Perhaps the most charged encounter between the "new" musicology and music theory is to be found in Richard Taruskin's work on Stravinsky. Taruskin first endows the notion of "octatonicism" with a nineteenth- century genealogy; then exposes the extent of Stravinsky's appropriation of folk material in the Rite; and finally, in a wonderfully stunning indictment, details the implicit collusion of the theoretical community in Stravinsky's suppression of the evidence of this appropriation (a suppression intended by Stravinsky to conceal a particularly shabby ideology) through its mythic celebration of the Rite a revolutionary act, an utterance sui generis which serves reciprocally to legitimize a formalist abdication of the public responsibilities of scholarship. In his haste to assemble this indictment, though, Taruskin overlooks some of the more compelling implications of his own evidence, and the possibility of a more telling critique. Specifically, he passes too quickly from Stravinsky's ethnography to his ethnology, and while condemning theory's reification of "the music itself" is curiously deaf to the ironies embodied in this phrase. Given the evidence of Stravinsky as transcriber, we must assume that the resistances encountered in representing an oral music--a performance sui juris--in a notation grounded in all manner of theoretical biases could but be compositionally fascinating; and moreover, that these resistances (and the way in which they color the notion of "the music itself") need not lend themselves only to local exploitation but more importantly to a general reconception of the nineteenth-century dialectic of phenomenal and nominal musics.

Although Francis Poulenc is best known today for his lighter compositions, he remained interested throughout his life in the works of the European avant-garde, met personally with Schoenberg, Berg, and Webern, and greatly admired their music. In his own later music, especially vocal works, Poulenc writes extended passages that are only distantly reminiscent of tonality or that are frankly atonal. Yet he moves with ease between these non- tonal sections and others with clear key centers and functional harmonic relations. These pieces challenge the analyst to develop tools to investigate and explain the integration of tonal and non-tonal materials in a single composition. ?       

Three features help to account for the coherence of these eclectic works. Interval-class saturation (with tritones, whole steps, or other intervals) ensures that even segments with very different harmonic bases will have a similar sound. Poulenc also employs symmetrical modes or chords; their symmetry at times renders them static and non-functional, but at other times their relation to diatonic, functional materials is highlighted. And relations of literal or abstract inclusion are particularly important in linking conventional tonal sections and more experimental harmonies. ?       

The intersections of tonal and non-tonal materials in Poulenc's music, and the concepts proposed for an analysis that will bridge the two, are suggestive as well for the analysis of similarly eclectic music of Poulenc's contemporaries.

Assessing the relationship between space and time proves fruitful when treating Debussy's music, as it affords a means of contextualizing Debussy's novel orientation toward the interaction of surface, middleground, and background events-an orientation that differs profoundly from the assumed norm for tonal pieces; and yet the principle of organizational control is never lacking in Debussy's music, even if his approach to linearity is antipodal to that of his predecessors.        

With "Du ríve" from Proses lyriques as test site, the study draws upon diverse theories, including Mikhail Bakhtin's conception of the chronotope in the novel, Jonathan Kramer's notion of multiply-directed time as an organizational principle in music, and David Greene's premise thatcompositions reveal distinct orientations toward temporality. Aspects of these theories help to account for Debussy's particular take on the compositional relationship between past, present, and future events. ?       

A chief means of conveying continuity at the foreground in Debussy's music results from the gradual transformation from one event to another; ironically, however, the procedure precipitates a melding together of present and future that infuses the moment-to-moment procession of the work with something of a timeless quality. At deeper levels of the structure, however, causal mechanisms and freely-taken decisions belie the sense of atemporality stemming from a surface replete with rapid changes of musical vocabularies. At levels removed from the surface, then, the concept of linearity is rearticulated, and as a result, time-to use Kramer's term-becomes multiply- directed.

The author views late works of Morton Feldman through the window of the metaphor 'living on the edge.' Analysis of the 1983 work Clarinet and String Quartet shows how fleeting hints of process, ordering and pattern engage the listener's perception at the threshold of intelligibility, and create a narrow 'zone of possibility' in which much of the activity of the piece takes place. In many ways the music adheres to the dictum formulated by Cage, Feldman, and their associates of the early 1950's: that sounds were to be heard 'as sounds themselves.' However, the author shows how the construction and presentation of material both validates and questions this idea.

Norwegian composer and ethnomusicologist Eivind Groven (1901- 1977) spent much of his life's work striving to bridge the gap between his native folk music and Western classical music. His most noticeable accomplishment in this regard was the construction of a 36-tone renstemt organ (based on just intonation) with an electronic interface, called the renstemningsautomat, which can automatically adjust the tuning dynamically during performance. Groven's organ uses a standard keyboard manual to which each individual key can be connected to one of three possible pipes each tuned to a slightly different frequency. Of the organ's two modes of operation--fixed and dynamic tuning--the former was intended primarily for playing arrangements of traditional Norwegian folk music, and the latter for Western tonal art music.

With various fixed 12-note scales, Groven tried to approximate the tunings employed by indigenous Norwegian folk instruments such as the hardingfele and seljefløyte. The real-time tuning function, on the other hand, allows for free modulation, while still preserving just-tuned intervals in all keys, as will be demonstrated in recordings of organ pieces by Bach and Handel. In closing, I will outline my proposal for the construction of an acoustic piano system modeled after Groven's organ.

Steely Dan is the name of a popular recording group whose musical style is often called jazz-rock fusion. Their music's originality lies largely in the way harmonies are constructed within what I call the "harmonic strata," a method of voicing chords in two tiers: a treble register triad or seventh chord (upper tier) above a bass note (lower tier), where this bass note is different from the root of the upper-tier triad. These voicings, used in succession, are specific to the music of Steely Dan. These successions often form larger spans of music, even entire songs bearing a distinctive sound and functionality of harmony. ?       

"Polychord" is sometimes used in jazz and pop theory to describe these two-tiered voicings, but more appropriate is the term "slash chord," which gets its name from the line drawn between chord symbols (or their roots). The term slash chord also describes three other harmonic possibilities: 1) inversions, 2) extended tertian harmonies, and 3) chords with an added bass; it is these that more often than the others comprise the voicings of Steely Dan. ?       

Assessing the originality of Steely Dan's music requires that we classify its individual slash chords according to structure, and that we study themethod by which Steely Dan constructs progressions of slash chords in terms of the ordering of slash-chord types and of the voice leading among the strata. The products of these analyses may then be used to demonstrate how slash chord progressions distinguish the sound and structure of Steely Dan's harmony, on the level of the phrase, the section, and the song.

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., )--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.

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.

 

 

 

Part of special session titled, "Discourse--Genre--Meaning: Explorations in Music"

Abstract for special session: 

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.

 

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?

 

Part of special session titled, "Discourse--Genre--Meaning: Explorations in Music"

Abstract for special session: 

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.

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.

 

Part of special session titled, "Discourse--Genre--Meaning: Explorations in Music"

Abstract for special session: 

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.

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.

Part of special session titled, "Discourse--Genre--Meaning: Explorations in Music"

Abstract for special session: 

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.

In my presentation, I will discuss the possibilities and rewards of considering music as a language. I base my argument on Mikhail Bakhtin's notion that all interactions between human beings are essentially dialogues, music included. By dialogue, Bakhtin means the particular ways in which a commonly associated group of people choose words, use phrases, and articulate their utterances so other participants in this linguistic sphere are able to respond, thus furthering the dialogue. To enhance my own argument, I will extend the seminal work done by Kevin Korsyn in his article, "Towards a New Poetics of Music" (Music Analysis 8/1-2 1991), contending that compositions do not have to be a Bloomian/Freudian battleground between composers, with the belated attempting to exorcise his/her artistic predecessor(s). Instead, music can be the grounds for a lively exchange, one inwhich a composer adds to the ongoing dialogue. In order for this exchange to occur, the notion of musical genre needs to be revisited and expanded so there can be common ground between composers (and listeners) as well as ways of composing and listening so that the discourse is better defined and understood. The end result of such a rethinking would be a better consideration of divergent points of view, one that has at its core a pluralistic view rather a drive for a singular one.

Part of special session titled, "Discourse--Genre--Meaning: Explorations in Music"

Abstract for special session: 

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.

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.

 

Our capacity to remember aural events is critical to our musical understanding. Musical memory enables us, among other things, to recognize a recurring theme, to notice that this theme has moved from the violins to the horns, to realize that the music has returned to the original key, and to hypothesize that those alternating tonic and dominant chords signal that the movement is nearly over. This does not mean, however, that musical memories must be encoded aurally -- that is, a listener does not necessarily remember a series of sounds corresponding to all previously heard music. Instead, musical memory might be encoded verbally, visually, or kinesthetically, for example.?       

Very few investigators have addressed strategies for encoding music. However, numerous psychologists examining visual, olfactory, and non- musical auditory memory have discovered a correlation between the ability to identify things verbally and the ability to remember them. I will summarize this research, present the results of an original experiment that suggests verbal encoding of timbre is common among trained musicians, and discuss the pedagogical implications.

Music theorists have long used spatial imagery to describe relations among tones, referring to pitches as high or low, intervals as wide or narrow, keys as near or distant. This paper will show how such relations metaphorically reflect our experience of physical space, revealing ourpropensity to map onto music image schemas derived from embodied experience (Johnson, 1987; Lakoff, 1987; Lakoff and Johnson, 1998). Two schemas in particular appear to be relevant to our experience of musical space: the CONTAINER schema and the SOURCE-PATH-GOAL schema.?       

This paper shows how the psychoacoustic properties of pitch lend themselves to different, yet complementary, mappings of pitch onto physical space. Within this space, keys, chords, and intervals can be represented as pathways and/or containers, which in turn map onto one another through their shared properties of enclosure, familiarity, and safety. Changes of pitch, harmony, and key can then be represented as motion passing within and/or between containers following pathways that lead to stable goals. These three metaphorical elements--containers, pathways, and goals--appear to serve as the basic building blocks for musical narrative, allowing us to hear in music such storylike features as confinement within a container, expansion of (or escape from) a container, the overcoming of blockage along a pathway, and the attainment of a goal at the end of a pathway. This paper provides evidence of the palpability of such features by showing how they contribute to the narrative structure of specific musical works.

In Style and Music: Theory, History, and Ideology (1989), Leonard Meyer proposes a general theory of musical style change grounded in the belief that such changes result from countless interactions between individual composers, performers, and audience members acting in concert over time. Of course, many factors contribute to the context of stylistic development, but the changes in musical practice fundamentally result from the individual choices made by composers. Meyer's theory closely correlates with descriptions of complex systems in other fields.       

Complex systems have an "evolving structure," that is, "these systems change and reorganize their component parts to adapt themselves to the problems posed by their surroundings." Fortunately, "the mechanisms that mediate these systems are much more alike than surface observations suggest. These mechanisms and the deeper similarities are important enough that the systems are now grouped under a common name, complex adaptive systems" (Holland 1994, 310).       

Music shares many characteristics with complex adaptive systems such as: 1) the presence of numerous autonomous agents and their interactions; 2) multiple feedback and feedforward loops; 3) distributed decision making; 4) atendency for diversity and complexity to increase with time and; 5) the use of internal schemata to aid adaptation to new environments.       

The models and metaphors emerging from the study of complex systems resonate with the dynamic nature of musical development and perhaps more importantly, with the diachronic nature of our musical experiences. The models provide avenues for exploring the system dynamics and thereby expanding our understanding, while the metaphors provide rich associations and powerful images to describe the dynamic character of music on a variety of levels.

After some 24 years of a correlated music theory and music history core experience for freshmen and sophomores, the Northwestern School of Music has been experimenting with a new sequence of courses. The history courses now begin in the sophomore year. The goals of the theory curriculum, broadly stated, are:

1. to present a learning-centered program of study, with a focus on what and how (and whether) students are learning, with special emphasis on how students mentally organize their knowledge;
2. to develop concrete strategies for having students apply what they're learning to music outside the theory classroom, especially to music they study with the private teacher and ensemble director, and to music which reflects their personal tastes;
3. to move away from a preoccupation with 4-voice partwriting toward using partwriting as a means of developing analysis and listening skills;
4. to give more time to the study of rhythm, and to begin the study of meter by analyzing metric structures as they are heard, and only then to proceed to how meter may be represented on the page; and
5. to incorporate pop music, jazz, and music of other cultures as models of "correlation or contrast" with the Western musical canon.     Since we have had a year's more experience with the freshman course, now in its third year, we limit our presentation to the three ten-week quarters of the first year of study. The materials available at the presentation provide three perspectives on the course: the structure, the content, and specific teaching/learning strategies.

Structure

        The fall and winter two quarters of study are uniform for most students. That is, the four sections of theory cover more or less the same material in the same way. During spring quarter, students register for a "break out" course in applied theory. Each of these courses focuses on a specific topic, while reinforcing the knowledge and skills developed in the previous two quarters. Students have a choice of four courses. In the past three years, topics have included The Sonata, Style Composition, Phrase Rhythm, Conducting and Analysis, Figured Bass, Introduction to Jazz Harmony, and Theory through Popular Music. Students with limited experience in the rudiments take Introduction to Theory, a "break-in" course, and then proceed through the two quarters of regular theory. Descriptions of these courses will be available, and the reasons behind this structure will be reviewed.

 

Content

        We take a "models" approach to voice leading and partwriting. Students are required to sing (in all keys) and mentally rehearse eight model progressions. These patterns serve as a starting point for writing and analyzing a variety of voice-leading elaborations. Each new pattern embellishes or expands a pattern learned earlier. Rhythmic concepts, introduced solely through listening at first, use a variation of Lerdahl and Jackendoff's method of illustrating metric structures. Some of the important aspects of rhythm and meter which seem to be neglected in theory training at the college level are incorporated. This discussion will lead naturally to the third part of the presentation.

 

Teaching/Learning Strategies

        We are working with specific teacher and student behaviors arising from the premise that analytical technique, in ways analogous to performance technique, equips the musician with the tools to learn music. It is therefore essential that our students sense that what they are asked to do in the theory classroom will result in their being able to internalize the sound and even the notation of a piece that they may not be able to play or sing. A small number of core works, referred to throughout the course are treated from a variety of tonal and rhythmic perspectives.

        In addition, we have initiated communication with our students' studio teachers, and have asked students to choose a piece they are learning to play/sing for study and analysis in theory. We are trying to establish a sense of community among all faculty and students, and make apparent to students that all their teachers are working to the same end, that of developing their musical imagination and skill to the fullest.

 

 

Presented as part of an "Interactive Pedagogy Session"

 

Most commercially-available aural skills materials intended for use in undergraduate core music curricula focus almost entirely on the study of tonal or twentieth-century techniques and literature. This approach, however, neglects the significant body of Medieval and Renaissance literature that provides the foundation for much of the study of Western music. Students do study this repertoire, of course, but often this exposure is limited to their music history coursework, with perhaps some coverage in their written theory training.?       

Our approach is much different. We believe that students should learn all historical styles of Western music from both a theoretical and an aural perspective, and therefore we incorporate a large number of Medieval and Renaissance ear training exercises into our second-year aural skills curriculum at the same time students are studying this material in both written theory and music history. These exercises include various types of dictation, sight singing, and "play-and-sing" drills, beginning with two parts and progressing to three parts.?       

A chronological approach to the modal repertoire beginning with Gregorian chant allows the instructor to focus on materials in a pedagogically- effective sequence. Chant dictation and singing, for example, focuses on predominantly stepwise motion, with little rhythmic difficulty. With early organum we introduce the concept of harmonic intervals, allowing for the progressive study of consonant and dissonant intervals. Notre Dame organum, with its emphasis on modal rhythm, allows us to incorporate rhythmic patterns in the dictation. Similar pedagogical concepts are introduced in the study of 14th-, 15th-, and 16th-century music, giving students experience in dealing with the modal pitch system and characteristic rhythmic devices from a practical "hands-on" perspective. This session will provide a sampling of techniques and musical examples that can be used by other aural skills instructors. In addition, some of the philosophical and musical issues of incorporating Medieval and Renaissance repertoire into the aural skills curriculum will be addressed.

 

Presented as part of an "Interactive Pedagogy Session"

The task of melodic dictation has long been an established component of the aural skills curriculum, having earned its place as a valuable and multi- faceted learning tool. While developing skill in melodic dictation is certainly valuable, choosing the most appropriate method for evaluating dictation solutions has been somewhat problematic. What factors should be involved in an instructor's diagnosis of error? Should evaluation methodology be affected by the style of melody presented to the student? Should certain types of errors be weighed differently than other types? In this study, these questions, as well as others, are addressed through the results of two surveys which examine scoring methods and preferences among college instructors with interest and experience in aural skills.?       
The surveys featured dictation "test" melodies along with dictation "solutions" that contained a variety of pitch errors. Included in the surveys were diatonic melodies, tonal melodies containing some chromatic pitches, and melodies that had atonal characteristics. Participants were asked to evaluate several different scoring methodologies according to their effectiveness for each melody and dictation solution.?       

This study will examine the implications of the survey results as they may be applied to goals within the aural skills classroom, both in development of student listening skills and in determining the most appropriate methods of evaluation of such skills. Also considered will be the potential benefit these results may have in assessing scoring methodologies currently in use on standardized tests that include melodic dictation tasks, such as the GRE and the Advanced Placement Examination in music theory.

Presented as part of an "Interactive Pedagogy Session"

Music Theory in various guises is a core requirement of nearly all undergraduate music curricula. In addition to addressing basic reading and analysis skills, theory instruction is often expected to develop other skills as well, most usually sight singing and ear training. In an effort to meet these demanding and complex challenges in a rigorous yet manageable way, theory instruction can become myopically focused on product---the correct voice leading, singing the notated pitches and rhythms with accuracy, or compositions that are formally clear and technically accomplished. Theallure of product--and its attractive quantified assessment of student progress- -is almost irresistible, but its seductive power to dominate teachers (and, consequently, students) often results in unmusical presentation and little or no transfer of concepts or skills to music making outside the theory classroom.?     

 In this presentation, I will attempt to analyze a number of traditional activities in the music theory classroom, including dictation, sightsinging, and analysis. I will first focus on the ways in which these activities are typically approached, including presentation and evaluation. I will then explore alternate ways of presentation, variations in student activities, and alternate models of assessment which might promote more student and teacher attention on the processes involved in the activities. I will conclude that emphasis on process might result in greater student engagement, higher levels of student motivation, greater emphasis on musicality, greater transfer and application of theory skills to other music making, and, ultimately, a technically accomplished and artistic product.

 

Presented as part of an "Interactive Pedagogy Session"

        Few pedagogical models have been proposed for the instructor of aural skills interested in engaging atonal or twelve-tone literature. This presentation offers a model for implementing an aural component to atonal and twelve tone theory and analysis, through a series of exercises and assignments based on musical literature from the second Viennese school. The model provides applications to music that build on more abstract exercises as presented by Michael Friedmann and Robert Morris. Schoenberg's Piano Pieces, op. 19, and Webern's Movements for String Quartet, op. 5, among other works, provide material for the introduction of new harmonic resources, compositional procedures, and other audible constructs for the student to perceive.

 

Presented as part of an "Interactive Pedagogy Session"

 

        Music theory is very often taught without including non-Western music. However, Western music relates, especially since the late 1800s, quite often to certain styles and genres of non-Western music. Furthermore, the development of Western popular music--which is dominating today'smusical life--was, and is, strongly influenced by non-Western music. For these reasons, world music should be included in any general music theory class.?       

Especially in Music Fundamentals courses for non-music-majors, popular music is of special interest, since these courses are most often taken by students with an almost pure popular music background. Here, an approach is necessary which includes different popular music styles as well as their music theoretical and aesthetical relations to world music. The presentation will outline a College/University level two-semester Fundamentals course, emphasizing the inclusion of popular as well as world music. Results of empirical surveys will support the world music approach. Generally, such a course rather enables students to get engaged with a whole set of different kinds of music to support learning music fundamentals. Here, world music plays an important role, whereby "classical" music is only being supplemented, not replaced. Goals, structure and contents of this course, in which students are forced into multi-cultural thinking, will be introduced.

 

Presented as part of an "Interactive Pedagogy Session"