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       M U S I C          T H E O R Y         O N L I N E
                     A Publication of the
                   Society for Music Theory
          Copyright (c) 1995 Society for Music Theory
| Volume 1, Number 3        May, 1995      ISSN:  1067-3040   |
  All queries to: mto-editor@boethius.music.ucsb.edu or to
AUTHOR: Kopp, David
TITLE: On the Function of Function
KEYWORDS: function, harmony, Riemann, Rameau, Weber
David Kopp
Brandeis University
Department of Music
Waltham, MA  02254-9110
ABSTRACT: The concept of harmonic function, far from carrying a
unitary and universally understood meaning, has signified many
different things to theorists past and present. This essay
examines some of the different meanings commonly associated with
the term today, as well as aspects of the harmonic theories of
Rameau, Weber, and Riemann, all regularly associated with the
concept. Notions of chord identity, scale degree, and logical
determinacy are considered.
ACCOMPANYING FILES:  mto.95.1.3.kopp1.gif
[1] Harmonic function is a term which, although it may seem to
express a simple and obvious concept, has grown uncommonly vague
through use. Loosely put, function signifies harmonic meaning or
action. But notions of what meaning and action constitute may
take many forms. In our time, any search for a commonly accepted
definition of function will be frustrated, for the meaning of the
word has proved adaptable to support a wide variety of statements
concerning harmony. For example, the harmonic meaning of chords
is often attributed to each diatonic scale degree and their
variants, serving as the roots of a variety of chords.(1) Thus we
may say that A-flat major functions as III in F minor, as V in
D-flat major, and as flat-VI in C major. The term function may
also be used in a stronger sense to signify a concept of the
intrinsic potentiality of a given chord to progress in a
particular way or to a particular chord; thus we say that V
expresses function in its tendency to progress to I. We may use
the term to group chords with similar syntactic behavior, e. g.
saying that II and IV often express similar function. We may link
it to the primacy of tonic, dominant, and subdominant in the key.
Or we may associate function with specific outcomes rather than
with unitary scale degree identity.(2)The term may be associated
with harmonic tendencies of individual chord tones as well as
chords.(3) It may be correlated with phrase-based syntactic
meaning.(4) The function concept has even been identified with a
prolongational scale-step notion.(5) We often use the term
function to denote meaningfulness or meaningful relation within a
key, as opposed to "color," which signifies a relation without
meaning in the tonal system. All of these and many more
contrasting notions of chord identity, potentiality, and activity
may be invoked by the same term. Yet we use it as if its meaning
were fixed and intuitively evident. None of the harmony textbooks
cited above, for example, treats function as a concept to be
defined in its own right or contains an index entry for the term. 
1. "Each scale degree has its part in the scheme of tonality, its
tonal function." Walter Piston and Mark DeVoto, *Harmony*, fourth
edition, New York: Norton (1976), p. 49.
2. "The IV has three common functions. In some cases, IV proceeds
to a I chord...More frequently, IV is linked with ii...(it may
also go) directly to V..." Stefan Kostka and Dorothy Payne,
*Tonal Harmony*, second edition. New York: Alfred A. Knopf
(1989), p. 103.
3. This approach is used by Daniel Harrison in his recent
*Harmonic Function in Chromatic Music: A Renewed Dualist Theory
and an Account of its Precedents*, Chicago: University of Chicago
Press (1994).
4. "In the Kuhnau, the tonic functions first as an *opening
tonic* At the end it is a goal of motion, thus a *closing
tonic*." Edward Aldwell and Carl Schachter, *Harmony and Voice
Leading*, 2nd. ed., New York: Harcourt, Brace, and Jovanovich
(1989), p. 84.
5. Willi Apel, *The Harvard Dictionary of Music*, 2nd. ed.,
Cambridge: Harvard University Press (1969), article on function.
[2] Furthermore, we commonly associate an idea of function with
the thought of many theorists of common-practice tonality, and
regularly identify the presence of "function" in theory which
significantly predates the introduction of the formal concept.
What we call function in these theories is not always the same
thing, nor is it always what we may think it to be. It is a
familiar idea that one's view of the past can be affected by
one's own manner of thinking (6); familiar terms may particularly
obscure. In the space of this short essay I cannot propose either
to trace either the development of the functional idea through
the history of theory or to identify all the theorists to whose
work we attribute function. Instead, I will restrict my inquiry
to an attempt to isolate and evaluate the aspect of three major
theories of harmony customarily associated with the function
concept, one each from the beginning, middle, and end of the
common-practice period. I hope to show how different this aspect
is in each case, and to argue that the use of the same term to
describe each unduly denatures its effectiveness.
6. Thomas Christensen has examined this issue in "Music Theory
and its Histories," in *Music Theory and the Exploration of the
Past*, ed. Hatch and Bernstein, Chicago: University of Chicago
Press (1993).
[3] Our tendency to identify function extends back to accounts of
Rameau, whose theory is often described in recent literature as
elucidating the harmonic functions of chords. Without a doubt,
notions of differentiated chord action are present in Rameau. But
did he really describe a property of the tonal system properly
characterized as function? His terms *tonique*, *dominante*, and
*sous-dominante* certainly evoke associations with Riemann's
three *Hauptfunktionen*. But where *Hauptfunktionen* define
harmonic states of triads, Rameau's chord types do not. Their
identities hinge on an extrinsic explanation. Rameau does not
identify chord types with harmonic meaning and identity.(7)
Rather, he concentrates on differentiating chords' tendencies to
progress: *dominante* by descending fifth, *sous-dominante* by
ascending fifth, and *tonique* by any acceptable fundamental bass
interval. Rameau accounts for the constrained, motivated natures
of *dominante* and *sous-dominante* by positing the universal
presence of dissonant minor seventh and major sixth in them,
whether actual or implied.(8) A *tonique*'s freedom to progress
stems from the absence of added dissonance. Thus the motivating
force behind these tendencies is not harmonic but contrapuntal:
the addition of a dissonant pitch to a consonant formation is the
necessary cause of the directed motion associated with certain
chord types. Rameau observes that dissonance is required for the
listener to desire the chords which follow.(9) Furthermore, only
the *sous-dominante* as defined is completely specific to scale
degree.(10) A dominante could be one of a number of diatonic
seventh chords; the dominant seventh chord on the fifth degree
required a special name, *dominante-tonique*.(11) And while
Rameau originally specified the *tonique* for the first scale
degree only, the prevalence of freely progressing roots on other
scale degrees in his fundamental bass analyses obliged him
eventually to distinguish between the true tonic and *notes
cense'es toniques*, or seeming tonics.(12) Thus there is no one-
to-one correspondence between the three chord types and the three
primary chords of the key. Example 1 shows Rameau's 1760 analysis
of a descending chromatic line with alternative *basses
fondamentales*. It contains *dominantes* and *dominantes-toniques* 
on various scale degrees, also *toniques* and a *note
cense'e tonique* in the first *b. f.* at letter *f*.
7. Lester, op. cit., p. 207. Lester uses the term function but is
careful to distinguish how Rameau's theory differs from modern
8. A thorough discussion of this "mechanistic" aspect of Rameau's
theory is found in Christensen, *Rameau and Musical Thought in
the Enlightenment*, Cambridge, England: Cambridge University
Press (1993), pp. 106-7.
9. Rameau, *Traite' de l'harmonie*, Paris (1722), p. 53; *Nouveau
syste'me de musique the'orique*, Paris (1726), pp. 56-57.
Reissued in facsimile by the American Institute of Musicology,
10. Rameau (1726), pp. 38, 61.
11. Rameau (1722), pp. 203-4.
12. Rameau, *Code de musique pratique*, Paris (1760), pp. 81-82.
Reissued in facsimile by the American Institute of Musicology,
1966-68. Example 1 from example p. 17.
[4] Does this constitute a theory of function? Rameau's theory
contains no formal concepts of chord identity based on scale
degree or of common harmonic identity shared by different types
of chord. To a remarkable degree, the theory does contain a
definite notion of how chords act differently from one another.
But while Rameau does demonstrate that the coherence of
progressions stems ultimately from the coherence of the
triad,(13) he attributes the determined nature of these
progressions to a contrapuntal tendency emanating from outside
the triad, not from scale-degree identity. In this light, any
view that Rameau's theory originates an idea of function as
inherent potentialities of chord actions is compromised by the
fact that for him these potentialities are in no way defined as
inherent in triads themselves nor essentially in their position
in the key, despite what is possible to read in behind what
Rameau says. Rameau clearly perceived differences in chord
action, accounting for them with his theory of added dissonance
and the three chord types. However, his theory differs so
dramatically from other conceptions of function that merely using
the term to describe it necessitates a great deal of explanation
as to what it really means. Claiming that function exists in
Rameau unavoidably invites associations with the term which are
not reflected in the theory. It would be useful to have more
precise, dedicated terms to denote different conceptions of
harmonic activity (e.g. notions of action-function,
identity-function, hierarchic/syntactic-function,
tonic-centering-function). Particular well-defined types of
function could then be adduced in a more specific and meaningful
way to clarify understanding of the essential nature of harmonic
systems such as Rameau's.
13. David Lewin documents this in "Two Interesting Passages in
Rameau's *Traite' de l'harmonie*," In Theory Only 4/3 (1978):10.
Also discussed in Christensen, op. cit., p. 106.
[5] Another theorist routinely identified with introducing
functional thinking is Gottfried Weber. Typical is this comment
on Weber's work by a mid-twentieth century historian of
nineteenth-century harmonic theory: "The author believes Weber to
be the first theorist to use Roman numerals as function
signs."(14) This account suggests that Weber, writing in the
1820s, was devising signs to denote the concept familiar to us.
While a clearly defined notion of function in harmony had not yet
been introduced, it could indeed be possible that Weber sensed
its existence and documented it in theory without being able to
fully articulate its nature. But Weber was adamant that his
theory was not meant to be a system explaining the genesis of
chords and their actions.(15) He rejected rules and explanations
for mechanisms properly linking chords; to do so would have been
to unnecessarily forbid perfectly good progressions. Weber fully
recognized the importance and ubiquity of I, IV, and V in the
key. But at the same time, he permitted and even encouraged the
use of any and all of the 6888 possible chord relationships he
defined within and between keys, refusing to forbid anything.(16)
He ascribed cadential power only to seventh chords resolving to
triads; thus V7-I was his model cadence, V-I only a frequent
progression between essential harmonies.(17) Moreover, Weber did
not require the presence of the dominant in a modulation and even
allowed for pieces containing no dominant at all.(18) Nor did he
offer any explanation for the motivation and dynamics of chord
progressions; he merely reported on the comparative strength and
plausibility of as many of them as possible.
14. Mark Hoffman, *A Study of German Theoretical Treatises of the
Nineteenth Century*, Ph.D. dissertation, Eastman School of Music
(1953), p. 65. The comment is innacurate; for a discussion of
earlier numbering systems, see Joel Lester, *Compositional Theory
in the Eighteenth Century*, Cambridge: Harvard University Press,
(1992), pp. 207-08.
15.Weber, *Versuch einer geordneten Theorie der
Tonsetzkunst*(1817), 3rd ed., B. Schotts So"hne, Mainz (1830-32),
preface, pp. x-xi.
16. ibid., bk. II, pp. 187-88, 213.
17. His discussion of V-I comes in serial order between IV-vii
and VI-ii during a taxonomic description of progressions by
fourth (not fifth!). The discussion is one sentence long; since
V-I is so common, Weber feels no need to explain it. Ibid., bk.
II, pp. 231, 242.
18. ibid., bk. II, pp. 7, 102.
[6] In essence, Weber's theory identifies chords by their
participation and position in a key, not by their relation to
each other or their tendency to progress. His method attributed
Roman numerals on a chord-by-chord basis: either a chord fit
exactly into the prevailing key, or else it was defined as
belonging to the closest possible key into which it fit. On this
basis diatonic music was readily analyzed in a single key. But
Weber had no concept of secondary/applied dominant by which to
show basic hierarchic relationships of chords within the key, nor
a theory of alterations by which to define variants of diatonic
chords. Consequently, he analyzed stretches of music containing
tonicizations of secondary degrees as quick successions of
modulations to different keys. Highly chromatic passages of
passing chords could, in his system, invoke one or more new keys
with every chord.(19) Thus while Weber's Roman numerals do define
chords by their identities within keys, they cannot demonstrate
how successions of chords with any significant chromatic content
display coherence within a single key, thereby depicting the
syntactic connections which can represent function to us.
Essentially, his Roman numerals designate chords: primary
diatonic triads and seventh chords. They do not represent the
scale degree rubrics we may associate with function, which do
more to subjugate chord identity to the key. Accordingly, simply
calling Weber's labels "function signs" can give a false
impression that scale degrees themselves, not chords, are being
19. His analysis of a passage of his own music documents twenty
keys in twenty-one measures, including chords which evoke two new
keys simultaneously. Ibid., fig. 234, meas. 15-end. Example 2
shows an excerpt from this analysis (meas. 21-33). The attitude
that individual chords may evoke a sense of key is not unique to
Weber, but rather points to an attribute of thinking of the time.
For example, A. B. Marx, writing in 1841, taught that even the
dominant and subdominant triads, in their roles as principal
triads of the key, bring with them a sense (*Erinnerungen*, or
reminiscences) of their associated keys. Marx, *Die Lehre von der
musikalische Komposition*, vol. 1, Leipzig: Breitkopf & Haertel
(1841), p. 73.
[7] Moreover, these symbols are a far cry from the "functions"
represented by Rameau's chord types. *Tonique*, *dominante*, and
*sous-dominante* are defined by action -- their relation to the
chord which follows. I, ii, iii, etc., are defined by identity --
their relation to a tonic. Used so broadly, these attributions of
function may confound as much as they illuminate. It is
interesting to note one shared idea: both theories require the
presence of a dissonant seventh in order for the dominant to
strongly imply the tonic. Neither attributes the will or power to
progress to the fifth scale degree of itself.
[8] Hugo Riemann's theory is indisputably a functional one in
some sense, since it was he who popularized the term. But his
notion of function and ours are worlds apart. In an early harmony
treatise predating his introduction of the concept, Riemann
demonstrates how a series of five chords containing direct
chromatic relations, normally understood as passing through four
keys, can be interpreted as belonging to a single key from
beginning to end.(20) The progression, with its alternative
analyses, is shown in Example 3. Riemann brings two lines of
thought to bear here: first, the acknowledgement of the
possibility of direct connections between the tonic and chords
with chromatic content; second, the identification of chords
containing chromatic pitches with diatonic chords from which they
draw identity and meaning while retaining individual character.
These lines of thought led to his concept of *Tonalitaet*, an
expanded notion of key encompassing both diatonic and chromatic
relations directly with the tonic, and to the mature concept of
*Funktion* of the 1890s. Both concepts stem from his underlying
urge to show that chromatic music retains and reinforces its
essential tonal aspect rather than subverting it.
20. Hugo Riemann, *Skizze einer Neuen Methode der Harmonielehre*,
Leipzig: Breitkopf & Haertel (1880), pp. 67-69.
[9] While Riemann was developing the concept that eventually
became *Funktion,* he also proposed an independent explanation of
the mechanisms of chord connection. This was an exhaustive
taxonomy based on intervals between roots and direction of
progression.(21) Riemann retained this system of
*Harmonieschritte* to explain chord progression even after
introducing the *Funktion* idea; both are essential elements of
his comprehensive harmonic theory. The advantage Riemann
attributed to the *Harmonieschritte* system is that its
particulars do not refer to key. He makes this clear in an
impassioned refutation of Weber's Roman numeral notation, arguing
for an essential identity of individual chord progression types
existing independently of the character which they take on in the
context of a key.(22) The system provides little explanation for
motivational aspects of the progressions; it has no recourse to
dissonance-based arguments such as those of Rameau and Weber.
21. This system was formalized by Henry Klumpenhouwer in a recent
article in this journal: "Some Remarks on the Use of Riemann
Transformations," Music Theory Online 0.9 (1994).
22. Riemann, *Katechismus der Musik*, Berlin: Max Hesse (1890),
p. 65.
23. Scott Burnham has carefully investigated Riemann's reading of
Rameau, and the differences in their harmonic concepts, in
"Method and Motivation in Hugo Riemann's History of Harmonic
Theory," Music Theory Spectrum, vol. 14/1, spring 1992.
[10] *Funktion*, on the other hand, has next to nothing to do
with chord progression. Rather, it concerns the _meanings_ of the
chords which progressions link. The principal significance of the
functional archetypes Tonic, Dominant, and Subdominant is that
they are the primary chords of the key, linked by the preeminent
interval of the fifth. Scale degree identification per se is
completely absent from the theory; any of the member pitches of a
functional archetype can represent functional identity. By
allowing for the identification of every possible diatonic and
chromatic chord with one of the three functional archetypes,
Riemann provided a means not otherwise available by which to
understand these chords as exercising meaning within a prevailing
key, rather than requiring constant reference to other keys. But
a chord's *Funktion* does not specify its probable course of
action. There is no counterpart in Riemann's theory to Rameau's
doctrine of characteristic dissonances, differentiating the
functions by their certain successors. Riemann's earliest
writings do draw on Hauptmann's dialectic to substantiate the
directed nature of familiar cadences.(24) But this aspect of
logical necessity virtually disappears in later works. It would
have been difficult to sustain as Riemann sought to account for
every possible triadic progression within his theory.(25)
Riemann's familiar prescription of T-S-D-T is often cited as an
example of logical necessity in his functional theory. But
perhaps his most characteristic argument for T-S-D-T appears in
his composition treatise of 1902, rather than in the speculative
works.(26) There Riemann painstakingly demonstrates to the
student that the succession T-S-D-T strengthens the perception of
tonic, while T-D-S-T weakens it. This argument is presented in
terms of the favored choice among possibilities, rather than on
the basis of any inherent properties of the functions themselves.
While Riemann concludes that T-S-D-T is naturally smoother than
T-D-S-T, there is nothing in his discussion to prove that the
weaker cadence cannot be functional, nor that the stronger one is
the only possible functional progression. The lesson is merely
that T-S-D-T works and sounds better; the purpose of the
discussion is chiefly to discourage the student composer from
writing the progression from D to S.(27)
24. Riemann, "*Musikalische Logik*", *Neue Zeitschrift fuer
Musik* 28, (1872), pp. 279-82.
25. Harrison (op. cit., p. 282) views this development as an
abandonment of higher principles, a deliberate move designed for
pedagogical expediency and market favor. Alternatively, though,
it could be seen as the progression from idealistic, derivative
student work to a more mature and tempered approach, implicitly
acknowledging the shortcomings of earlier ideas while advancing
newer ones as fruitful intellectually as they were financially.
26. Riemann, *Grosse Kompositionslehre*, vol. I (1902), p. 33.
27. Further evidence comes from Riemann's principal analytic
work, the complete Beethoven sonata analyses of 1918-20. T-S-D-T
does predominate in the analyses; however, along with numerous
other successions, Riemann identifies several instances of
T-D-S-T, nearly always occurring in principal thematic areas.
Riemann, *L. Van Beethovens saemtliche Klavier-Solosonaten*,
vols. 1-3, Berlin: Max Hesse (1920).
[11] Carl Dahlhaus has examined Riemann's use of the terms
*Funktion* and *Logik* and found both wanting. He has observed
that while the term *Funktion* suggests a definite mathematical
process by which to formally account for getting from chord X to
chord Y, this kind of specificity is not to be found in Riemann's
theory.(28) Likewise, Dahlhaus reproaches Riemann for claiming
the attribute of musical logic for his system. Dahlhaus observes
that, while the system does explain harmonic content of chords
and the relations of chords within the tonal system, it must also
supply rules and norms of harmonic progression in order to be
truly logical. He finds that such rules are completely lacking in
Riemann's system, which as a result appears more descriptive than
logical. Ultimately, Riemann's functions inhere as tonal meanings
in individual chords; they do not determine action from one to
the next. One chord cannot imply another simply on account of its
28. Carl Dahlhaus, "*Terminologisches zum Begriff der
harmonischen Funktion*," *Die Musikforschung* 28/2 (1975), pp.
197-202. Newer mathematical approaches, such as the
transformation system proposed by David Lewin, are sounder, but
(deliberately) shift the focus of meaning from individual chords
to progressions in order to rectify the perceived emptiness of
Riemann's concept. Lewin, *Generalized Musical Intervals and
Transformations*, New Haven: Yale University Press (1987), p.
177. Brian Hyer has also addressed this issue in his talk "The
Concept of Function in Riemann," referenced in Burnham, op. cit.,
note 26; he argues a relational aspect for the *Funktion*
[12] Clearly, Riemann's seminal idea is far removed from familiar
concepts of function associating harmonic identity with scale-degree 
relations. But there is a more basic divergence having to
do with the purpose of the systems. One way we use the term
function is to signify the quality of harmonic relationship which
makes music tonal. Used in this way it is an exclusive concept:
there are functional relationships and there are non-functional
relationships in harmony, with many different ways proposed to
differentiate the two. For Riemann, function also represented
that quality of harmonic relationship which makes music tonal.
But his was an _inclusive_ concept. The objective of his
elaborate system was to show that all possible chords and
progressions could be accounted for in its terms as occurring
within the key in relation to a tonic. While the cadential
strength of progressions and their centrality to the key could
vary, there was ideally no such thing as a non-functional
progression within *Tonalitaet*. 
[13] What we are looking for in these older theories, I think, is
a reflection of our belief that one of the important things
chords do is imply other chords, and furthermore that they do so
because of their function, whatever we understand that to be. All
three of the theories discussed above fall short in this regard,
each in its own way. Rameau provided an explanation showing how
some chords imply other chords according to type, but ascribed
their motivation to progress to non-chordal dissonance. Weber
developed a way to clearly specify the position of each chord in
its key, but allowed for all chord connections equally, and
preferred not to speculate on motivational causes. Riemann
explained harmonic coherence with a two-pronged approach:
function specified the meaning of a chord in relation to its
tonic and its key; the interval of root relation, which is
independent of position in the key, specified the strength and
directness of progressions. The motivational aspect of his theory
was formulated as the concept of musical logic (not function),
whose development he pursued early on but abandoned as his ideas
matured. In our minds the lack of true teleological components in
these theories of harmony can represent a serious shortcoming.
Thus we may tend to read them in where they do not exist, or to
lament their absence when it is undeniably perceived. It may be
hard to imagine that all theorists of the common-practice era did
not share our beliefs in the dynamic nature of harmonic identity,
yet this is what close readings of at least these three theories
reveal. But we need not conclude that these differences
constitute failings on the part of the earlier theories. Rather,
a clear understanding of the contrasts between earlier theories
and our own can help to shed light on the expectations of our own
[14] It has become natural for us to expect the ideal harmonic
theory to explain how chord progressions are determined and goal-
directed. Some of the responsibility for this, ironically, can be
laid at Riemann's feet, for he was the one to introduce the term
*function* in the first place. In his own work he explicitly
associated *Funktion* with *Bedeutung*.(29) But the word
naturally evokes more dynamic associations. After all, in
everyday usage, the function of any object or concept has to do
with what it does more than with what it is. It is inevitable
that this sense of the word would have influenced our notion of
harmonic function, leading us to associate the concept with the
behaviors of chords and to transform it into an active verb
("functions as"). The positivistic model of much modern inquiry
also orients us toward explanations which invoke logical
determinacy. Moreover, the  familiar feel of the term makes
strict definition seem unnecessary. Yet this familiar feel
derives more from informal usage (as the varied uses of the term
cited at the beginning of this essay demonstrate) than from any
rigorous and shared music-theoretic concept. Attempts to
articulate the specific powers of chord function appropriately
take the form of empirical summaries of chord behavior, such as
the one quoted above in paragraph 1, note 2. It would be a
formidable task to successfully formulate predictive rules to
further specify exactly how and when each of the common functions
of the IV chord as described must come into play. Such a fully
rule-governed theory of harmonic function has proved on one hand
to be an elusive goal, and on the other to be somewhat beside the
point, since we have more satisfying deterministic explanations
of music these days.
29. This was his original definition of the term, I believe.
Riemann (1890), p. 27.
[15] One of the principal teachings of Schenkerian theory is that
the quality of goal-directedness in tonal music derives from
short- and long-range contrapuntal and prolongational processes
imbedded in the musical texture rather than from integral
chord-to-chord progressions on the surface. If we accept this
explanation of *Tonwille*, then perhaps it is unnecessary to
require that our concept of harmonic function account fully for
the same quality. A notion of function short on teleological
implications might initially strike us as empty. But explanations
of harmonic meaning and coherence remain necessary and important.
If we limit our vision to recognizing diatonic scale-degree
chords and their variants, then function becomes subsidiary in
our minds to other musical processes. If, though, we open our
view to imagine an enhanced system of diatonic and chromatic
relations anchored to a tonic, something like Riemann's
*Tonalitaet*, it may open our minds to contemplate in a positive
way the greater structural potentials of the tonal system as
exploited in mid-nineteenth to early twentieth-century music.
Thus I would not like to suggest that we discard the function
concept in our own descriptions of harmony or reject useful
notions of harmonic identity and action. Function is a suggestive
term which is still inspiring creative work in theory after over
a century of use. But careful definition and elaboration is
crucial. I do feel that we should be circumspect in attributing
the function concept wholesale to theory before Riemann. The term
carries so many associations for us that it is difficult not to
read some of them into the historical subject, thereby occluding
perception of subtle yet important differences from our own
views. Even if we know exactly what we mean, there is no
guarantee that our reader will accurately grasp our meaning when
we use the term without scrupulous qualification, since there are
so many acceptable interpretations of the concept. Furthermore,
the widespread and casual use of the term nowadays has diminished
its descriptive power. It may prove helpful to investigate our
assumptions and more clearly articulate and differentiate the
myriad concepts which function has come to represent for us.
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