The application of organicist metaphors to discussions of rhythm is difficult because rhythmic motives are not typically accorded the same degree of transformative plasticity as are pitch-based ones. Analyses centered on rhythm and meter have also focused on networks of metric states instead of transformations between them. This paper explores a process-based approach as a complement to such analyses that allows the discussion of motivic progression of rhythm in a musical passage. Rhythmic functions are used to model the being and becoming of musical moments in Brahms’ Alto Rhapsody, a piece often described as being organically unified in analyses. Using three classes of actions—repetition, proportional change in duration, and addition of material—this method shows how small motives can be propagated to create longer spans, and how complex passages may be interpreted as resulting from the interaction of different functional series. More generally, the method also demonstrates how rhythm can be dynamically transformed into form. By acting as enabling connectives between the musical before and after, rhythmic functions engender a conception of rhythm and meter that allows it to become more compatible with discussions of pitch-based motivic development in repertoire that invites the use of organicist metaphors.

That unity in a work can be achieved through the repetition of a single motive on the surface of a work and at deeper structural levels is one of Schenker’s most profound insights into our understanding of tonal music. By addressing the interaction of these “motivic parallelisms” with the various metric processes prevalent in Tchaikovsky’s Valse,from his Symphony No. 5 in E Minor, the present study introduces the concept of “first-order metric parallelisms.” Using Allen Cadwallader’s definition of a first-order motive as a point of departure, I first establish the neighbor-note configuration as the essential unifying motivic force within this work. Then, inspired by Harald Krebs’s terminology regarding metrical consonance and dissonance, I demonstrate that an analogue to “neighboring” motion also motivates the metric domain of the work. I argue this phenomenon to be a “first-order metric parallelism.” The concept has analytical relevance in that I am able to demonstrate that the metric and the motivic domains of the Valse are each governed by analogous processes. In sum, the introduction of first-order metric parallelisms permits a deeper understanding of the relationships that can be intuited between meter and voice-leading processes, while contributing to the recent research on Schenkerian approaches to rhythm and meter.

In the literature on rhythm and meter, a particularly interesting avenue of study has been devoted to the phenomena of “rhythmic dissonance,” first defined in Maury Yeston’s book The Stratification of Music Rhythm (1976) and later refined (and renamed “metric” dissonance) by Harald Krebs. In the work of both Yeston and Krebs, dissonance is conceived as a result of discrepancies between various layers of motion in the music. It is a little known fact that the term “rhythmic dissonance” was also in the lexicon of the American composer Frank Zappa. Zappa’s conception of rhythmic dissonance, like Yeston’s, is based on arithmetic relationships between the integers that represent the different active layers of motion in the music. Due to Zappa’s strict separation between rhythm and meter, I will follow Yeston, and also Zappa, in considering the dissonance “rhythmic” as opposed to “metric.” Nevertheless, many of Krebs’s more extensive theories prove elucidative for Zappa’s rhythmically dissonance music, particularly his concept of “indirect” dissonance.

In this study, I examine a number of instances of rhythmic dissonance in Zappa’s music, in works that span over ten years of his career. The pieces to be discussed employ rhythmic dissonance to the extent that it becomes the “premise” for the music; movements into and out of rhythmic dissonance define the experience of the music. Besides explaining how local instances of rhythmic dissonance conform to Zappa’s comments on the subject, I also demonstrate how rhythmic dissonance may interact with a more fundamental “metric” dissonance.

In the late nineteenth century, the near universality of the tonal system was beginning to erode. Within this new context of tonal ambiguity, formal elusiveness, and increased dissonance, the tonic triad remained the only true harmonic consonance. While it was regularly evaded in compositional designs, the expectation of consonance to achieve tonal closure persevered, especially in Germanic works by Wagner, Mahler, and their contemporaries. In fin-de-siècle France, however, the sanctity of triadic consonance began to be challenged as new compositional strategies now featured cadences to chords greater than triads in closing rhetoric. Composers—including Debussy and Ravel—seem to have “relativized” consonance such that increased levels of dissonance in non-tonics are balanced to roughly the same degree with new chordal possibilities in tonic resolutions.

Building upon the work of Jacques Chailley, Daniel Harrison, and others, this paper analyses cadential moments in a number of French musical pieces composed around 1900, and proposes a limited collection of possible “dissonant” tonics. These harmonies are dissonant in only a strict sense—the added tones are not dissonant in that they require resolution, but rather they “color” the chord with sonorous extensions. The presentation illustrates how these harmonic variants both fulfill Tonic function, especially in major keys, and provide a moment of consonance. The paper concludes by suggesting how this innovative use of “dissonant” or “extended” tonics participated in a tonal evolution in twentieth-century art music and jazz.

Augmented-sixth chords and tritone substitutes have long been recognized as enharmonically equivalent by musicians conversant with both classical and jazz idioms, yet no commentary of any depth exists in the scholarly literature. The relationship of these two chord classes is generally described as two different perspectives on the same syntactic structure: in classical terminology, an augmented-sixth chord; in jazz, a tritone substitute. Indeed, an obvious distinction in their typical contexts is that augmented sixths are most typically found in art music of the eighteenth and nineteenth centuries, while tritone substitutes have been commonly applied in improvised jazz performances since the bebop era or slightly earlier. For purposes of comparison to augmented-sixth chords, I have selected examples of “composed” tritone substitutes from published arrangements of jazz standards.

Several structural features are shared by augmented-sixth chords and tritone substitutes, including pitch-class content, nonessential fifths, underdetermined roots, structural positioning, and two possible harmonic functions (pre-dominant or dominant). However, a significant distinction can be made between these two chord classes on the basis of their behaviors: they differ in their voice-leading conventions of contrary vs. parallel, normative harmonic function as dominant preparation vs. dominant substitute, and enharmonic reinterpretation as modulatory pivot vs. dual-root dominant approaching a single resolution.

 None of Frédéric Chopin’s Nocturnes ends as aberrantly as the Nocturne in B Major, Op. 32/1. Although most of the piece is in a placid mood, its final bars are ineluctably tragic, ending in the parallel minor key. Recitative figures in this tragic context suggest the voice of a musical agent, somehow dissociated from the prevailing musical discourse.

But more subtly, agency is also developed through musical gestures. The Nocturne fashions a portrait of an agent in which a single gesture—a musical representation of a “lifting” sensation—is emblematic of his or her expressive state. In the most untroubled major-key contexts, that gesture is light and buoyant, but it sounds heavier as the agent becomes briefly waylaid by tragic undercurrents and endeavors to restore composure. Throughout the Nocturne, the metaphor of gravity underscores interpretation of the gesture, as an indicator of the agent’s response to tragedy. As tragic incursions become more severe, the figurative effect of gravity upon the gestures becomes more pronounced, and the music consequently conveys a greater sense of effort. Only after the music shifts irreversibly to B minor do the exertions lose their effect, and the agent weakly acquiesces to the heretofore restrained tragedy.

The Nocturne’s popular reception often fancifully infers the voice of Chopin at the Nocturne’s conclusion. Regardless of the identity the music’s agent assumes in interpretations, that agent must not stand detached from the preceding music, but rather as the same subjectivity who enacted the music’s gestures from the opening.

Musical scholarship on the relationship between analysis and performance continues to flourish. The first wave of this research, conducted throughout the 1980s and early 1990s with predecessors in Schenker, sought to establish a correspondence between marked structural events and their interpretation in performance. A second, more recent wave, dissatisfied with the formalism of such analyses, has sought to balance the contributions of the analyst and the performer in a more holistic musical understanding.

The rise of performance-driven analysis mirrors the growing work on musical agency. As yet, these two streams remain distinct. This paper seeks to examine the relationship between agency and performance using the first movement of Schubert’s Sonata in A Minor, D. 845, as a text. I will propose an agential reading of the piece and demonstrate how various performances by established pianists recast and ultimately enrich that reading. By modulating the marked oppositions within their jurisdiction (i.e., expressive timing, dynamics, and articulation), performers can attenuate the listener’s sense of narrative or refute it altogether.

No performer projects all aspects of my agential analysis; however, I do not assert that my reading is the only possible narrative. Rather, my aim is to show how the concept of agency can be a useful tool for comparing different performances. By speculating on the expressive motivations of performance choices, a theorist can interpret the microstructural variables behind such easy labels as “romantic,” “passionate,” or “mechanical.” This approach complements hermeneutic analysis by according the performer a more equal role in the creation of musical meaning.

Several overtly Schenkerian undergraduate theory texts have been published in the last decade. Each in this new generation of texts uses part-writing to introduce voice leading. However, there are some fundamental conflicts between part-writing procedures and Schenkerian voice leading and prolongation principles. The problems stem from the failure to differentiate between a part and a voice and, as a result, there is confusion over the types of motion and constraints appropriate for each.

In this presentation, a part will be defined as any series of pitches performed by an instrument or singer (e.g., a violin part, soprano part, etc.). A voice will be defined as a member of a harmony. Parts can move both within and between harmonies, by common tone, leap or step. Voices remain as common tones or proceed by ascending or descending step only when the harmony changes. I will examine some of the obstacles part-writing presents to incorporating Schenkerian voice leading and harmonic prolongation principles into undergraduate theory instruction. I will suggest strategies for recasting part-writing as the compositional elaboration of underlying voice leading. Finally, I will demonstrate how a compositional approach to part-writing can be integrated with harmonic prolongation.

Even as pitch-class set theory has been widely integrated into undergraduate music theory curricula, it has remained one of the more difficult topics of the typical undergraduate program for instructors to illuminate and for students to master. A number of factors contribute to this phenomenon: the atonal repertoire for which it was devised is shunned by many students; its association with mathematics makes it seem “unmusical” or frightens some students; the theory’s particular employment of inversional equivalence has no clear antecedent in musical theories already familiar to undergraduates; and the theory’s jargon seems forbidding and arcane to the uninitiated. As Joseph Straus once put it, “Atonal set theory has a bad reputation.”

This paper offers practical suggestions regarding the initial presentation of the theory to help students quickly acquire an easy fluency with both its fundamental tenets and its analytic value. Proffered strategies include the overt emphasis of musical relevance via a carefully chosen excerpt, using M&M candies to ingrain the concept of set inversion, and employing architectural safety as a metaphor for selecting normal order. This approach also advocates delaying the introduction of mathematical abstractions such as integer representation of pitch classes.

In teaching elementary serial techniques, one topic that often presents a stumbling block is the derived series. Students find it easy enough to understand that a twelve-tone series may consist exclusively of transposed and/or inverted statements of the same trichord or tetrachord, but the attempt to construct such a series tends to be a frustrating trial-and-error exercise. A derived-series calculator may be found on the Web——but it is a “black box” that does not reveal how the row is calculated. Moreover, it is restricted to trichordal generators, and returns only one possible ordering of the series for a given trichord.

In this poster I offer a simple sieve procedure that allows students to construct a derived series from a given trichord or tetrachord, with minimal need for backtracking. This procedure also helps students to understand why certain set classes are incapable of generating a derived twelve-tone series.

The genre of tragedy has, since ancient Greece, provided an arena for communicating and experiencing the troubles of the human condition. Aristotle writes in the Poetics, “Tragedy is an imitation of an action that is admirable, complete, and possesses magnitude, in language made pleasurable, effecting through pity and fear the catharsis of such emotions.” How can instrumental music convey a tragic plot structure and thereby elicit this same experience? This question gets to heart of eighteenth-century discussions on the value and power of purely instrumental music. Based on Hatten’s theory of the “expressive genre” (1994), a musical genre of tragedy will be proposed that is both emergent and teleological, with the goal of catharsis as its defining principle. Catharsis in this context functions as a global response to the tragic musical scenario, involving both an intellectual and emotional clarification as experienced by the listener; a response which is not only designed by the composer, but explicitly staged in the work.

As an exemplar of this expressive genre, Haydn’s Variations in F Minor (Hob. XVII:6) will be examined. The analysis will demonstrate how the tragic governs and motivates sequences of events which can be viewed as dramatic incidents, contributing to what Hatten describes as a “coherent dramatic scenario.” The problematic concepts of Aristotelian catharsis and mimesis will be discussed: their relationship to tragic pleasure, as well as their reinterpretation by both modern and eighteenth-century thinkers. Finally, a three-stage model for musical catharsis will be proposed based on the Haydn analysis, demonstrating how other instrumental works exemplify the tragic expressive genre.

Janet Schmalfeldt points out that speaking of the tonic as the “home key” imbues it with connotations of comfort, identity, and stability. The moment of expected return to the tonic, when combined with return to the opening theme, is an especially emotionally charged event: it is where musicians “return home,” or where the protagonist reenters. In some Chopin mazurkas, the return of the opening theme is, by contrast, homesick: it fails to recapture the opening key, or its character is transformed by the events of the preceding section. This paper analyzes a few examples using the combined analytical insights of Leonard Meyer and Schenkerian theorists.

The head motive of the Mazurka Op. 41/1 reappears in the central section, such that the reprise shares what Meyer calls conformant relations with two previous sections. The double conformance underscores the neighboring motion in the motive and foreshadows a transformation of the opening theme into a closing outburst of grief. Structural multivalence is particularly rich in Op. 59/1, whose “wrong key” reprise occurs at an overlap among three parameters: thematic design, functioning bass scale-step, and key area. The return to the original key area is achieved in a nearly imperceptible manner, giving a sense of anticlimax to the return and placing more emphasis on its epigrammatic ending. These analyses show that Chopin was concerned with transforming the Mazurka, which tended to fall into discrete units, into a fluid form that can even suggest narrative elements.

The ability to recognize and interpret musical symbols is often essential for attaining a comprehensive understanding of the music we study. This statement is especially true when evaluating the abundant and often complex text/music relationships embedded within lied settings. While hermeneutic significance is admittedly suspect to individual interpretation, informed readings that incorporate the elucidation of musical symbols have much to offer listeners and performers alike. Carl Schachter has pointed to a double-neighbor motive in Schubert’s “Death and the Maiden,” D. 531, that links together the song’s contrasting sections and helps reveal the Maiden’s mental states through its various inflections. Using Schachter’s groundwork, this paper seeks to illustrate the coexistence of the Maiden’s motive with a second motive representing Death. I assert that these motives, through their successive transformations and interactions at both the Schenkerian foreground and middleground, play out the dramatic action inherent in the text, providing us not with just a parallel of the emotional progress of the poem as Schachter suggests, but with lucid images of the Maiden’s inevitably futile struggle against death and even glimpses into the psyches of the two main characters.

In this paper, I propose relocating our analytical efforts from an emphasis on large pitch collections to a focus on the specific pitch realizations that generate these collections. I will discuss these realizations through the language of transpositional combination (TC), as developed by Richard Cohn. My analysis of Crumb’s Lux Aeterna will show how specific details of TC influence aspects of form in the composition.

My analysis will proceed in two directions, each path illustrating one half of a multifaceted view of form in this piece. The initial perspective views Lux Aeterna as a series of formal sections that are defined by certain TC or non-TC properties. An alternate path shows how details of particular TC operations influence the dramatic trajectory of the composition. I will discuss how properties of specific realizations of TC operations inhibit or encourage climatic moments, and show how these observations are manifest in the composition. Throughout the paper, I will focus specifically on features of the composition that would be obscured in a collectional analysis, but are emphasized in a TC analysis.

Phrygian Gates, composed for piano by John Adams in 1977–78, has a provocative rhythmic and metrical organization. Although there is an almost obsessive eighth-note pulse in the opening section, and a similar sixteenth-note pulse in the closing section, how one might count a tactus is not altogether clear. Further, the printed notation is not that helpful in clarifying meter, because there is rarely a printed time signature, and the bar lines do not seem to fill a metric function. In the absence of clear metrical structures, however, I explore how Adams uses a series of three texturally accented notes as signifiers of a proportional durational structure that can be traced from the smallest sub-phrase level up to the largest section level.

In addition to the three-note textural accent pattern, Adams uses another subtler technique of articulating the joints of this proportional structure. The contrapuntal interaction of the pitch patterns provides another vehicle for structural articulation. I use a modified version of John Roeder’s pulse-stream analysis to explore how pulse streams create and demarcate form and proportion. The pulse streams created in each line are not equivalent in duration, and thus initially may seem to be non-metric. However, the moments in which the contrapuntal patterns align create “super-pulses.” The process of entrainment to these super-pulses allows metrical structures to emerge, which along with the overarching proportional structure impose a sense of pacing and direction onto this seemingly amorphous composition.

The word “bridge” suggests a connecting or transitional function. A physical bridge is an agent of transition, used to get from one side of a gap to another. When applied metaphorically to the analysis of form in rock-pop music, however, the section traditionally labeled as the “bridge” does not necessarily connect two sections. Often, there are no harmonic and/or melodic associations with the surrounding material. Therefore, the label “bridge” does not adequately describe the function of the section.

Using melodic, harmonic, lyric, and reductive analyses of “bridge” sections in the music of Irish rock-pop group U2, this paper defines and illustrates the interverse, a new term that replaces bridge in rock-pop songs. Specifically, four types of interverses are identified, each based on its relationship to preceding and succeeding material. A more specific definition of this section allows for detailed classification of structural and stylistic features a particular musician or group employs, thereby promoting a more thorough understanding of the formal processes and song construction and more detailed differentiation between artists and genres. Second, this paper uses the methods mentioned above in conjunction with selected terminology from Moore (2001), Stephenson (2002), and Covach (2005) to define, illustrate, and distinguish the other sections of a rock-pop song, namely the introduction, verse, chorus, refrain, interlude, transition, and conclusion. Third, this paper demonstrates that U2’s sustained success is due not just to marketing and commercial promotion, but also to a combination of a unique sonic signature and a diversity of musical forms among their songs.

Early studies of Scriabin’s late works (i.e., those after Op. 58) offered various explanations of its harmonic language, the most common of which was to use the mystic chord (a member of sc 6-34 [013579]) as a source of its harmonic material. However, none of these address the overall harmonic syntax. More recently, Callender 1998 goes beyond the confines of the mystic chord. He discusses the presence of other collections (e.g., octatonic, whole-tone, etc.) and relates them through FUSE and SPLIT operations. In the current paper, I extend Callender’s approach and shift the focus from the harmonies to the voice leading that connects them. I use Scriabin’s Opp. 63/1, 69/2, and 71/2 to show that certain recurring voice-leading gestures—particularly those involving symmetrical motion—shape the musical discourse and give rise to a variety of harmonies, including but not limited to the mystic chord.

I use pc-space voice-leading graphs and three operations: a generalized version of Callender’s SPLIT and FUSE, and a new operation, MOVE. While Callender’s SPLIT and FUSE operations involve three different notes, mine involve only two. For example, Callender’s SPLIT transforms pc C# to pc C and pc D, while mine transforms it to either pc C# and pc D, or pc C# and pc C. The FUSE operation is the inverse of SPLIT—i.e., pc C and pc C# FUSE onto either pc C or pc C#. Finally, the MOVE operation is a half-step movement of a single pitch either up or down (e.g., pc C# moves to either pc D or pc C). In this generalized framework, the voice leading in Scriabin’s late works involves symmetrical converging around a single pitch class or an actual chord (i.e., horizontal and vertical symmetry). Thus, the unity of each work is assured through both harmonic recurrence and through symmetrical voice leading.

In looking for sources of musical unity, previous theorists have turned to harmony. In contrast, the three operations discussed above allow me to construct voice-leading symmetries that recur throughout each of the three above-mentioned works. My paper shows that symmetrical voice leading is a significant underlying mechanism joining the harmonies in Scriabin’s late works.

In 1962 George Perle composed a set of three inventions for solo bassoon. These inventions were written within the context of “twelve-tone tonality,” his original compositional method that combines inversional symmetry with interval cycles. It was not until the 1970s that Perle published his book Twelve-Tone Tonality, in which he explicates his theory. But even in the present day, Perle’s theory of twelve-tone tonality still is not widely known outside theoretical settings. This fact presents the performer of Perle’s music with some basic issues to be addressed regarding interpretation. Can one give a credible performance of a work if the fundamental aspects of its composition are not comprehended?

Perle’s virtuosic inventions are technically demanding and utilize the entire range of the bassoon. Although Perle has provided dynamics, articulation, and tempo indications in the score, the inventions are nonetheless enigmatic in terms of their formal structure. Combined with their atonal pitch organization and lack of phrasing slurs, these inventions mount numerous challenges for the performer.

This paper shows how an awareness of Perle’s use of symmetrical formations and expansion techniques facilitates in developing an interpretation that makes the music intelligible to both performer and listener, and that aims to realize the composer’s intentions. In the absence of conventional tonal demarcators, the formal relationships in each invention are discerned through an analysis of motivic processes and expansion, driven by the underlying force of symmetry. The paper highlights these fortifying relationships both within each invention and across the entire set of three pieces. 

The mosaic-like formal structure that would eventually come to be known as “moment form” was first discussed in Edward T. Cone’s article “Stravinsky: The Progress of a Method” (1962). Although Cone makes no such claim, the impression is made that Stravinsky was the originator of this formal structure. This paper will argue instead that the origins of moment form are actually found in the works of Debussy, most notably in “Ondine” from his second book of piano preludes (1911–13). Debussy’s overwhelming enthusiasm for early silent cinema, and the similarity in structure of cinematic montage and stratified musical form, both suggest that the influence behind Debussy’s formal innovation lies outside the realm of music.

While “Ondine” exhibits abrupt juxtapositions of material, the form of this prelude is generated primarily from the consistent opposition between diatonic and chromatic harmony, the latter defined here as symmetrical scales or Messiaen’s “modes of limited transposition.” While this harmonic opposition is certainly found in Stravinsky’s works as well, Cone instead finds the generation of Stravinsky’s form in the surface discontinuities of his works. By shifting the generating principle of Cone’s theory from formal discontinuity to harmonic opposition, the concepts of stratification, interlock, and synthesis between the various musical lines of a work are more easily identified. Finally, two aspects unique to Debussy’s approach to this formal structure further validates aspects of Cone’s theory, as they both clarify and strengthen the interplay between the initial strands of each musical line.

Charles Ives borrowed freely and often from a diverse body of extant music. Although he quoted from well over a hundred different pieces, eight tunes were used more than a dozen times. Of these—according to James Sinclair’s tabulation in A Descriptive Catalogue of the Music of Charles Ives—the patriotic tune “Columbia, the Gem of the Ocean” (“The Red, White, and Blue”) appears in at least fourteen published or recorded works.

In my presentation, I will explore how Ives incorporates the tune into his music by dividing its appearances into two categories: suggestive and structural. Suggestive uses of “Columbia” are intended to evoke a feeling or emotion, and often appear in passages featuring quotations of a similar style (patriotic songs). These examples are fleeting and fragmentary, and sound like quotations, rather than as part of the deeper fabric of the piece. On the other hand, when “Columbia” is used structurally, as in The Fourth of July, it serves an important role in the melodic, harmonic, and formal framework for substantial portions of a composition. By consulting the manuscript sketches, my analysis traces how “Columbia” is developed from the earliest pencil sketches, where Ives offers several versions, to the final score, where the tune is pervasive in every section. Furthermore, Ives distorts “Columbia” rhythmically and melodically so that it becomes a new entity ripe for development.

Gorecki’s third Symphony is one of the most commercially successful pieces of contemporary classical music to date. It has sold over a million copies worldwide, topping the US classical charts for 38 weeks and reaching number six on the UK pop-album charts in the year 1993. While the existing academic literature attributes this success to the influence of mass media promotion and the emotional weight of extra-musical associations, this paper takes a look to the intrinsic musical virtues of the work, by offering an in-depth analysis of the canon that opens the piece. Although simple and straightforward, this canon generates a complex web of processes. Most of these processes converge at the climax of the canon, reinforcing its effect. However, one such process, the canon’s registral expansion, reaches its peak before all the others, creating a dynamic counterpoint of tensions at both micro and macro levels. In addition, some processes are more irregular than others, and the contrast between the regularity of their evolutions contribute to their dramatic interplay and add to the structural and expressive depth of the canon. This paper analyzes this canon using the metaphor of a stepladder to facilitate the conceptual understanding of the similarities, differences, and interaction among the different processes. The analysis suggests that intelligibility of the individual processes is an important prerequisite for the generation of structural depth.

Attempts to interpret modal polyphony harmonically have had mixed success. The Phrygian mode in particular—by which I include both Phrygian proper and Hypophrygian, or tones 3 and 4—has proven a stumbling block. Scholars have, however inadvertently, fostered questionable hearings of pieces with Phrygian subjects as either ending on the dominant, or ending on the tonic but with the Phrygian final as scale degree five. These hearings are “questionable” in that they imply that the Phrygian final is not really the final; that the Phrygian pieces are not really in Phrygian.

In this presentation, I will use the chorale “Ach Gott, vom Himmel sieh’ darein” to open out historical and theoretical issues involved in harmonic interpretations of Phrygian polyphony; this examination will (1) reveal the source of distorting presuppositions about Phrygian to be the unnecessary assumption of a coincidence between the actual modal final from a harmonic standpoint and the root of a conclusive triad; and (2) suggest a new interpretive framework for Phrygian polyphony—a framework whose harmonic and voice-leading components draw upon the western-ecclesiastical tradition of modal theory, and whose viability I will demonstrate with reference to a setting of the chorale by Martin Agricola.

One of the characteristic things we do when we hear tonally is hear sounding pitches “as” scale degrees. That is, in a tonal context we might hear a given pitch (an acoustic entity) as, say, % (an ideal category or perceptual quale). The result is a fused esthesic structure, part raw sonic fact, part mental representation. Our experience of “interval” in tonal music arguably obtains between such fused esthesic structures—that is, between sounding entities “heard as” scale degrees.

This paper presents a direct-product GIS designed to model such intervals. The GIS is formally simple but conceptually rich. It illuminates a host of familiar tonal phenomena, including: consonant, dissonant, and enharmonically equivalent intervals; modulation and pivot chords; diatonic (tonal) and chromatic (real) transposition and inversion; and chromatic alteration of diatonic scale degrees. Two “exotic” species of interval in IVLS are of particular interest: those that indicate a change of scale degree with no change of acoustic signal (as found in pivot chords or enharmonic reinterpretations); and those that indicate a change in acoustic signal with no change in scale degree (as found in chromatic alterations). The GIS interacts with and extends existing transformational methodologies (such as neo-Riemannian theory), allowing such approaches to provide a richer account of the tonal kinetics of the music under study.

The GIS’s analytical potential is illustrated in passages from Bach, Mendelssohn, Liszt, Wagner, and Mahler.

Notation is in many ways a central focus of college music-theory courses, in which students spend much of their time learning to mediate between audible sounds and the written symbols that represent those sounds. This focus poses certain difficulties for blind students, however. One might assume that these students can depend on braille versions of printed scores and texts, but in practice the two notational systems often signify music differently. While both systems are invaluable tools for music performance, their differences can be tricky to negotiate in the music-theory classroom. By examining these issues, this paper seeks to add to the ongoing discovery of how notational systems result from, as well as constrain, the ways in which human beings think and talk about music. The paper uses examples from activities undertaken in the music-theory classroom, with emphasis on analysis, part-writing, and “sight” singing. A study of the metaphorical notions that underlie both types of notation provides a basis for understanding some of the differences between modes of representation, and leads to a discussion of strategies for integration and enhanced accessibility.

Brahms’s song “Schön war, das ich dir weihte,” Op. 95/7, sets a brief text by Georg Friederich Daumer. A single melodic disjunction figures prominently in Brahms’s setting; in treating this disjunction, normative voice-leading expectations are thwarted. Around these violations crystallize the central expressive issues of each song, involving not just melody, but harmony, phrase structure, and form. Other issues include the discursive phrase structure in the B section, as well as Brahms’s musical treatment of the subjunctive mood.

Schenkerian analysis will be used to explicate the unique melodic processes at work in Brahms’s setting, and the relationship of these melodic processes to Daumer’s text. The tangled phrase structure of the middle section will also be examined using a more phenomenological model, which will yield yet another layer of implication for Daumer’s poem. Nearly every parameter and time point in the song can be identified as multiply-directed, a spectrum of possible continuations or meanings presented at every turn; Brahms seems to make a marked effort to avoid some of the most likely continuations. Brahms’s setting thus focuses our attention on the multiply-directed moments in the song by meeting expectations with various levels of denial or surprise. This analysis also highlights moments of melodic anomaly not usually highlighted in voice-leading analysis, but which are essential to the expressive value of a song.

In this paper, I present an analysis of pitch-class transformations as they engage with Walt Whitman’s text in “Come Lovely and Soothing Death,” the climax of George Crumb’s song cycle Apparition (1979). My interpretation responds to Emersonian themes in Whitman’s verse, a portion of the “carol of death” from “When Lilacs Last in the Dooryard Bloom’d.” I suggest that Ralph Waldo Emerson’s idea of compensation—a broad concept that embraces cyclicity, periodicity, binary opposition, and a Transcendental convergence toward the divine—offers an appropriate alternative to the loosely Hegelian figural language of post-Beethovenian musical thought. I show how compensation and its characteristics of balance and convergence illuminate pitch, pitch-class, and Klumpenhouwer network transformations within and among the octatonic, diatonic, whole-tone, and chromatic sonorities Crumb uses.

Modern scholarship of rap music has tended to focus on rap as a sociological phenomenon, examining its status as a uniquely African-American form of expression or critiquing its often violent and misogynistic lyrics. Although such studies are appropriate, there have been very few actual published analyses of rap. Scholars have generally not analyzed rap as they would classical art songs, by providing a musical analysis that demonstrated the interplay between text and music. There are several reasons for this, among them a reluctance among scholars to accept rap as a valid art form, the lack of any of the pitch structures that normally form the basis for traditional analysis, and the lack of coherent meaning in many of the lyrics.

This paper, however, will suggest an altogether different reason. I will assert that the text/music relationship in rap is reversed, because unlike any other western music, rap music is composed before its accompanying text. Rap originated as an accompaniment to tracks created by DJs, which were themselves an accompaniment to dancers. The lyrics, originally improvised, were created less to convey meaning than to add a new, variable rhythmic layer that draws on rhythmic motives from the sampled music to interact with the accompaniment. With analyses from A Tribe Called Quest and OutKast, I will demonstrate some ways in which rappers use the rhythm of the text to reinforce the rhythm of the music. This paper will therefore provide a new analytical approach to rap music by inverting the traditional text/music relationship into a music/text relationship.

(Please note that some of the examples discussed in this paper will contain profanity.)