Functional Harmony Revisited: A Prototype-Theoretic Approach
Eytan Agmon · Music Theory Spectrum · 1995
ions, for neither exists in work of a single theorist in as pure a form as their hypothesized rivalry suggests. 13See especially Oswald Jonas, Introduction to of Heinrich Schenker, trans. and ed. John Rothgeb (New York: Longman, 1982), 127-28, and Rothgeb's review of Hellmut Federhofer, Akkord und Stimmfiihrung in den musiktheoretischen Systemen von Hugo Riemann, Ernst Kurth und Heinrich Schenker (Vienna: Verlag der Osterreichischen Akademie der Wissenschaften, 1981) in Music Spectrum 4 (1982): 131-37, where the recognition of only three principal is dubbed specious (132). See also Federhofer, Beitrage zur musikalischen Gestaltanalyse (Graz: Akademische Druck, 1950) and Akkord und Stimmfiihrung; and Matthew Brown, A Rational Reconstruction of Schenkerian Theory (Ph.D. diss., Cornell University, 1989), 192-99. Both Brown and Wason (Viennese Harmonic Theory, 134-35) present synopses of Schenker's arguments. i and independence of seven harmonic degrees. Morer, unlike Funktionstheorie, wher p im y harmonic el is -IV-V-I progression, Stuf ntheorie leans a ily on cycle of d sce ding fifths IV-VII-III-VIcharacter,' does it not follow necessarily that all scaledegrees-not only I, IV, and V-must be recognized as scaledegrees in their own right?14 The Schenkerian approach: hierarchy and voice leading. While Schenker's 1910 critique of functionalism is of a clear, Stufent orie origin, subsequent development of his theories, with its well-known emphasis on voice leading and hierarchical structure, has inevitably led to friction of quite a different sort. Jonas, for example, states that functionalism had to fail, because it neglected fact that two occurrences of same chord could be worlds apart in meaning, and that everything depended on context.15 In a footnote to that statement, John Rothgeb concedes that functionalism allows a secondary chord, such as III, to assume different functions in different contexts, but nevertheless insists that the theory fell far short of a recognition of phenomenon of composing-out, and, as a result, failed to discriminate between vertically and horizontally generated chords. My response to all of these important objections rests on three major points: (1) proposed version of functional theory is not Riemann's; (2) theory is not meant to exhaust harmonic domain; and (3) proposed theory is compatible with a hierarchical approach. Departures from Riemann. Certain controversial aspects of Riemann's theory have no counterparts in proposed theory. Most notably, proposed theory abandons Riemann's 14Heinrich Schenker, Counterpoint, vol. 1, trans. John Rothgeb and Jiirgen Thym, ed. John Rothgeb (New York: Schirmer, 1987), 23, 27. As John Rothgeb explains in a footnote on p. 348, the application ... [of theory of tonal functions] is especially problematical in passages involving 'sequences' by descending fifths. This led Riemann to declare that 'as was recognized first of all by Fetis, however, true harmonic movementthe cadential progression-remains stationary for duration of sequence....' The reference is to Hugo Riemann, Handbuch der Harmonielehre, 7th ed. (Leipzig: Max Hesse, n.d.), 202. 15Jonas, Introduction, 127. ,' oes it not fol ow neces arily that all scalet only I, IV, and V-must be recognized as calei t eir own right?14 erian approach: hierarchy and voice leading. e er's 1910 critique of functionalism is of a clear, rie origin, subsequent development of his , ith its wel -known emphasis on voice leading and i al structure, has inevitably led to friction of quite t sort. Jonas, for example, states that functionalism ail, because it neglected fact that wo ccurrences e chord could be worlds apart in meani g, and that i depended on context.15 In a footnote to that , ohn Rothgeb concedes that functionalism allows chord, such as III, to as ume dif erent functions This content downloaded from 157.55.39.162 on Thu, 11 Aug 2016 05:37:20 UTC All use subject to http://about.jstor.org/terms 204 Music Spectrum notion of apparent consonance (Scheinkonsonanz), which truly deprives so-called secondary triads, right from start, of any potential independence.16 More generally, Riemannian sense in which a secondary degree is said to represent or substitute for a primary degree does not exist in proposed theory. Unlike Riemann's somewhat ambiguous use of tonic, subdominant, and dominant to refer to both functions and/or chords, in proposed theory these terms are used exclusively to refer to functions, that is, categories of chords; reference to individual chords is made by Roman numerals.17 II, for example, represents an abstract category (namely subdominant), which is also represented by IV; at same time, IV is of course more prototypical representative of that category. The proposed theory largely bypasses another highly controversial aspect of Riemann's theory, namely dualism.18 After all, there is no necessary connection between functionalism and dualism, however essential it might have seemed to Riemann to view rules of harmony and major/ minor polarity as stemming from a single source. Indeed, there is no lack of evidence that functionalism can flourish16See Dahlhaus, Studies, 38: the concept of functions can be separated from Riemann's method of demoting secondary degrees to dissonant variants of primary degrees, so that one can retain concept of fundamental progressions without giving up concept of For Dahlhaus's elaboration of this statement, see especially pp. 57-59. 17Concerning Riemannian chord/function ambiguity, see Dahlhaus, Studies, 50. In a paper entitled Idea and its Politics: Hugo Riemann's Treatment of Harmonic Function, delivered at 1992 annual meeting of Society for Music Theory, Daniel Harrison has argued that chord/ function ambiguity is not so much inherent in Riemann's theory (as Dahlhaus implies), as it is an unfortunate result of Riemann's attempts to make his theory more generally accessible. 8sThe closest counterpart in proposed theory to Riemann's dualism is principle of symmetry, discussed in connection with Figure 2. tion of apparent c sonance (Scheinkonsonanz), which ly deprives so-call d secondary t ads, igh from art, of any potent al independence.16 More generally, ie a nian sense in w ich a secon ary degree is said to resent or substitute for a p imary degree does not exist in e proposed theory. Unlik Riemann's somewhat ambigus use of tonic, subdomina t, and dominant to refer to both ctions and/or chords, in proposed theory these terms e used exclusively to refer to fu ctions, th is, categories chords; r f rence to in ividual chords is made by Roman erals.17 II, for example, represents an abstract category a ely subdominant), which is also represented by IV; same time, IV is f course m re prototypical resentative of that category. e proposed theory largely byp sses another highly conoversial aspect of Riemann's theory, namely dualism.18 Afa l, there is no necessary connection between functionis and dualism, however essen ial it might have seemed iema n to view rules of harmony and major/ inor polarity as stemming from a single source. Indeed, quite apart from any attendant commitment to a dualistic doctrine.19 The scope of theory. As already indicated, harmonic theory is viewed in present article as a composite of two main subtheories: a theory of functions and a theory of chord progression. This view is indebted to historical FunktionstheorielStufentheorie opposition; however, correspondence is far from exact. Most notably, proposed functional theory is static, in sense that it merely describes three harmonic categories and their internal structure; T-S-D-T paradigm of functional succession (a venerable component of Funktionstheorie) is not within its scope. The exclusion of functional succession from functional theory might seem a bit odd. However, although excluded from functional theory, T-S-D-T paradigm remains a part of harmonic theory in general-that is, interaction of theory of functions with a theory of chord progression. Once scope of functional theory is reduced, it cannot be faulted for failing to deal convincingly with cycle of descending fifths. The priority of descending-fifth relationship is clearly an aspect of theory of chord progression, not theory of functions. When Schenker and his followers point out, for example, that II in II-V is not merely a IV-substitute because a descending-fifth relationship obtains between II and V, they are certainly correct; but their argument concerns theory of chord progression (as it interacts with theory of functions), not theory of functions per se. It is surely senseless to reject a theory 19Since a number of American theorists have taken renewed interest in Riemann in general and dualism in particular, it might be clarified that intention here is not to rekindle dualism controversy; rather, intention is merely to rebut criticisms of Riemann's dualism that might be addressed toward proposed theory. An example of American Neo-Riemannism is David Lewin, A Formal of Generalized Tonal Functions, Journal of Music 26 (1982): 23-60. c it e t to a dualistic This content downloaded from 157.55.39.162 on Thu, 11 Aug 2016 05:37:20 UTC All use subject to http://about.jstor.org/terms Functional Harmony Revisited 205 outright merely because its success is limited, to one degree or another, in terms of total domain under consider-