Recent scholarship suggests that in the late nineteenth century, the intimacy between bass lines and functional voice-leading sometimes dissolves--bass lines occasionally behave quite independently of the other voices. If that is indeed the case, then we must find a way to extract harmonic function from difficult passages without relying on a partner that may be as fickle as a nineteenth-century bass line. I isolate this problem by examining music whose voice-leading seems logical, perhaps in devotion to the "law of the shortest way," but whose supporting bass line offers little or no help to formulate a clear functional interpretation. Although there is, by definition, a lowest-sounding voice, this is chromatic music that (for the most part) lacks a structural bass line. 

In this paper, I present a theory that questions some traditional assumptions of harmonic function in light of this problematic circumstance. I adapt and extend work by Daniel Harrison (1994) in a way that incorporates well-held tenets of harmonic prolongation and explores a more thorough graphic expression for these ideas. While affirming the hierarchic status of harmonic prolongation, I pursue a study of prolongation as a fluid and dynamic process by paying close attention to the trace elements of harmonic function themselves.  Roman-numeral symbology is abandoned in favor of an analysis that focuses entirely on harmonic function exhibited by scale degree behavior and subtle key affiliation.

Stravinsky's harmonic practice has been a challenge to theoretical notions that propose to integrate chromaticism within a prevalent diatonic-invoking surface. Octatonicism has been posited as the primary cause for such integration, whether acting at the surface or controlling larger-scale formal articulations as a background space. However, such ambitious explanations attributed to octatonicism have recently been questioned, opening up the possibility for other pitch relationships to emerge, especially in neo-classical pieces, like the Serenade en La, in which superimposed and juxtaposed diatonic segments equally resist octatonicism and tonal interpretations.

This paper proposes a pitch-class framework capable of modeling the superimposition and juxtaposition of scalar segments as well as accounting for their syntactical progression. The paper advances the notion that scalar segments can be thought of as specifying locations within a framework which integrates all diatonic phenomena. This framework, which I label Guidonean space reflecting its conjunct hexachords, is specially suited to model various types of pitch relationships which are prevalent in the "Hymne" from the Serenade en La.

The paper explains the theoretical model underpinning the Guidonean space, addressing its intervallic structure and measuring the movement between its pitches (through an operation I call ). It also contextualizes this space within a larger family of hybrid spaces. The paper then provides an analysis of the whole "Hymne," as well as some passages of the last movement, the "Cadenza Finala."

This paper examines aspects of harmonic structure that arise in the slow movements of Ligeti's late music by investigating pieces whose pitch organization alludes to relatively conventional concepts of harmonic syntax. My point of departure derives from the composer's description of pieces such as his Piano Etude No. 15 (1995) as "diatonic, yet not tonal," and his Hamburg Concerto (1998-99) for solo horn as embodying "harmonies, which have never been used before [that] sound 'weird' in relation to harmonic spectra." Despite the composer's vague remarks concerning his "new" approach to harmony, a discernible harmonic association between his middle period microcanonic works and his more recent pieces is evident. However, the compositional design of the late period works is based on new organizational procedures that conceal a structural simplicity beneath the surface complexity.

I demonstrate that Ligeti's 'weird' harmonic structures stem from a procedure that utilizes transpositional combination in a pitch-space environment beyond the usual mod-12 universe. With transformational operators derived from specific musical contexts, I show how Ligeti organizes his apparently disparate and idiosyncratic harmonic successions in accordance with concepts of consonance and dissonance. Additionally, it appears that many of the quasi-stable harmonic regions in his late music stem from the same harmonic device, identified as the "Ligeti signal" (i.e. Tn set class (035)), that the composer began exploring in the 1960s. Moreover, a unifying set class that links many of the analyzed excerpts is the generic tonal triad, 3-11 (037), which appears as an embedded structure within more complex or concealed structures that arise through transpositional combination of (035). The analytic readings support the composer's claim that his recent music is relatively diatonic in contrast with his earlier works, yet not tonal in any traditional sense.

Nearly forty years ago, Edward T. Cone proposed the idea of the sonata principle: "important statements made in a key other than the tonic must either be re-stated in the tonic, or brought into a closer relation with the tonic, before the movement ends." Although the concept of the sonata principle has been recently questioned, I contend that it still remains a useful analytical tool. In this presentation, I will demonstrate how Cone's sonata principle can be used to craft an elegant analytical approach to predicting and understanding the behavior of principal themes built over auxiliary cadences in recapitulations and codas of sonata movements.

A principal theme constructed over an auxiliary cadence is gradually destabilized as it is pushed away from tonic, even though it may never have been transposed. This kind of principal theme reaches its most distant relationship with tonic precisely at the beginning of the recapitulation. Thus it must be recontextualized within tonic--not simply by being restated in tonic but exchanging its auxiliary-cadence underpinnings for a complete tonic progression.

In this presentation I will consider in detail two sonata-form movements by Beethoven: the first movement of the Piano Sonata in Eb Major, Op. 31, No. 1, and the String Quartet in Eb major, Op. 127. I will show how their principal themes are destabilized in the exposition and development, left unresolved in the recapitulation, and, in the spirit of the sonata principle, "brought into a closer relation with the tonic" only in the coda.

The musical collage, as represented in works written in the late 1960s by composers as diverse as Berio, Zimmerman, and Rochberg, presents a special challenge for the analyst. Concentrating on the technical implications of the process of quotation, theorists have described various associative formal, motivic, transformational, and structural relationships between disparate elements in a musical collage. These have yielded insight into many of the essential components of this musical style, including possible models for voice-leading, harmonic structure, form, and large-scale coherence.

This paper addresses how the transition between disparate elements is achieved. In other words, it seeks to describe the process of modulation in a musical collage. Although the juxtaposition of disparate quotations often results in formal as well as perceptual discontinuity, there are also many ways in which disparate quotations are linked to create larger spans. Examples from three contrasting but representative pieces in this style: Zimmerman's Musique pour les Soupers du Roi Ubu (1966), the first movement of Rochberg's Music for the Magic Theater (1967), and the third movement of Berio's Sinfonia (1968), reveal surprising correspondences in the way that modulation between highly contrasting sound worlds is achieved. Three different techniques for linking disparate quotations emerge: overlap, chromatic insertion, and rhythmic plasticity. These techniques interact to traverse the space between disparate quotations, creating relationships that are akin to the sophisticated types of modulatory techniques that operate in tonal music on both a local and large-scale level.

 Takemitsu (1930-1966) considered himself a composer in the Western musical tradition, profoundly influenced by composers such as Debussy and Messiaen. However, Takemitsu argues that artists cannot escape the cultural heritage into which they are born and raised. While the compositional materials in Takemitsu's music are sometimes comparable to those used by Western composers, many listeners nonetheless identify a Japanese quality, even in pieces that do not use traditional Japanese instruments. I argue that the primary quality that marks Takemitsu's music as Japanese is its form: whereas the temporal mode of Takemitsu's music is primarily Western, in the sense that his music is linear, has a definite beginning, and has continuous relationships between musical events, its form is not hierarchical, reflecting the influence of Japanese aesthetics.

 Piano Distance lacks form-defining features such as melody, harmony, counterpoint, thematic or motivic statements, or cadential gestures, as well as metrical or rhythmic units, time signatures, notated durational values, or any periodicity generated by a recurring pulse. I perceive this music in linear time--a linearity determined by the implications that arise from earlier events in the piece.

 The form-building process of Piano Distance reflects the Japanese mode of consciousness, as examined in Maruyama's article "'Ancient stratum' of Historical Consciousness." Three basic concepts, "naru (become)," "tsugitsugi (in succession)," and "ikioi (force)," combine as "force that becomes one after another" to describe the principle governing the continuity of Piano Distance. The metaphor of musical structure becomes fluid rather than solid; with the elimination of metaphors such as background foundation, structural pillars, and surface features, the musical structure is no longer hierarchical.

Claudia Gorbman's book, Unheard Melodies (1987), laid the groundwork for the serious, theoretical study of music in film.  In recent years, however, her theory that film music is largely "unheard," lowering the audience's threshold of belief and easing it into the world of the film, has come under scrutiny by many scholars.  Even these scholars, though, still tend to regard the music as subservient to the events onscreen, no matter how much it is heard.  What has not been discussed is how music in film sometimes goes even further, so that it does not merely comment on the narrative but punctures it, overtakes it, and disrupts the cinematic illusion.  This paper looks at several examples of what I call "super-heard melodies" in a variety of films including Stanley Kubrick's Paths of Glory, David Lynch's Mulholland Drive, and Lars Von Trier's Dancer in the Dark.  In these examples, characters sing songs that command so much attention as to overwhelm other elements of the film.  Borrowing from Carolyn Abbate's work on opera's "voices" and from recent work in trauma theory, I show how the films' narratives are ruptured by these melodies just as their characters' worlds are ruptured by traumatic experiences.  I hope to suggest a new way of hearing these breakthrough moments, and more generally to demonstrate what insights can be gained by bringing the fields of film theory, trauma theory, and music theory together.  

In 1957, Orson Welles completed production on Touch of Evil. Welles had just finished the first cut of the film when Universal Studios took it out of Welles's hands, adding and re-shooting a few scenes. Unhappy with Universal's product, Welles wrote an impassioned memo detailing necessary changes, which Universal declined to make. However, in 1998 Universal consented to a re-cut and re-mix of the film using the memo as a guide. Today, there are two distinct versions of the film, the original 1958 release and the 1998 restoration. 

When music underscores any film, musical structures such as phrases, periods, themes, and key areas align with dialogue and visual cues (e.g., changes of camera angle and character movements). These alignments create segments that help lead the viewer through the scene, giving emphasis to salient points. I will demonstrate the important part that segmentation plays in scene interpretation by analyzing the same scene from both versions of Touch of Evil, the scene that introduces Tania. In this scene the music (and segmentation pattern) has been significantly altered from the 1958 release. Originally, a player piano sounded throughout the scene, alternating between two main sections of music, creating an ABAB-tag structure. In the restored version, the latter half of the scene is silent and a portion of the remaining music is truncated, producing a segmentation pattern that completely alters the dynamics of the original scene. Initially, the reprise of A occurred on the corrupt cop Quinlan's first comments to Tania, but now it begins just after Tania speaks. Thus, whereas the music originally granted Quinlan dominance, by placing his lines at an important structural music event, the restored version gives this to Tania.

Discussions of electroacoustic music often deal more with the means of producing sounds than the theoretical or analytical aspects of the music. This paper will propose some possible avenues of inquiry into theories of electroacoustic styles.

The term "electroacoustic" refers to music that is performed through loudspeakers. Unlike acoustic music, electroacoustic music lacks a set of expected or readily identifiable parameters. An even more difficult problem for the theorist who wishes to study this music is the fact that this music exists almost completely without reference to a printed score.

Graphic scores, such as that created by Xenakis for Mycenae Alpha, while imparting some information about volume and texture, are of limited utility. The study of oral traditions of transmission can be much more fruitful for the theorist wishing to study electroacoustic music. This paper will seek to propose some categorizations of stylistic features that can foster a discussion of electroacoustic styles as "music," and not merely as synthesis, frequencies, programming languages, and gadgetry.

Paradigms associated with traditional analysis must be rethought. For example, instead of harmony, it is more appropriate to discuss the presence of single or multiple frequencies, and the relative magnitude of the textures created through layering frequencies. Instead of melody, it is more cogent to discuss sounds and sound sources. Sounds can be categorized as referential or non-referential, depending upon whether they are heard as a sound that comes from everyday life. A partial list of types of identifiable sounds will be proposed.

This paper presents a measure of textural intricacy, inspired by Albert Bregman's Auditory Scene Analysis, and applies it to several important sound-color compositions from the 1960s by Penderecki, Ligeti, and Lutoslawski. Taking its impetus from music perception research, the proposed method aims to yield a measure of intricacy that is relevant to the ear while it provides a new perspective for analysis. From this new perspective, we can chart the rise and fall of textural intricacy over the course of a composition and begin to document exactly how different sound-color compositions use the musical domain of textural intricacy as a means of expression.

Measuring textural intricacy can provide different kinds of insight into the different pieces we investigate in this paper. In a piece such as Penderecki's Threnody, which is a three-part form with a clear sense of beginning, climax, and ending, the proposed technique allows us to examine how patterns in texture combine with other musical domains to create beginnings, climaxes, and endings in this music. Ligeti's Atmospheres uses an arch form, with similar patterns in melodic and orchestral color disposed symmetrically about the center of the piece, but the levels of intricacy do not follow this same symmetry. I explore this interesting incongruity and suggest possible reasons why Ligeti would return to the same orchestral color and melodic motives and yet change the texture (what Bregman would call the "granularity") of the music. Finally, the paper discusses

Lutoslawski's Jeux vénitiens, revealing how sectional durations and textural contrasts work together to produce momentum as the first movement builds to a climax and then draws to a close.

While much attention has been given in recent years to the question of how musical contours contribute to musical meaning in common practice period music (e.g., in the writings of Kivy, Ridley, Cook and others), less attention has been given to the role played by musical sonority, including simultaneities and individual timbres.  This paper investigates the roles given to the vertical musical dimension in several twentieth century theories of musical meaning (e.g., Pratt, Zuckerkandl, Langer, Kivy, Budd, Addis) and argues that, contra Kivy and Scruton, musical sonority is best understood as related to inner feeling or experience, including somatic sensations and what Budd calls "felt evaluative attitudes."  By drawing on recent work in neuroscience and the psychology of emotion which gives a prominent role to notions of felt experience in the makeup of human consciousness (e.g., Antonio Damasio and Paul Griffiths) as well as on the implications of individual musical passages, this paper argues that musical expressiveness results from resemblances between music and both inner and outer components of human experience.  Furthermore, by placing a given melody in different harmonic contexts, I argue that musical expressiveness derives not so much from the contour of the melodic line itself as from the interaction of the melodic line with its harmonic context.  In this way, the harmonic dimension provides a context of feeling which enables the listener to decode properly any melodic contours present.

Artists are adept at embodying human gestures in their works. Poets capture physical movements with a variety of linguistic, sonic, and orthographic codes that enrich signified meanings. Composers, too, evoke gestural images in music through manipulations of elements such as pitch, texture, and rhythm. When a poem is set to music, though, a tension can arise between musical and poetic gestures. Since a musical setting tends to change the sonic codes of a poem, it is difficult to address what happens to the poetic gestures once that poem is set to music.

My paper considers this tension using the example of William Blake's "Ah! Sun-flower" (1794). The first word of the poem--"ah"--adds a rich sonic dimension to the poem by simulating an exhalation. The addition of audible materiality and physical gesture to the poetic reference thus "breathes" life into the image of the poem. The first syllables of the words "arise" and "aspire," which appear in the penultimate line, recall this physically grounded sound. 

I compare two settings of the poem: one by Britten from his Songs and Proverbs of William Blake (1965), and another by Vaughan Williams from his Ten Blake Songs (1958). The analysis examines how the music of each song enhances and constrains notions of human breath encoded in the sonic gestures of the poem.

Literary critic Linda Hutcheon describes parody in twentieth-century art forms as characterized by "complex forms of transcontextualization and inversion." Hutcheon distinguishes parody from satire on the basis of its underlying ethos or intent: satire is scornful or ridiculing, while parody is neutral, deferential, or contesting. Irony is a trope used by both genres, a rhetorical strategy used to signify the opposite of what it was intended. I attempt to formalize the contexts by which parody assumes an ironic inflection in music by drawing on concepts introduced by Robert Hatten, D. C, Muecke, and Esti Sheinberg.

Hatten explains irony as a trope that emerges from a juxtaposition of contradictory or incongruous types of musical expression. In simple terms, it serves as a negation of a metaphor. A more complex model of irony emerges through the progressive decontextualization of a parodied element through distortion or incongruous juxtaposition with other elements. The two procedures are often combined in dramatic contexts in order to sustain the effects of irony at multiple levels of structure.  To illustrate, I refer to Maxwell Davies's Eight Songs for a Mad King (1969) and Louis Andriessen's Writing to Vermeer (1999).  Irony in the former arises through the incongruous juxtaposition of styles: the tonal stability of stylized quotations is inversely correlated with King's madness while seemingly unstable atonal passages are correlated with moments of lucidity. Irony in the latter arises through the progressive distortion of the leitmotifs based on the quotation of Sweelinck's tunes. The tonal themes and dissonant harmonization result in a kind of musical chiaroscuro without tending toward reconciliation. In concluding, I explore the semantic implications of parody with ironic inflection as a specific type of intertextual discourse.

The tonal design of Copland's music presents clear challenges to the analyst. Many passages exhibit clear tonal centers, though those centers are usually posited through means other than those of conventional functional progressions. By examining the tonal centers explored in a particular work and the processes used to move between those centers we find criteria that illuminate interesting and telling tonal structures.

Inspired in part by analytic techniques suggested by Arthur Berger, Joseph Straus, and Edward T. Cone, I will explore the presentation and organization of pitch centers in the last movement of Copland's Third Symphony. The movement starts with a near-complete paraphrase of the composer's Fanfare for the Common Man, though this paraphrase introduces several changes in centricity not present in the original fanfare. These striking tonal shifts suggest a method for cataloging possible movements from one diatonic collection (and its associated pitch center) to another, a classification that depends upon the relative preservation of key common tones from the "old" diatonic collection and the prediction of those common tones as they emerge in the "new" collection. This classification of tonal shifts has direct bearing on the movement's tonal organization when considered in combination with the music's formal design. Specific types of tonal shifts are linked with specific themes, and tracing the paths outlined by these shifts/themes illuminates a deeper-level structure that parallels a motive from the fanfare.

Like many minimalist compositions from the 1960s and '70s, China Gates (1977) begins by unleashing germinal material that, through a series of pitch and rhythmic transformations, generates the future of the piece. Indeed, one can imagine the initial right and left-hand cells in m. 1 traveling through a machine with the sleek contours of a hyperboloid. As these cells glide through Adams's machine, they mutate through a series of transformations. Yet, while these and other transformations lend the music a forehearable future--they allow listeners to predict precisely where the music will next move--the music does not come without surprises. In certain sections, pitch, rhythm, and modal changes oscillate with nervous erraticism, producing no clear patterns--those marked for immediate aural notice--like those during other moments in the piece. Predictable musical transformations grind to a halt, Adams's machine breaks down, and to-and-fro shifts between anticipated and unanticipated musics supplant the mode of listening China Gates initially projects: the solace of being able to anticipate, then experience, particular predetermined musical futures.

In this paper, I (1) lay out the precompositional plans for China Gates (its transformations and proportioned modal regions) in terms of schematics for a perpetual motion machine, and (2) explore various phenomenal repercussions of these blueprints. In so doing, I extend Ernst Kurthian metaphors of music as energy to China Gates by hearing the piece in terms of centrifugal and centripetal forces, potential and kinetic energies, motility and mobility of musical lines, etc. These metaphors, I argue, clarify the ways in which listeners interact with the music, most decisively in terms of how we experience its time.

In this paper I analyze the formation process of works' gestural interpretation by performers. The research material includes video recordings of the rehearsal processes of the Finnish composer Einojuhani Rautavaara's three piano concerti. The foundation of the paper lies in the observation that some gestures drop out or recede during the process and do not find their way to the performance. I explain the functions of these gestures and the reasons for their disappearance before the performance.

Rehearsal gestures are important tools for the performers as they construct performance gestures. Some rehearsal gestures will not, however, integrate with the work's interpretation in performance and are thus discarded; accordingly, I call these gestures scaffolding gestures. I divide scaffolding gestures into two main categories. Didactic gestures act as a performer's didactic effort to "teach" his or her interpretation to other performers. The aim of negotiating gestures is to negotiate about interpretation as performers defend their own views or compromise in collaborative interpretations. The effects of these gestural categories are achieved with help of other gestures supporting the didactic and negotiative goals. The didactic aim, for instance, can be obtained by gestural exaggeration, on the part of the conductor or the soloist. Didactic gestures with this sort of exaggeration recede during the work's repetition in the rehearsal process and become part of the work's scaffolding. In other words, they are part of the rehearsal's gestural language through which the performers discuss gestures and create the (more elegant) gestural language of performance.

The attention paid by the music-theoretic community to Milton Babbitt's oeuvre has focused largely on structural attributes, and to a lesser degree on listening experience and critical reaction, neglecting in large part performing experience. Our paper examines Babbitt's None but the Lonely Flute (1991) from the points of view of flutist and theorist. We focus on the virtuosity--compositional and performative, apparent and hidden--that permeates the work.

The performer of Lonely Flute faces virtuosic demands in many arenas. Difficult couplings and rapid changes of register and dynamic, complex rhythms, few rests--these demand precise control and flexibility of embouchure, air stream, and mental focus. Furthermore, the work's rich musical cross-references challenge the performer to project both registral/dynamic counterpoint and long surface line, to communicate the "swing" of the rhythms, and to shape the trajectory of details and whole.

 Compositional virtuosity lies in the work's abstract pre-compositional structure, in its realization, and in the play of its structure, surface, and external associations. The elegance of Babbitt's arrays is well known, as is his virtuosic treatment of the composing out of his arrays, although his virtuosity in the use of tp arrays is less universally acknowledged. Babbitt's control of detail of pitch and rhythm contrasts with sparse indications of articulation and timbre; the performer must determine inflection and emphasis. Thus, the performer's virtuosity lies in realizing the overabundance of notated details, and in interpreting the hidden elements of the music.

 Our paper demonstrates specific examples of compositional and performance virtuosity, explores how it is concealed or displayed, and traces its role in defining the narrative of Lonely Flute.

This paper examines the function of metric dissonance in the second movement of the Jupiter Symphony with respect to the rich tapestry of stylistic references at play, including the relationship between topoi, gesture, and rhetoric suggested by the musical discourse. My discussion begins with meter's function in the opening bars (1-6) and probes the issue of metric ambiguity by revisiting the divergent interpretations of Cooper and Meyer, and Wallace Berry. My analysis treats the phenomenal accentuation that suggests metric conflict between the perceived duple and triple pulses as a grouping dissonance.

The expressive consequences of this opening are then explored in the reprise (bars 11-18), where a thematic juxtaposition between the sarabande figure and lyrical figuration yields a disruption in topical content that is also underpinned by metric displacement. Next, I examine the relationship between metric dissonance and the ombra topic in the bridge section (bars 19-22, and 23-27). Over the course of its two passages, subtle and more overt pulse conflicts expand the range of grouping dissonance to three levels of the metric hierarchy. I then demonstrate how these transformations in pulse layer relate to the status of meter in the second key and development sections in terms of strategic process. 

In this movement the appropriation of certain topics becomes associated with uncharacteristic metric effects, suggesting the degree to which our conventional notions of stylistic categories may be constrained. The study of metric dissonance in Classic music may provide a renewed perspective on eighteenth-century syntax, while also probing some assumptions regarding topoi in particular.

In a 1981 article analyzing Brahms's op. 76 no. 8, David Lewin proposes that the 3:2 ratio between a 3/2 meter's triple division of a dotted-whole-note duration and a 6/4 meter's duple division of the same time span is comparable to the 3:2 ratio of a perfect fifth. The same comparison to pitch can be made for the 3:2 ratio between a 6/4 meter's triple division of a dotted-half-note duration and a 12/8 meter's duple division of the same time span. Therefore, Lewin concludes that 6/4 can be understood as analogous to tonic, in that both are flanked by 3:2 ratios: 3/2 as dominant, and 12/8 as subdominant. In the "Rondo alla Zingarese" that concludes Brahms's Piano Quartet in G Minor op. 25, the rondo theme and two subordinate themes that span the same duration occur in three different hypermeters and three different keys and/or modes. According to Lewin's theory, the subordinate G-major theme, instead of the rondo theme, would be in the tonic hypermeter given the metric context of the other two themes.

 Fourteen measures before the end of the movement, Brahms introduces a striking gesture: all four instruments, playing the longest unison passage of the movement, iterate an inverted fragment of the rondo theme. This fragment is three eighth notes long, creating the movement's most pronounced metric grouping structure that is dissonant with the barline. This unison gesture affords an expansion of Lewin's theory by recontextualizing the three hypermeters of the rondo theme and two subordinate themes such that the rondo theme's 12/8 becomes tonic.

 This reorientation reflects analogous harmonic practice. On the phrase level, equal presentations of subdominant and dominant often situate tonic. On the movement level, however, the role of subdominant as tonal counterbalance is often relegated to a relatively brief nod in the coda. The unison gesture mentioned above can be understood as a similar metric "nod." The rondo theme's 12/8 hypermeter, although not the logical Lewinian tonic, is convincing as a metric tonic through its consistent association with the rondo theme. The coda's unison gesture confirms on a logical level what has already been established on a rhetorical level.

Given the profusion of work that has occurred in response to Lewin's Generalized Musical Intervals and Transformations, studies done outside the realm of pitch are surprisingly scarce.  Rhythm is emerging as an area for extending models of musical transformation, but the beat-class universe has yet to be explored as exhaustively as that of pitch. Other domains which could broadly be considered "musical" have received even less attention. The present study applies some of the ideas of transformational theory to these less-explored areas, specifically by modeling and analyzing the music of banjoists Earl Scruggs and Bela Fleck.

This paper models banjo music in two ways: 1) as permutations of the set of fingers picking the strings; and 2) as relations and transformations among the beat-class sets resulting from these permutations. From a beat-class perspective, the pick permutations contribute to sets modulo 8 which can be generated from the integers 2 and 3, depending on which permutation is at work. The beginning of a cycle does not always represent the beat class of greater structural importance, though, so the permutations compete with a host of other factors in determining which bcsets come into relief from a generally steady stream of sixteenth notes. The other factors include register, dynamics, ornamentation, timbre, and the fret and string played.   

 This study  concludes by examining the transformational properties among beat-class sets and their interaction with metric hierarchies typical of bluegrass music. Ultimately, this interaction contributes to the idea of "drive" discussed by bluegrass performers and listeners alike.

Much has been made about possible extra-musical grounds for Debussy's turn to the sonata as a genre in what was to become the final stage of his career. My project takes as a given that both musical composition and analysis are contextually positioned. I offer an inter-reading of the three late Debussy sonatas wherein I present a series of post-modernist inspired vignettes centered about the following concern: how, in these three specific works, is "musical meaning" instilled via the interpretive act?

 The central character is the mythical Achilles, whose encounters with the sonatas reflect various entrenched and at times mutually exclusive viewpoints.  In one scene, the concept of an overarching shape governing the whole of each work is challenged, even in the light of evidence to the contrary.  Here Achilles is a mask for the mélange of Dahlhaus (1975) and Street (1989); he trumpets their calls to resist the time-honored conceit that "musical unity" is either a given or even a necessary condition in any composition. He must contend with two issues: that material from the first movement of the Trio and the first movement of the Violin Sonata reappears (albeit altered) in the Finales of the respective pieces; and, furthermore, that the attacca between the middle-movement "Serenade" and the Finale of the Cello Sonata belies the concept of fragmentation that lies at the heart of the Dahlhaus and the Street articles. In another vignette, Achilles appears before us as Proust and Bergson, who, as contemporaries of Debussy, advance multiple temporal readings in the concluding movement of each of the three Sonatas.  What constitutes "before" and "after" in these movements, and what is "causal," is variously interrogated in each movement.

One of Schenker's greatest contributions to Bach scholarship is his description of Bach's genius in structuring large forms through ornamental detail. The Adagio from the Sonata in B Minor for Violin and Cembalo, B.W.V. 1014 exemplifies Schenker's notion of the organic as the violin and cembalo develop musical motives through a growing symbiotic relationship. More recently, Susan McClary identifies the nature of the trio sonata texture to capture our attention through erotic tensions and delayed resolutions.  A musical analysis of the Adagio coupled with a closer look at historical documents on intimacy reveals a new historically gendered approach to hearing the connections between ornamental detail and form. 

The cembalo begins the Adagio with an integration of ornamental detail within its expression of the melodic goals, progressing toward a completion of the Urlinie. The violin enters with seemingly sporadic and ornate material, but soon we hear the cembalo leading the violin to regulate her melodic material, becoming a more active participant in the expression of the Urlinie. The two voices become intertwined, exchanging rhythmic figures and motives that the cembalo presented in the beginning.  Our musical intuition tells us that what began as the cembalo leading the violin, becomes a partnership, one that intimately shares musical details.  

 An exploration of contemporaneous medical and cultural documents concerning intimacy and eroticism sheds light on relevant social attitudes about gender, while raising the notion of mutual and simultaneous pleasure as a relevant aspect of intimacy. Our musical intuitions as performers and listeners resonate with the mutuality and sensuousness uncovered in documents on intimacy, and in this light Schenker's metalanguage invites us to hear the synthesis of ornamental detail more sensitively.

Much has been made about possible extra-musical grounds for Debussy's turn to the sonata as a genre in what was to become the final stage of his career. My project takes as a given that both musical composition and analysis are contextually positioned. I offer an inter-reading of the three late Debussy sonatas wherein I present a series of post-modernist inspired vignettes centered about the following concern: how, in these three specific works, is "musical meaning" instilled via the interpretive act?

 The central character is the mythical Achilles, whose encounters with the sonatas reflect various entrenched and at times mutually exclusive viewpoints.  In one scene, the concept of an overarching shape governing the whole of each work is challenged, even in the light of evidence to the contrary.  Here Achilles is a mask for the mélange of Dahlhaus (1975) and Street (1989); he trumpets their calls to resist the time-honored conceit that "musical unity" is either a given or even a necessary condition in any composition. He must contend with two issues: that material from the first movement of the Trio and the first movement of the Violin Sonata reappears (albeit altered) in the Finales of the respective pieces; and, furthermore, that the attacca between the middle-movement "Serenade" and the Finale of the Cello Sonata belies the concept of fragmentation that lies at the heart of the Dahlhaus and the Street articles. In another vignette, Achilles appears before us as Proust and Bergson, who, as contemporaries of Debussy, advance multiple temporal readings in the concluding movement of each of the three Sonatas.  What constitutes "before" and "after" in these movements, and what is "causal," is variously interrogated in each movement.

Teaching the analysis of twentieth-century concert music to undergraduates presents the instructor with several challenges. The students are generally unfamiliar with the repertoire and the composers; thus we must teach the history of this century's music in addition to its theory. Given the diversity of this music, even a relatively unambitious and limited course must cover a bewildering array of analytical systems and terminology. Establishing meaningful threads of continuity throughout the course can be a daunting task.

At the pseudonymous Midwest University, the fourth semester of the required undergraduate theory sequence for music majors essays an outline of the theory and analysis of twentieth-century music. Throughout much of the semester, we concentrate on music from the first half of the century, which we organize into units: impressionism, atonality and serialism, neoclassicism. This paper discusses three more recent works that we cover at the end of the course: John Adams's Shaker Loops, Arvo Pärt's Cantus in Memory of Benjamin Britten, and "Automne à Varsovie" from György Ligeti's first book of Etudes. These three pieces serve as a capstone for the course: their analysis rests on concepts developed throughout the semester, and they top off and complete theoretical structures built up in previous weeks.

These three pieces resonate in multiple ways with compositions and ideas from earlier in the course. Brief analytical comments about each piece offer suggestions about how an instructor may convey its pitch, rhythmic, and textural organization to students. The conclusion suggests some factors that instructors should consider when selecting repertoire for broadly focused twentieth-century analysis courses.

Although dictation exercises can be constructive, they can have damaging costs as well. Dictation exercises can paralyze rather than develop students' ears--a syndrome we refer to as aural anxiety. Furthermore, if the classroom contains a mix of students with and without perfect pitch, dictation can polarize the class. 

We propose game playing as an effective antidote that promotes aural skills more efficiently. Game playing is designed to challenge and stimulate students, without discouraging or undermining their confidence. Four games that we have found successful in a conservatory setting are: Growing Melody--encourages memory, concentration, and melodic conceptualization; One-Note Wonder--develops relative pitch and sensitivity to scale-degree function; Rhythm Boggle--helps to conceptualize rhythms in terms of beat patterns; and Imitation-Canon--promotes multi-tasking abilities essential for ensemble playing.

For Growing Melody, the teacher provides a map of scale degrees, establishes tonic, and provides an opening melodic incipit, which all students sing back on scale degrees. Each student then gets a turn to sing the previous melodic incipit on a neutral syllable and add one last pitch. After each student has had a turn, the class sings the resultant melody together on scale degrees and/or writes it down. The game builds memory skills, particularly the transfer of pitches from short-term to long-term memory, and encourages students to remember pitch as scale-degree functions. Eventually, students learn to improvise compelling melodies while experimenting with motives, harmonic structure, and balance. This helps them develop an ability to recognize melodies not as a string of individual pitches, but rather as building blocks of melodic figures. We illustrate this and the other games with video performances from first- and second-year conservatory aural skills classrooms.