(alphabetical by author's last name)

Invariant Interrelationships within Schoenberg's Hexatonic Works


Joe Argentino, McMaster University

Arnold Schoenberg's Suite op. 29, Ode to Napoleon op. 41, and Modern Psalm op. 50c, feature row or hexachord series based on the third-order all-combinatorial 6‐20 (014589) hexatonic hexachord. Hexachordal invariance plays a critical role in each of Schoenberg's aforementioned compositions, and the relationships between each composition's hexachords can generally--but not always--be expressed through the conventional Tn or TnI operations. However, rather than relying on traditional transformations the relationships among each composition's row class can be defined using contextual transformations that reveal important correlations between each piece's uniquely ordered source hexachord forms.

The purpose of utilizing contextual transformations is to reveal important relationships between groups of related pitch classes; in other words, the importance of contextual transformations is not relegated to how the hexachords are related to one another, but rather why they are related to one another. The contextual transformations that I advance govern entire passages or large sections within each composition showcasing the types of invariant relationships expressed by Schoenberg within each of these works. This paper will commence with an examination of the hexatonic hexachords used in Schoenberg's Suite and Ode to Napoleon, and conclude with an in-depth analysis of Modern Psalm.


Music of Intensity: Jennifer Higdon's Steeley Pause


Jeremy Beck, Louisville, Kentucky

Winner of the 2010 Pulitzer Prize in Music for her Violin Concerto, Jennifer Higdon’s music has been praised by the New York Times for being “imaginative, richly orchestrated and accessible.” Commissioned by most of the major orchestras of the United States, recorded on dozens of CDs, and enjoying hundreds of performances a year of her compositions, Jennifer Higdon has established herself as one of the major American composers of the twenty-first century. Studies of some of this important composer’s works are now beginning to emerge. This presentation analyzes one of her earlier compositions, Steeley Pause (1988). Composed by Higdon while she was “thinking about creating intensity in music and about the challenge of writing a piece that is full of tension,” this four-minute work for four C flutes provides a window into certain features of Higdon’s musical language and style that may suggest a continuum in her composing up through the present day.

One of the most refreshing aspects of Steeley Pause is its lively and engaging rhythmic language. Rhythm, as it informs the texture, is a major element in this work, more important than pitch.  My analysis of Steeley Pause will examine Higdon’s approach to structure in this short composition with a focus on both the rhythmic and harmonic elements she uses to achieve the clarity of form she successfully communicates in real time. This analysis should provide a certain basis for other theorists and musicologists interested in exploring the catalogue of this vital composer.


Textual Rotations, Generic Norms and the Two Tempo Rondò


Matthew Boyle, Indiana University

Studies of musical form in eighteenth-century arias have only recently explored form-defining aspects of conventional text-setting. This paper proposes that a very common text-setting procedure in the eighteenth century--one where multiple settings of the same text appear within a single aria--plays a key role in defining the generic meaning of the two-tempo rondò and in articulating its formal boundaries and closure. This procedure, which I call textual rotational form, strongly parallels a musical principle that Hepokoski and Darcy call rotational form, which is a structuring device “that extend[s] through musical space by recycling one or more times [...] a referential thematic pattern established as an ordered succession at the piece’s outset.” Textual rotational form is consequently concerned with the cyclic ordered presentation of poetic lines during the course of an aria.

In eighteenth-century opera, textual and musical rotations were conventionally aligned. Many two-stanza arias in the 1780’s were set in a bi-rotational manner, both textually and formally, with opening textual rotations having a strong correspondence to musical expositions. This alignment of text and music is also present in the two tempo rondò , an aria type associated with serious characters, which gains core aspects of its expressive potential through how it interacts with the principles of textual and musical rotations. The rondò generally consists of an initiatory slow ternary section, setting the first eight lines of poetry, followed by a faster section that has a more flexible formal design, usually setting the final four lines of text. This paper will briefly describe several different text-setting and formal strategies of the rondò . These text-setting strategies ultimately correspond to a series of miniature generic and textual breakthroughs that dramatically lead to an aria’s final expressive state.


Filters, "Stasis," Motion and Anticipation in Beat Furrer's Invocation VI


David Dominique, Brandeis University

In Invocation VI, for bass flute and soprano, Beat Furrer utilizes materials and techniques influenced by minimalism, spectral music, musique concrète instrumentale, and electronic music, to construct a musical narrative that oscillates between stasis and motion. Locally, this dynamic is observed in high energy, cellular patterns and perpetually shifting timbres. Formally, a cyclical recurrence of transforming motives heightens tension throughout the piece, which is structured as a series of Stravinskyan tableaux.

Fundamental to Furrer’s music is a system the composer calls “filtering.”1 Essentially, Furrer applies layers of processes to small numbers of recurring gestures. On the smallest scale, filters behave like switches, deleting and substituting instrumental and vocal techniques for individual pitches of fixed sequential sets. Sectionally, Furrer utilizes both fixed and continuous filters. A fixed filter applies a static operation to a block of material, while continuous filters effect enveloped transformations.

In Invocation VI, as well as in other recent pieces, Furrer builds a thick tension that is never released. Central to his style is a feeling of anticipation and the thwarting of points of arrival. By crafting material that often ascends locally, constructing long-range ascending voice leading, and using filters to build dramatic entropy, Furrer manufactures the expectation of a momentous cadential arrival; instead, the climax of the piece spills into an abrupt sparse coda. In this way Furrer can be considered alongside his European Modernists colleagues, many of whom seek to explore new approaches to form through radical subversion of narrative conventions.

1 Interview with Beat Furrer by David Dominique; Vienna, Austria; June 29-30, 2012.


Connecting the Dots: Compositional Process
in Elliott Carter's Fourth String Quartet


Laura Emmery, University of California, Santa Barbara

 Deciphering the sketches for Elliott Carter's Fourth String Quartet (1986) can be a daunting task. The sheer number of folios is a staggering 1117 pages, and the content is seemingly impenetrable; most of the material is devoted to morphological analysis of rhythmic patterns, interval structure, and pitch sets. Due to their intricate nature, some scholars have found the sketches to be counter-intuitive in retracing Carter's compositional process, in that the repeated preparatory exercises often appear to have no direct relation to the final product. My examination indicates quite the opposite— the repetition of rhythmic patterns, beat divisions, and calculations is not only methodical, but necessary. I argue that by the time Carter finished sketching the rhythmic and harmonic processes, he had already conceived the entire quartet.

At first reading, the sketches appear to lack an intermediate compositional phase; Carter seemingly shifts from scattered dots to a final score. However, by focusing on the details of each folio--calculations of the pulse divisions, subtle changes in rhythmic alignments, and harmonic charts--I reveal a logical hierarchical system. After outlining the general long-range polyrhythmic structure of the quartet, Carter uses dots to map distinct characteristic rhythmic ostinati to each instrument. By superimposing the underlying pulsations of each part, he marks points of polyrhythmic alignment, and forms a higher-level composite rhythmic structure. Within a small subset of measures, Carter transforms this dot-notation into elaborate rhythmic figures that fit within the previously established framework of aligned pulses. With thoroughly-planned polyrhythmic details of the four instruments--their tempi, ratios, rhythmic relations, motives and cycles--Carter assigns unique intervallic restraints to each instrument. Lastly, Carter adds a general formal outline of the piece, descriptive character of instruments in certain sections, and the desired effects. He repeats these stages for each section of the piece.


Fuzzy Relations in Analysis and Performance: Schoenberg's Op. 19 No. 4


Daphne Leong and Hunter Ewen, University of Colorado

Writings on analysis and performance often imply that analyses and performances of a particular piece belong to an equivalence class. The class's members are those interpretations that are afforded by the score. We demonstrate the problems inherent in this assumption, and suggest an alternate model, that of a fuzzy set or similarity relation.

After discussing issues related to a score's under-determination, its dual function as text and script, and the mutable relation between score and interpreter, we present five interpretations of Schoenberg's Sechs kleine Klavierstücke Op. 19 No. 4: one analysis (by Leong), three recordings (by Pollini, Uchida, and Steuermann, analyzed empirically), and one live performance (by Leong).


Play This, Hear That: Three Contrasting Approaches
to Modularity in Contemporary Music

Christopher Gainey, University of British Columbia

Some patterns within a piece of music seem unrelated beyond the fact that they are  contained within the same harmonic space. Although this may be frustrating from a  transformational perspective, isolating discrete patterns allows for analytically interesting  descriptions of their role as functional components, or modules, of a larger formal structure. The  extent to which the structure of a piece of music may be said to result from the interaction of a  limited number of identifiable functional patterns may be summarized as its degree of  modularity. The fewer discrete modules, the higher the modularity, as each module contributes  relatively more to the structure of the piece.

This paper will apply this analytical perspective to three highly modular contemporary  pieces, and suggest ways in which an awareness of a modular design may enrich the experience  of listening to or performing this music. In Figment II for solo cello, Elliott Carter uses the  complement union property of the all-trichord hexachord (012478) to establish harmonic spaces  defined by the four possible combinations of (04) dyads with a single (0167) tetrachord. In his Second Mazurka for piano, Thomas Adès uses a series a series of alternating (015) and (025)  trichords to establish harmonic spaces defined by clear tonal centers. In Papillon II for solo cello,  Kaija Saariaho establishes a harmonic space defined by registral expansion/contraction. The  experience of this expansion/contraction is organized by a limited set of bowing patterns that  create the sensation of hierarchical pulse streams within an active, but steady, rhythmic texture.


Verbal Borrowings and Hermeneutic Consequences in Charles Ives's Songs


Chelsey Hamm, Indiana University

Though scholars have extensively examined musical borrowings in the songs of Charles Ives, discussion of verbal borrowings--quotation of or allusion to the text of a document (musical or non-musical) within a song’s text--is rare. Furthermore, scholarly discussion of potential hermeneutic consequences of verbal borrowings is virtually non-existent. In this paper, I describe several categories of verbal borrowings that are found in songs that span over two decades. Next, I analyze and interpret two songs in detail, “Soliloquy” and “The Things Our Fathers Loved,” through the lens of verbal borrowings found within them. In the former I show that verbal borrowings reinforce the song’s formal design, harmonic structures, and symbolism to create a Transcendentalist-influenced statement concerning humankind’s relationship with nature.

This claim is supported by a verbal borrowing from Emerson's “Plato” essay in Representative Men (1850). In the later I demonstrate that verbal borrowings work in tandem with musical borrowings to support a reading of the song as a musical manifestation of values and rights evoked by the its subtitle. This reading is supported by a verbal borrowing alluding to the patriotic song “Columbia, the Gem of the Ocean,” which is employed alongside a musical borrowing of “The Battle Cry of Freedom.” My second analysis explores the trope formed by this layering, and discusses how this passage (among others) could be heard as a musical manifestation of values and rights evoked by the song's subtitle. To conclude, I briefly identify a few other songs that contain verbal borrowings, such as “A Christmas Carol.”


Compositional Process in the Postwar Music of Henry Brant:
Unifying a Diverse Output


Joel Hunt, University of California, Santa Barbara

The postwar compositions of Henry Brant exemplify an incomparable diversity of style, genre, form, texture and timbre.  As such, they pose a significant challenge to researches seeking a unified definition of Brant’s compositional identity.  Previous efforts to characterize this music have explored the logistics of Brant’s polystylistic-spatial technique, but they have neglected large-scale structural commonalities that more accurately unify the repertoire.  A study of Brant’s sketch material, housed at the Paul Sacher Foundation, makes clear the highly organized sectional structure of the music, and illuminates audible characteristics that unify Brant’s postwar compositions in the absence of more traditional rhythmic, harmonic, melodic, and stylistic commonalities.

The sketches for nearly all of Brant’s postwar compositions indicate that he composed each piece according to the same compositional process, which he termed “prose-report” composition.  Prose-report composition featured a sectional preplanning system in text.  It allowed him to rationalize and expedite the final compositional act, virtually eliminating the need for drafts and edits, and abolishing his previous reliance on the piano as a compositional tool.  In the following paper, I will trace the prose-report process from start to finish in the opening of Brant’s 1978 orchestral composition Trinity of Spheres.  Using audio excerpts from select compositions, in combination with corresponding sketch material, I will show how the process manifests audibly in all of Brant’s postwar compositions, thereby unifying many seemingly unrelated works.  Ultimately, I will argue that the sectional nature of the process consistently yields music with large-scale structural characteristics that are identifiably Brantian.  Thus, in light of the prose-report process, we can more accurately characterize Brant’s postwar music, and clarify his unique compositional identity. 


Musical Process as an Image in Motion: Text Expression
in Schoenberg's Three Songs, Op. 48


Wing Lau, University of Oregon

Written in Schoenberg's year of turmoil, 1933, the Three Songs op. 48 do not feature the composer's own notion of Gedanke, which explains Schoenberg's music through a process of conflict and resolution as illustrated by Patricia Carpenter, Severine Neff, Jack Boss, Gordon Root, etc. These settings of poems by Jakob Haringer, a poet who fled from Nazi Germany just like Schoenberg, depict psychology that constantly moves between opposites, like flipping between "two sides of the coin": the protagonists' contradicting emotions of optimism and pessimism. These opposites alternate and coexist, therefore, they never are resolved. This poetic image is closely depicted by Schoenberg's musical processes.

The use of images to describe musical operation has been demonstrated by David Lewin, Andrew Mead, Richard Kurth, Stephen Peles, etc. Building on this scholarship, my paper maps set-classes and row forms onto visual images. To depict the unresolved psychology, these images do not transform. Instead, they trade places or retrograde themselves. Therefore, the unfolding of the whole piece or the whole section is in fact a global image of steady and unchanged smaller images being set in motion. Here, three images in motion will be introduced: a flipping image, a displaced image, and a stratified image. These dynamic images will facilitate parallels between text content, poetic structure and musical process.

Throughout op. 48, the word "star" is used to symbolize blessing and internal peace. Its literary absence implies sorrow, disappointment and death. Taking this symbolic meaning, the whole set can be interpreted as the poet's journey in search of "stars." Referencing the time of composition, my paper suggests that op. 48 is a deepest yearning of the composer for rescue from racial crisis and political turmoil.


Mapping graphs onto physical spaces in multidimensional tonal music


Bennett Lin, University of Washington

The increasing prevalence of touchscreen mobile devices and multiplayer online worlds allows for a new theory of tonal composition in which voice-leading graphs are mapped onto the two- and three-dimensional physical spaces suggested by virtual realms. A single musical piece composed in this manner can be heard in countless different ways based on each listener’s path of movement within the virtual realm.

Multidimensional harmonic progressions involve temporal sequences not of chords but of mappings, of which the simplest example is any bijection. However, the palette of possible mappings grows richer as the order and dimensionality of voice-leading graphs increase relative to the virtual realm, granting more options for the former to be reduced and “flattened” onto the latter. For example, graphs of equal cardinality may intersect and have their voice leadings combined to include additional chords such as diminished triads (which lie outside the hexatonic cube) and major sevenths (which lie outside the octatonic tesseract).

The additional temporal dimension in the notation of such progressions underscores the same issues that arise with the addition of each new spatial dimension. This fluid interchangeability between time and space may help point the way for expansion of this theory into extra dimensions in both voice-leading graphs and virtual realms.


Formal and Affective Dichotomies in the Adagio of Haydn's Op. 76, No. 4


Lucy Liu, Indiana University

This paper analyzes the Adagio of Haydn’s String Quartet in B-flat, op. 76, no. 4, with the goal of demonstrating a multi-parametric tension between syntax and rhetoric in this movement. As such, I offer two competing formal analyses. The syntactically typical reading understands the movement to be in sonata form, albeit highly condensed, while the second reading (a cross between “sonata without development” and Sonata Theory’s type 2 sonata) is syntactically doubtful but rhetorically tempting, for it better captures the piece’s affective dichotomy: positive transcendence, associated with the major mode and struggling ascent to a higher register, and plodding negativity, associated with the minor mode and the relinquishing of high register for the movement’s final, low obligatory register. Furthermore, I ask the question of what it means to experience the form of this movement phenomenologically.

In the second reading, the hypothetical recapitulation begins by retracing the movement’s opening 8 bars in the minor mode, emphasizing the difficulty that ascent (Anstieg) poses for the movement as a whole. Next, one hears a parenthetical insertion that disrupts the putative recapitulation--a transcendent, major-mode “vision” which is nevertheless thwarted by the sharp drop in register before the “actual” recapitulation. Indeed, the latter sounds highly qualified, for it borrows its densely imitative texture from the exposition’s transition section. Via imitative entries, suspensions, and chromatic voiceleading, 1̂ works its way up to 5̂ in the higher register, only to witness the Urlinie descend in minor. In the coda,flat-6̂ is ever-present and the movement ends in the opposite mode than its exposition.
Had one only listened to the exposition, one would not foresee the second half’s turn toward negativity, for the exposition unfolds with textbook clarity. In contrast, the second rotation not only brings about formal ambiguity, but calls attention to the important role that mode, registral play, and texture play in one’s diachronic engagement with the piece.


There and Back Again: A Musical Journey in Middle-Earth


Meghan Naxer, University of Oregon

In 1964, British composer Donald Swann set out on a journey to compose a work based  on text from J. R. R. Tolkien’s The Lord of the Rings. A collaboration between Swann and  Tolkien resulted in The Road Goes Ever On, a cycle of seven songs originally published in 1967.  This cycle has a complex history with roots in Tolkien’s “linguistic aesthetic,”1 a story told  through literature, and songs “sung” in poetic form within a larger story. Each song in the cycle  is paired with a singer or speaker and context from the narrative. This paper will show how each  song represents the different cultures of Tolkien’s narrative and how the cycle as a whole  represents Tolkien’s larger mythology of Middle-Earth. 

Because each song is presented in Tolkien’s story in the form of poetry, a rhythmic  analysis will be used to compare the poetic setting of each song with Swann’s musical setting.  Drawing upon the work of William Rothstein, Harald Krebs, and Yonatan Malin, I will explore  how Swann uses hypermeter and “declamatory schemas” to capture the different cultures of  Tolkien’s story. Tolkien’s poetic style, in short, varies depending on the depicted culture and  Swann employs comparable rhythmic identifiers in the music. Additionally, the song cycle  mirrors the cyclic properties of the songs and story in Tolkien’s narrative while conveying  Swann’s theme of journeying. The Road Goes Ever On offers a rare glimpse into the  collaboration between author and composer. Furthermore, it represents a fascinating attempt to  depict a fantastical world in musical terms. 

1Humphrey Carpenter, ed., The Letters of J.R.R. Tolkien (Boston: Houghton Mifflin Company,  1981), 220. 


Delaying the Inevitable: Humorous Retransitions in Haydn's Chamber Music


James Palmer, University of British Columbia

The retransition is one of the most specific and easily definable formal functions in Classical music. Retransitions return a composition to its home key, establish the home key's dominant harmony, and repeat musical ideas with increasing fragmentation. These features create smooth connections with, and momentum toward, the recapitulation, whose point of arrival feels predictable and inevitable to an attentive listener. Yet Haydn occasionally throws a wrench into the retransitional process, bending stylistic norms, thwarting listeners’ expectations, and turning the music into humorous diversion.

This presentation discusses retransitions in the finales of Haydn's String Quartet Op. 33 No. 3 and Symphony No. 98 and in the third movement of Symphony No. 66. In each example Haydn creates stylistic incongruities in the music's rhetorical flow, thwarting expectations predicated upon a listener's knowledge of Classical conventions and the expected moment of recapitulation. In each retransition Haydn plays with different musical processes making the music seem to trip over itself in a different way and leaving listeners to wonder how it will pick itself back up. Whether by false starts, awkward voice-leading, or excessive post-cadential extensions, Haydn finds fresh ways to create musical humor in an area of the form that one might not expect to reward careful listening.


Nono and Schoenberg: The Origins of the
Variazioni Canoniche
in the Ode to Napoleon


Bruce Quaglia, University of Utah

Luigi Nono's first publically performed work, Variazioni canoniche sulla serie dell'op. 41 di Arnold Schoenberg (1950), was nominally composed using the twelve-tone row from Schoenberg's setting of Byron's Ode to Napoleon. It has frequently been suggested that Nono chose this particular precursor by Schoenberg because it is a clear example of "committed music." Overtly political works are certainly rare within Schoenberg's catalog and so Nono's choice to use the row from Op. 41 is particularly redolent in light of his own subsequent political stances. While Schoenberg's work possesses its own specific contexts as a "stand against tyranny," Nono's work is by contrast that of a young Italian who came of age during the partisan war. His commitments are instead expressed subtly, via his intertextual navigation of purely musical elements from the past and present, and coalescing in his presentation of these in a profoundly individual voice. 

My paper argues that Nono found in Op. 41 more than a texted theme of protest, but also a model that pointed harmonically towards his own contrapuntal conception of a new form of musical presentation which was ever conscious of the current historical moment. Neither Nono's own work, nor Schoenberg's Op. 41, consistently feature an ordered twelve tone set as part of the musical surface. Each work instead presents its own distinct permutations of the unordered hexachord 6-20, a source set which is hardly unique to Op.41, but which Schoenberg also used in the Suite Op. 29 and elsewhere. Nono's compositional techniques advance an element of Schoenbergian serial harmony by privileging unordered subsets over ordered segments and secondary harmonic sets, and then presenting these within a richly complex contrapuntal framework.


Stravinsky as Performer and Structure as Practice


Malia Roberson, California Lutheran University

Stravinsky’s dogmatic approach to performance practice focuses on a metrically-strict style that makes every effort to curtail expressive devices by the performer. His quest for objectivity branded performers as “executants” and suppressed individual interpretation, which Stravinsky considered to be “the root of all errors.” This paper examines the connection between Stravinsky’s musical structure and the creation of his ascetic performance style as the piano soloist of the Concerto for Piano and Winds (1924). In addition to tracing some of the initial reception of this early neoclassical work, I subscribe to Pieter van den Toorn’s rationale that Stravinsky’s performance practice, the “executant-style”, was due to structural reasons, specifically, the concentrated presence of metrical displacements. A steady beat was necessary to highlight the metric and rhythmic invention of his music. To illustrate metrical conflict, my analysis isolates various metrical layers as per Harald Krebs. Most of my musical examples keep to the Concerto, but passages from other piano works will be offered, as well as comparisons with the influential ragtime style.

The notion that structure itself dictates practice competes with the suggestion by Richard Taruskin and others that objectivity in performance is related to the social-cultural conditions of “dehumanization,” in this case, replacing the individuality of musical interpretation with a purely technical, automaton-like function. Due to my own performing experience with the Concerto, however, I speculated that the work’s metric organization also generated its performance style and execution. The executant-style is a consequence from the perceptual breakdown of metrical hierarchy. In other words, a highly irregular surface produces a highly regular execution.

As the piano soloist of the Concerto, Stravinsky was described as an “impersonal scientist”, “mechanical”, and “unemotional.” These reviews cultivated and solidified his objectivist aesthetics as the “authoritative” performer of his own music, yet his “vibrant”, “stirring”, and “sensuous” playing was not merely machine-like.


Temporal Interplay in Ligeti's Lux aeterna


Duncan Schultz, University of Wisconsin

James Gibson posits time as an “intellectual achievement” we impose on the world by perceiving permanence versus change in an environment. In Music as Heard (1983), Thomas Clifton adapts this idea to music, noting that we, as active listeners, effect a temporal process on music by perpetually connecting past, present and future events. This constant temporal interplay is a cornerstone of Clifton’s musical phenomenology, with pieces exhibiting what he calls static succession pushing the boundaries of this claim. Without the presence of external change in static pieces, time, as understood above, can’t be inferred. This prompts Clifton to turn inward, pointing to the listener’s varying mindsets as the change needed to effect a temporal process on the music.

But imposing temporal connotations on music constructed to negate these types of implications seems counterintuitive. For example, György Ligeti’s static composition Lux aeterna (1968) goes to great lengths to frustrate our ability to retain and predict. The opening fourteen seconds act as a microcosm of this process, as eight voices sustain a single tone. Retaining the past in the present becomes fruitless during this passage as the two remain equal, provoking the listener to assimilate these temporal modes. With this assimilation, the ability to predict the future becomes more labored since there’s nothing to base one’s predictions on except the constant presence of the sustained tone. Further, the ability to anticipate new events succumbs to this opening span since we can only effectively anticipate events two-point-four seconds in the future (London 2004). As if highlighting this ineptitude, the permanence of the tone is reemphasized around every two seconds as a new voice enters. What’s left is a piece where the present becomes the focal point of perception, leaving the past and future outside the listener’s peripherals.


Pierre and the Pygmies: Contour Theory, Transformational Spaces, and Cross-Cultural Musical Analysis


Rob Schultz, University of Massachusetts

Musical contour theory is, in essence, a theory of generalities. By disregarding specific intervallic distances between elements of a given domain, contour theory elucidates musical structure strictly in terms of its broader gestures and shapes. One major advantage this approach offers is applicability to a diverse array of musical languages, styles, and cultural traditions. Indeed, it is little wonder that present-day musical contour theory can trace its lineage back to several important ethnomusicological, as well as theoretical studies.

Since its arrival on the scene in the mid-1980s, however, the music-theoretical literature on contour has focused almost exclusively on western art music of the twentieth century. This is hardly surprising given contour's perceptual immediacy coupled with the characteristic absence of tonal hierarchy in many of the compositional languages and styles of this period. Nevertheless, contour has been shown to play an important role in various global musical traditions as well. For instance, Arom and Fürniss (1992) have demonstrated how the vocal polyphony of the Aka people of Central Africa is fundamentally pentatonic, yet the pitch structure of a given song is characterized not by any measure of fixed interval size or absolute pitch, but in fact by its melodic contour profile.

Contour theory thus provides an important entryway into the realm of cross-cultural musical analysis. As a preliminary step in this direction, this paper presents a novel transformational methodology of musical contour relations, and juxtaposes analyses of the opening section of Pierre Boulez's Messagesquisse (1976) and the dìyèì, or yodel part, of the Aka divination song Dìkòbò dámù dá sòmbé. Points of contact and divergence between these analyses will then serve as a springboard for examining some of the complex issues involved in comparative musical analysis of this kind.


Webern's Use of Guitar in Op. 18 as Model
for the Orchestration of Later Works


Adam Shanley, University of Oregon

The evolution of Anton Webern's orchestration and composition style from his early  atonal works, Opp. 1-16,  through to his mature works, Opp. 20-31,  is made possible  largely through inclusion of the guitar. Op. 18, for soprano, E-flat  clarinet, and guitar,  becomes, in this light, more of a pivotal work than previously considered and displays the  composer moving towards the full realization of his aesthetic.

Kathryn Bailey asserts that Webern's Opp. 17-19  stand as Webern's pre-serial  work  and most agree that the Op. 20 string trio marks the beginning of his fully realized serial  compositions. One can see Webern's musical style evolving through these pre-serial  works  towards pointillistic orchestration that features wide leaps, mixed rhythms and sharp  attacks resembling characteristics extrapolated from the guitar. It is his use of guitar as  continuo in Op. 18 and 19 that was necessary to further developing these characteristic  details of the composer's later compositions. Though the folk instrument roots of the instrument were perhaps the impetus behind  Webern's selection of the guitar; it also serves as the means to another end in providing  Webern with an instrument that can support an ensemble harmonically while simultaneously  lending melodic support in the form of negotiating large leaps and extremes of range.

With his developing musical language Webern suggests the natural evolution of  Lieder through use of folk texts, and folk instruments. It does not simply denote an evolution  in Webernʼs organizational ideas about pitch but also considerations of orchestration,  voicing of simultaneity and spacing of those pitches. It is with these considerations that I assert the importance of the guitar to Anton  Webern's growth as a composer as well as the higher degree of importance that should be  placed on these pre-serial  works, Opp. 17-19.


A Musical Representation of Time: Carter's Esprit Rude II


Cecilia Taher, McGill University

This paper intends to illuminate the comprehension  of Carter's Esprit Rude II through the composer's conception of time as well as to clarify Carter's theoretical thinking as expressed through his compositional practice. Following the composer's ideas developed after 1940, the capacity of music to create interest in the listener lies in the communication of his personal experience of time. Carter's idea of time as a continuous evolution resulting from the simultaneity of independent events is suggested in Esprit Rude II  by the durational organization of the three instrumental parts in connection with their pitch structures. The layered durational organization of the parts suggests three synchronic metric structures and speeds that are consistent within themselves but diverging among them.

Three different tempi interact creating a continuously changing polyrhythmic texture. The beats of the independent temporal streams approach and separate from each other throughout the piece, originating unrepeatable simultaneous moments, and converging only once, at the end of the work. The pitch structure provides internal coherence to the three temporal streams at the same time that, more interestingly, allows the manipulation of the degree of proximity among the parts in pitch space.

Unlike many compositions by Carter, in  Esprit Rude II   each temporal stream is not based on a collection of pitch classes or intervals that remains constant throughout. It is precisely this peculiarity that allows for a converging/diverging fluctuation among the parts in pitch space. Finally, in  Esprit Rude II, three individual parts coexist to generate a continuously changing, uninterruptedly progressing musical texture. The interplay among three periodic parts conveys a sense of forward  rather than cyclic direction: regularity is a mere way of organization of an ever-changing phenomenon, just as it happens with time. In this context, the resulting musical form becomes an objective representation of time itself.


The Price of Assimilation in Schubert's Sei mir gegrüsst


Anders Tobiason, University of Wisconsin

Schubert's haunting "Sei mir gegrüsst" ultimately assimilates its chromatic interior to its
exterior, but it does so at serious cost. This paper investigates the lengths the song goes to in order to deny the emotional and tonal consequences of a chromatic seam that opens up over its course. The refrain-like four-bar phrase that sounds again and again throughout the song sags in its middle between F-sharp and F-natural, but this sag is not the space where the chromatic seam is pulled apart. The seam occurs in the increasingly desperate sections that each lead to the refrain (Ernst Kurth also recognizes this harmonic desperation). In the refrain the poet sings directly to the beloved "by me be greeted, by me be kissed." It is like a mantra in which he reiterates his increasingly frantic message.

As the song moves forward it becomes clear that this message is not one of truth but of illusion. By the time the refrain repeats a few times we come to realize that the song is organized cyclically. Because the refrain has an embracing and framing function, we hear it as the defining matrix within which the telos of the song is being unfolded. By hearing the song as rotationally informed, each cycle through the rotation obsesses over the same emotion (loss), heightening this feeling each time. And there is something ritual to the way that he continually repeats the refrain despite the increasingly certain implication that she is not going to return to him. Each time chromatic warmth threatens to overwhelm the poet he returns to the refrain and soothes himself with it. This increasing chromaticism ensures that the song must somehow assimilate it in order to maintain the illusion of her return. And this occurs; the refrain ends the song. But this assimilation comes at a price: the continuation of the diatonic delusion of her presence.


The Rite of Spring at 100: Reflections on Meter


Pieter van den Toorn, University of California, Santa Barbara

With the “Evocation of the Ancestors” in Part II as its point of departure, this paper examines the explosive nature of the rhythmic patterning in The Rite of Spring, tracing much of its explosiveness to the underlying metrical forces of parallelism and displacement, forces which, ultimately irreconcilable, lead to disruption. The argument is that these forces play themselves out on the smallest of scales, conspicuously in the “Evocation,” with the main motive of the top layer and its immediate (shortened and displaced) repeat. An irregular seven quarter-note beats in length (although sometimes shortened by a note or two), the main motive is repeated thirteen times in succession. The sort of development that may be inferred from this invention is discussed, along with the requirements for performance. In effect, features of melody, harmony, rhythm, instrumentation, and articulation that might earlier have been subjected to a “developing variation” are kept intact in order that they might serve as a foil for what does change, namely, alignment. The rationale behind this train of thought is one that Stravinsky’s critics, in condemning the repetitious, static, mechanical, and intransigent qualities of The Rite of Spring and other Stravinsky works, have all but ignored.