather with using oppositional structures to explain the tonal system as he found it. Helmholtz countered this theory with a scathing critique supported by the natural sciences-a discipline so much in vogue at the time that his critique carried a great deal of weight. To counter Helmholtz's argument, Ottingen invoked Hauptmann's Having/Being dialectic in the context of the overtone series, and constructed a natural basis for the minor mode (thus for harmonic dualism itself) in his explanation of Tonicity/Phonicity. Ottingen's rationale in the natural sciences was sufficient for Riemann to devise his system of harmonic function and transformation. Although he misread Ottingen's theory when he proposed his infamous "undertone series," Riemann later revised his argument to find its basis in the mind rather than in nature, and thus realigned his theories more closely with Hauptmann's original formulation. Harrison's dualism is likewise unconcerned with providing a natural basis for the diatonic system; simply, Harrison finds the explanatory power of oppositional pairs to be a useful entry into chromatic harmony. Since this kind of dualism offers substantial explanatory power, it is therefore a valid vehicle for musical analysis. The primitive of Harrison's dual system is the simple opposition of major and minor, from which he generates a dual network of scale degrees. Onto this network, Harrison grafts a second postulate, that of the "three-termed dualism," which places a neutral Tonic in between the marked extremes of Subdominant and Dominant. From these central 34

See Klumpenhouwer2002, 459-62, for discussionaboutthe degreeto which authenticallyHegelian thought can be ascribedto Hauptmann's theoryas opposedto Hauptmann'smereuse of dialecticlanguagewithout a deep understandingof true Hegeliandialectics.

ASPECTS OF PLURAL FUNCTION

postulates, Harrison then explores the harmonic function that can be inferred from each individual scale-degree in the tonal system, and accordingly, in scale-degree assemblies. In relation to a Tonic, the basic functional dualities, S and D, are represented by 4 and 5 in particular, but also by the primary triads projected from 4 and 5. When placed in the lowest voice, either 4 or 5 normally suffices to convey a sense of its respective function and to subsume the remainder of the Klang to its purpose. When placed in an upper voice, 5 requires the support of its functional agent, 7. 4 is not burdened by this constraint, as it is not found in either of the Functional other primary triads (Harrison 1994, 46 ff.). thirds of the "are (the triads) entirely dediprimary agents cated to the function in question" (Harrison 1994, 49) and thus operate unconditionally. Functional bases have the power they do in large part because they imply the presence of their agents. Functional associates (the fifths of the primary triads) are weak functional signifiers; they are able to amplify their comrades, but unable to bear functional expression alone. Any Klang may be disassembled and may represent a functionally mixed structure; witness Harrison's disassembly of the supertonic triad. Since the function of the Klang as a whole is dependent on the functional status of its constituents, the supertonic triad is functionally mixed: 4 and 6 are base and agent of S function; 2 expresses a weak D function. Thus, there resides in the supertonic triad a latent Dominant potential. Compare the two progressions in Example 34. The first progression provides a context where the latent Dominant potential of the supertonic triad is apparent-the supertonic triad is subsumed into the function of the Dominant. The metric context and shared bass scale step suggest that the soprano 2 is an arpeggiation within the dominant harmony; 6 is a dissonant upper neighbor to 5. In the second progression, however, the metric context suggests that the soprano 2 has a greater degree of independence from the leading tone that follows. The leaping bass supports a compelling change of harmonic function.

IN CHROMATIC MUSIC

281

A.

4.i

n-

T EXAMPLE

D

I

T

T

DP D

T

34. Modelprogressions involving DP(2)?-D.

In Harrison's theory, a similar argument is advanced for the dominant seventh chord. In V7, the seventh, 4, provides a strong element of S function, and thus empowers this harmony with S potential, especially if 4 is found in the bass. Context or competing functional elements coexisting in a Klang do not deny the potential of the functional primitives in the system. For Harrison (following Erpf), functional mixture is an abstract property of a chord. In musical contexts, these elements are reconciled as the scale steps compete for functional presence. REFERENCES

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Jovanovich. . 2003. Harmony and Voice Leading, 3rd edition. Belmont, CA: Wadsworth Group/Thompson Learning.

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Benjamin, William E. 1975. "Interlocking Diatonic Collections as a Source of Chromaticism in Late NineteenthCentury Music." In TheoryOnly (11-12): 31-51. Blasius, Leslie. 1996. Schenker'sArgument and the Claims of

Music Theory.Cambridge:Cambridge University Press. Burkhart, Charles. 1978. "Schenker'sMotivic Parallelisms." Journal ofMusic Theory 22: 145-76.

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Forte, Allen. 1979. Tonal Harmony in Concept and Practice,

3rd edition. New York:Holt, Rinehart and Winston. Harrison, Daniel. 1994. Harmonic Function in Chromatic Music: A Renewed Dualist Theory and an Account of its

Precedents.Chicago and London: University of Chicago

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1995. "Supplement to the Theory of Augmented-

..

Sixth Chords." Music Theory Spectrum 17.2: 170-95.

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Robert.

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Musical Meaning

in Beethoven.

Bloomington & Indianapolis:Indiana University Press. Kinderman, William and Harald Krebs,ed. 1996. The Second Practice of Nineteenth-Century Chromatic Tonality. Lincoln

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by Thomas Christensen. Cambridge:Cambridge University Press. 456-76. Kopp, David. 2002. Chromatic Transformations in Nineteenth-

CenturyMusic. Cambridge: Cambridge University Press. Kostka, Stefan and Dorothy Payne. 1995. Tonal Harmony with an Introduction to Twentieth-Century Music, 3rd edi-

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Harmony." Journal of Music Theory

•-

. 1991. "Tonal and Formal Dualism in Chopin's Scherzo, op. 31." Music Theory Spectrum 13.1: 48-60.

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Schenker, Heinrich. [1954] 1980. Harmony, ed. Oswald Jonas, trans. Elisabeth Mann Borgese. Chicago and London: University of Chicago Press. Smith, Charles J. 1981. "Prolongations and Progressions as Musical Syntax," in Music Theory. Special Topics.Edited by

Richmond Browne. New York:Academic Press. 139-74. . 1986. "The Functional Extravaganceof Chromatic --.

Chords." Music Theory Spectrum 8: 94-139. 2003. Functional Fishing with Tonnetz.: A Dualist Syntax of Transformations. Paper presented at the annual

meeting of the Society for Music Theory, Madison, Wisconsin. Stein, Deborah. 1985. Hugo Wolf's Lieder and Extensions of

Tonality.Ann Arbor:UMI Research Press. Whittall, Arnold. 1995. "Review of Daniel Harrison's Harmonic Function in Chromatic Music." Music and Letters 76.3: 457-60.

MusicTheorySpectrum, Vol. 27, Issue 2, pp. 249-282, ISSN 0195-6167, electronicISSN 1533-8339. ? 2005 by The Society for MusicTheory. All rights reserved.Please direct all requestsfor permissionto photocopy or reproducearticlecontent throughthe Universityof California Press's Rights and Permissions website, at http://www.ucpress.edu/ journals/rights.htm.