Music Theory Midwest

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

Paper Abstracts:

        Much post-tonal music is drawn from chromatic, octatonic, diatonic, whole-tone, or pentatonic collections. These collections can be understood as modular spaces because they each partition the octave in a unique way. Works that use two or more of these modular spaces have posed a problem for analysts, because musical motives therein often appear in more than one space. In such works, a given motive will be described by different set classes when appearing in different modular spaces, though its various forms are all equivalent in an important way: they are all expressions of the same basic musical idea. This paper introduces two new kinds of equivalence classes: "modular sets" and "modular set types." A "modular set" is defined as an unordered collection of step classes (i.e. positions within a modular system), and a "modular set type" (abbreviated M-type) is defined as an equivalence class representing a family of modular sets related by transposition or inversion. Each M-type thus represents all pc sets that are realizations of that M-type in chromatic, octatonic, diatonic, whole-tone, and pentatonic spaces.

        A geometric model in a 12-dimensional Euclidean space, termed "root space", is proposed as a method to overcome pitch-class set theory's inability to differentiate instances of collections with high (>9) cardinality. A simplification of the virtual pitch algorithm first developed by Terhardt et al., and modified by Parncutt, is used to map sonority instances to distinct points in the space; "multidimensional harmonic analysis" then consists of analyzing the path traced over time by these points. Differences between Parncutt's version of the virtual pitch algorithm and the currentsimplification are discussed. Applications are given for aggregate spacings in Lutoslawski's music, especially the aggregate cycle in the opening of Mi-parti(1975-76); several passages containing sets of lower cardinality are discussed as time permits.

        Recent writings in transformational theory by David Lewin and Henry Klumpenhouwer have introduced the "Klumpenhouwer network," which recognizes both transpositional and inversional relations within a single pitch-class collection. This paper examines extensions to Klumpenhouwer networks. Whereas standard Klumpenhouwer networks may form isographies in which invariant transpositional distances are combined with changing inversional operations, this paper demonstrates another kind of isography, deemed "axial isography," in which an inversional relationship is preserved. The paper draws from music of Schoenberg and Berg to illustrate operations that map axially isographic networks onto each other. This paper demonstrates how positive, negative, and axial isography can work together for a single analysis. The results thus broaden transformational theory to encompass a wider range of musical contexts.

        In tonal music, sequences can be produced either diatonically or chromatically. A chromatic sequence exactly replicates the initial harmonic and/or melodic cell at each sequential interval; a diatonic sequence, on the other hand, incorporates slight alterations in order to contain essentially the same pattern at different pitch levels within a particular key. Because alterations in diatonic sequences are entirely systematic, both diatonic and chromatic sequences can be defined with equal rigor using scale steps rather than exact intervals. Any variance of scale-step sizes is then considered to be a by-product of a particular scale type rather than a sequential incongruity.
        In atonal music, many analysts overlook sequences that do not maintain exact intervallic patterns. Perhaps this is a reflection of our well- established transformational models and the ways in which they define equivalent interval and set types. Nevertheless, there are many examples in which a sequential pattern is masked by unequal step sizes (and hence non- equivalent set classes) that fall out of a particular collectional space. Many commonly used scale types--such as diatonic, pentatonic, octatonic, and hexatonic (e.g., <C, C#, E, F, G#, A>)--feature two sizes of scale step, and other less common scale types may feature three or more scale-step sizes. I will demonstrate some unusual properties of sequences on both well-formed and non-well-formed scales and show how generic scale-step-based definitions can help elucidate some passages in works by Messiaen, Lutoslawski, and others.

        In the past ten years, music theory scholars have explored new avenues of criticism. The search for new perspectives resulted from a need to expand the ways in which we speak about music, exploring beyond the limits of traditional analytical approaches. This panel seeks to continue along this path, discussing issues and implications that center on the concepts of discourse, genre, and meaning in music analysis.
        While greatly aiding and adding to our understanding of what music entails through various analytical paradigms (most notably Schenkerian and pitch-class set theory), the traditional music theory enterprise has been limited by the philosophy that grounds these analytical models. This philosophy has been characterized as one that is primarily concerned with the notes as they appear on the page and not with any of the other circumstances that contribute to the compositional and listening process. Over the years, a number of writers have put forward different means of exploring music, writers such as Leonard B. Meyer, Edward T. Cone, and Thomas Clifton. For the most part, these writers were the exception. In recent years, a new generation of authors, including Kofi Agawu, Robert Hatten, Kevin Korsyn, Marion Guck, and Joseph Straus, have explored beyond the confines of the predominant structuralist models, providing new ways of imaginingcompositions as well as questioning what is meant by music theory and analysis. As a result, readers (and listeners) are offered a greatly enhanced picture of music theory, one that is not limited to just the page on which the music rests.
        In closing, we envision this session to include a short presentation by each of the panel members, approximately twenty minutes in length, followed by an inclusive discussion exploring these topics and others. We intend this session to be a forum in which ideas can be presented without the need for closure or conclusive solutions. For the purposes of this panel, we will address five issues; they are encapsulated below.

        Although we tend to associate the field of ethnomusicology primarily with non-Western musics, the cultural approach to explaining music that the methodology of this field advocates has important implications for traditional music analysis. In particular, I propose that a cultural perspective offers the basis for a reconciliation between the respective positions of music historian, critic, and analyst, as well as a version of semiotics more attuned to the meanings of art and music within the experience of a particular society.
        Although the influence of the anthropologist Clifford Geertz has been felt in musicology by such figures as Gary Tomlinson, insights into cultural experience gained by a "contextual" semiotics of art and music might rescue us once more from a strictly synchronic, purely theoretical engagement with music that is common with analysis. For Geertz, such an approach would sacrifice the generalizations of systematic theory in order to uncover the unique experiences of a particular cultural location, a kind of knowledge that is local and experiential in nature, and would take the form of a hermeneutic dialogue with cultural contexts both historically and geographically. In addition to considering the role of cultural meaning in recent applications of semiotics in musical analysis, I will explore briefly other possibilities suggested by this approach, and will both raise questions about its applicability and offer promise for a more meaningful music analysis.

        The period from 1781 to 1871 represents the Age of Emancipation in the history of German Jewry. During this period a social contract evolved during which rights would be conferred upon the German-Jewish subculture in exchange for education and acculturation. This project amounted to what the historian David Sorkin has called the transformation of German Jewry. At stake for the German-Jewish subculture were questions that ranged from economic and social opportunity to basic issues of selfhood and individuality. The question that I wish to discuss in this paper is: To what extent does the ideology of emancipation that arose in that subculture express itself in its participation in the dominant culture vis-á-vis music theory? In other words, what are the aspects of the music theory of A. B. Marx, Saloman Jadassohn, Heinrich Schenker, and Arnold Schoenberg, among many others, that could be understood as being socially driven or socially informed by the project of emancipation?

        As Edward Said puts it, the "transgressive element in music is its nomadic ability to attach itself to and become part of, social formations, to vary its articulations and rhetoric depending on the occasion as well as the audience, plus the power and gender situations in which it takes place" (Music Elaborations, 70). In contrast, the aesthetic of autonomy of music persists as a social construction that produces music's intrinsic significance, as self-contained (or independent of) intertextual reference, authorially complete and organically whole, and/or separate from the discourse and reception of others. The problematic relations of signification and materiality in and of music underlie its interplay of contexts and forms. Music forms are not simply fixed or waiting for a context to inflect them with meaning; neither are they impervious to or swallowed by the demands of context and social use.
        The interplay of form, context, and subjectivity poses problems for music analysis: the aesthetic problem, the articulation of a sense of presence or of distance and abstraction in music; the analogy problem, the role of difference in apprehending similarity; and the problem of subjectivity, singular relationships with, and articulations of, social-cultural orientations andidentities. I will explore, from the angles of a Chopin prelude and a Cole Porter song, how music encourages and resists "reversals," shifts and crossings between categories and meanings that reveal the forces at play in experience and interpretation.

        The history of analysis is tied in with models of understanding developed in other domains. Yet, it is a necessity that these models be transposed to the realm of musical analysis. I will address one such model, the analysis of rhetoric in the work of Mattheson (1739), comparing its use of rhetorical devises in analysis with contemporary theories of language by Diderot (1748) and Lessing (1766). At stake are the standards by which language engages the world according to a series of binary oppositions: spatial/temporal, motivated/non-motivated, natural/arbitrary. These dichotomies are highly fluid in linguistic practices, according to both Diderot and Lessing. Mattheson's analyses reach an impasse when trying to account for repetition, a phenomenon that cuts across the binary oppositions.

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