Music Theory Midwest

1999 Tenth Annual Conference
Butler University
14-15 May 1999 - Indianapolis, IN

Paper Abstracts:

        In Die Lehre von den musikalischen Klangen (1879), the Czech musicologist and aesthetician Ottokar Hostinsky sought to provide a "psychological-aesthetic" foundation for harmonic theory by forging connections between then-recent work in acoustics and long-standing rules of musical art. The first half of my paper explores Hostinsky's notion of the "psychological-aesthetic" factor and its implications with respect to his treatment of triadic relations. Departing from a critique of Helmholtz's and Oettingen's theories, Hostinsky presents a two-fold scheme of tonal relations, including relations based on melodic proximity (Nachbarschaft) as well as those based on harmonic connection (Verwandtschaft). His belief in the priority of acoustically-based harmonic connections to any musical system prompts him to include non-diatonic triads among direct relations, and the principles of harmonic connection and melodic fluency together admit at least the theoretical possibility of connecting any two triads, whether directly related or not. Hostinsky's views are compared and contrasted with those of Oettingen, Helmholtz, and Riemann. The second half of the paper examines these findings and other aspects of Hostinsky's work (such as his re configuration of Oettingen's Tonnetz) within the context of a broader historical project, suggested in Richard Cohn's 1997 article "Neo-Riemannian Operations, Parsimonious Trichords and their Tonnetz Representations," demonstrating the existence of a nascent group-theoretic perspective within the acoustically-conceived harmonic theories of nineteenth-century writers.

        A simple algebraic framework is proposed for studying triadic transformations. Included are the "neo-Riemannian" transformations P, L,and R, and other transformations recently studied by Cohn, Hyer, and Lewin. Hyer's group of 144 transformations is extended to a group of 288, in which composition of transformations may be defined in a simpler and more unified fashion. The 144 non-Hyerian transformations include some of particular musical importance, such as the "diatonic mediant" transformation. Briefly, each transformation is represented by a sign (indicating mode-preserving or mode-reversing) and two transposition levels (one for major triads, one for minor). The study of the structure of this group generalizes some results of Cohn about the self-inverse property of some neo- Riemannian transformations, and provides some clarification of the relationship between those transformations that behave in characteristically "neo-Riemannian" ways and others (such as the "dominant" transformation) that do not--a relationship that some have found disturbing. The group may be regarded as the group of intervals in a suitable Generalized Interval System in the sense of Lewin. The methods presented are readily adaptable to transformations of set classes other than triads and to equal-tempered systems other than that with 12 notes.

        David Lewin and Brian Hyer have used L, R, and P transformations to examine relations among triads without relating them to a tonic. However, these transformations combine to form at least two cycles, the L-P and R-P cycles, which partition the 24 consonant triads into distinct sets. Richard Cohn has suggested using the L-P cycles as harmonic regions. I will show that in the first movement of his Eb Major Trio, D929, Schubert uses the sets created by both these cycles as functional harmonic regions. Further, I will show how the piece can profitably be heard as using either set of cycles, the L- P or the R-P, as the harmonic regions. I will examine the way each hearing makes sense of the harmony in three passages.
        In general, the kinds of statements made to support one hearing are roughly the same kinds of statements made to support the other hearing. There is no principled way to choose between them, and indeed, the piece is more interesting if we accept them both.

        After placing "dialectical opposition" in a larger historical frame, the paper discusses "dialectical opposition" in Schoenberg's music and thought through close readings of passages of his various pedagogical and critical writings. The paper closes with some general thoughts on various types of opposition as they are addressed in the field of music theory.

        Theorists generally rank the pointillistic abstractions of Anton Webern as the epitome of modern analytic formalism, befitting Ernst Krenek's description as "marvelous gems of constructive perfection and fantastic complexity, integrated like a Chinese puzzle." A postmodern reappraisal, however, suggests that the composer's romantic and intuitive alter ego has been undeservedly overlooked. Was Webern's exclusive association with a formalist aesthetic a cultural bias fostered by modernism's reification of systematic relationships in all music, particularly his? Did the Darmstadt- Princeton axis seize upon and essentialize one aspect of his music to fit its own narrow formalist conceit? Who then is the real Webern?
        Sketch material available since the composer's modernist canonization reveals a very different image of a lyrical poet whose intellectual concern for constructive coherence is tempered by an intuitive appreciation of the expressivity of ambiguity. This is no longer the meticulous musical engineer who memorized train schedules and calculated intervallic timetables, determined to extricate himself from the excesses of Romanticism, but rather soulful humanist invoking his poetic sensibility to avert an aesthetic crisis caused by an overly mechanistic and arid compositional technique. In postmodern eyes, Webern invites us to celebrate flaws and wrinkles instead of always trying to iron them out, hinting at creation through deconstruction rather than integration.
Must the act of composition or analysis inevitably imply defeating incongruities by bending them into patterns and postulating some totalizing principle to resolve aberrations? Ironically, it is "St. Anton," the patron saint of musical modernism, who suggests not.

        Recently, Richard Cohn has issued a challenge to the Schenkerian view of motive, maintaining that the theory and practice contained unresolved contradictions. The problem will be illustrated by my own analysis of a Wolf song, in which a motivic pitch string is used a metaphor for angels. This usage is reminiscent of one of Schenker's metaphors: "The fundamental structure accompanies each transformation in the middleground and foreground, as a guardian angel watches over a child." But the motives in the Wolf song are in no way coherent individual entities in the middleground; they are never completely congruent with the composing out of the background tonic triad. It is not clear how they can take part in the organic coherence of the piece or indeed whether recognized as entities at all. In fact, a large number of analyses by Schenker himself recognize motives not congruent with the voice-leading structure, enough to represent an essential part of Schenker's practice.
        I will begin by demonstrating that for the later Schenker it is the general concept of parallelism that is significant. I will describe a model in which parallelism acts at right angles to the hierarchy of structural levels. Along any level from middleground to foreground, any contiguous series of pitches is available for parallelistic repetition and it is advantageous for synthesis if this occurs. Nonetheless the content of motives is restricted: not just any pair of non-contiguous tones can be picked out, but only those made available by structural coherence. I will argue that this model of dual organicisms does not indicate inconsistency or contradiction in Schenker's thinking, but rather shows a more complex view of coherence.

        The application of Schenkerian analytical techniques to post-tonal music historically has been an issue which has sparked great debate in the field of music theory. Is Schenkerian analysis compatible with post-tonal music? Much theoretical scholarship in the decades since Schenker's death has been devoted to this question. In recent times, James Baker (1983) has been rather critical of existing post-tonal Schenkerian analyses, but since then (1990, 1993) has adopted a method relying on the strict application of Schenkerian methods in the analysis of music by Schoenberg, Ives, Bartók, and others. This paper includes a critical review of a portion of Baker's 1993 analysis of the Scherzo from Bartók's Op. 14 Suite, relying in part on the work of Joseph Straus (1987) to bring to light many of the problematic assertions contained in Baker's analysis.
        The second part of the paper is intended to illustrate that convincing analyses which reveal large-scale structural coherence in post-tonal works are indeed possible to achieve without resorting to the familiarity and security of traditional prolongational devices. Structural analyses of two pieces from Bartók's Mikrokosmos will provide models for the approach, which draws upon the work of Paul Wilson (1992), a theorist obviously influenced by Schenkerian ideals yet still only implicitly Schenkerian. The method yields interesting analytic findings, including the revelation that certain hallmarks of Bartók's style which appear on the surface of each piece (symmetry, modified tonal structures, and conflict between diatonic and chromatic elements) are consistently projected onto that piece's higher structural levels.

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