Befitting a contemporary composer of such international stature, Elliott Carter's music has been the focus of much theoretical, analytical, and historical research. Several studies have particularly investigated (1) the combinatoric properties and intervallic makeup of Carter's compositional materials and their realization in later instrumental miniatures and (2) his attention to text-music relationships in vocal works from before 1990. However, there has been a relative lacuna in scholarship on Carter's "late-late style" compositions with text. This seems somewhat surprising considering the composer's academic background in (and continued fascination with) the field of literature. My paper provides a close analysis of two complete songs from Carter's 1999 cycle Tempo e Tempi—"Segreto del Poeta" and "Una Colomba" (both settings of poems by Italian modernist Giuseppe Ungaretti). I hope to shed light on how Carter simultaneously interprets the structures of Ungaretti's intricately symbolic poetry and underscores their narratives with his recent compositional language. My analysis will incorporate Carter's favored pcset materials such as all-interval tetrachords (AITs) and all-triad hexachords (ATHs) with text painting, aggregate completion, moments of intertextuality, and Michael Riffaterre's concept of poetic "ungrammaticality."

Ever since the term “metric modulation” was introduced by Richard Franko Goldman to describe certain passages in Elliott Carter’s Cello Sonata, it has become customary (perhaps even compulsory) for analysts to identify such modulations in Carter’s music to demonstrate metric modulation. As a result of this attention, metric modulation has become a signature technique for much of Carter’s music—one that many theorists and musicologists would use to help them identify his style.

Yet, despite the common familiarity with the term, there remains much to be learned about metric modulation. The musicological community has not yet debated whether metric modulations can be achieved by more than one compositional technique, nor have they discussed which musical events, that affect meter or tempo, can properly be considered as metric modulations. This paper will recognize and label a group of techniques for metric modulation in an earnest effort to begin that important discussion. In this presentation, four different types of metric modulation—Pulse Modulation, Duration Modulation, Abrupt Modulation, and Written Accelerando Modulation—and four different functions—Formal Division, Transition, Time Control, and Character Designation—will be discussed. Compositions spanning fifty years of Carter’s career will be used to illustrate these classifications and designations of metric modulation.

Elliott Carter states that, “In post-tonal music, it’s simply that each composer, every time he writes a piece, has the opportunity of ‘making up his own language,’ so to speak, conditioned only by the requirement that it be a language, i.e., that from the point of view of the imagined listener the morphological elements have a recognizable identity in each case and that their status as musically relative ‘norms’ and ‘deviants’ (as Meyer puts it) be clearly established in the works.”

What exactly are these “morphological elements” for the listener? Furthermore, how is the status of “norm” or “deviant” established in a work? This paper argues that the “recognizable identities” to which Carter is referring are essentially musical gestures. Defined as discrete, aurally discernable units, these musical gestures take a higher status within post-­?tonal pieces for many listeners. Even without a tonal syntax as a structural canvas, the post-tonal listener can nevertheless latch on to sound-shapes and cluster them together into an established “norm” for each individual piece. This paper demonstrates how different types of musical gestures may function in a post-tonal idiom.

I analyze Carter’s multifaceted use of musical gesture in three works: Three Poems of Robert Frost, Voyage, and Of Challenge and of Love. My analytical purpose is twofold: first to explore the ways in which musical gestures establish a normative framework for musical understanding; second how they might strengthen or contradict this framework within each piece. Ultimately, this type of gestural analysis may offer a method of informed listening of post-tonal music.

Orlande de Lassus’ Prologue to the Prophetiae Sybillarum sounds strange and provocative, with abrupt changes of accidentals. It is surely in part for this reason that Lowinsky (1961), Mitchell (1970), Berger (1980, 1985), and Lake (1991) have sought to make sense of it. These analyses, however, conflict as to the degree to which the piece does or does not “fit” tonality or a hierarchical modal system. In addition, beyond Lowinsky’s reference to “excessive modulation within so small a space” (39), these scholars do not adequately explain what makes the piece sound so bizarre. This presentation will attempt a more complete explanation of this piece by modeling abstract and literal counterpoint.

This presentation will proceed in three parts. First, I will describe the ways 16th-century and modern scholars have talked about abstract counterpoint. Second, I will demonstrate the (mostly) strict rules Lassus used to create sounding counterpoint, and how this relates to the process of composition in the 16th century as described by Owens (1997). Finally, I will use the concepts of abstract and literal counterpoint to show that the most interesting and shocking aspect of this piece is not just that it is chromatic, but that it is so chromatic because of its carefully chosen, contrapuntally-correct path.

A curious phenomenon pervades the majority of Scriabin’s post-tonal piano miniatures: the thematic areas of his binary works become separated by a tritone, much like the tritone link witnessed in his tonal pieces. But how exactly does Scriabin arrive at this tritone divergence and what rules govern this transformation? The two most prevalent voice-leading theories on Scriabin’s post-tonal music, parsimony and transposition, are ostensibly split on these matters. By reinterpreting parsimonious motion through Joseph Straus’s fuzzy transposition, one can fuse the two theories into a singular system that accounts for motion between similar and dissimilar pc sets. This approach reveals an intimate link between the interval class vector and transpositional level of a pc set. Specifically, it indicates that pc sets in Scriabin’s music are principally preceded by a transposition that reflects the most saturated interval classes of its interval class vector. In this paper, I will clarify the invariance based voice-leading procedures in Scriabin’s post-tonal piano miniatures and interpret how they are manipulated to create large-scale tritone divides.

My paper complements previous analytical approaches to chromatic passages in Prokofiev by exploring how semitone-related triads substitute for fifth-related triads and evince harmonic function. This method builds on the work of Stephen Brown, who devised an interval space built from fifths and semitones, and Robert Morris and Daniel Starr, who defined the M operation to model alteration from fifth to semitone. Unlike the previous writers, I focus on the role of fifth-semitone exchange in key-defining progressions.

In Prokofiev’s “March,” Op. 3, No. 3, a number of altered dominant-functioning chords resulting from altering root relation from fifth to semitone. The opening period toggles between privileging root motion by these two intervals. The contrasting middle provides a prolongation, through an inversionally symmetrical sequence, of an altered dominant chord whose root is a semitone above the work’s final tonic. Semitone-related triads provide a different harmonic function, specifically dominant preparation, in Prokofiev’s “Gavotte” from Four Pieces, Op. 32. In the first section, each cadential dominant is prepared by a different semitone-related triad.

These analyses provide explanations of passages that other theories strain to account for, and because similar analyses could be repeated for other works, they lay a foundation for a broader understanding of the functional potential of semitone-related triads in Prokofiev’s music. The analyses also provide insight into Prokofiev’s droll musical humor, which often inverts what is perceived as normal and abnormal harmonic syntax.

Charged with the task of confirming the new key in the exposition then resolving to the home key in the recapitulation, the second-theme group performs what are perhaps the defining actions of any sonata form. Locating the start of this group, however, is not always a straightforward affair, and debate continues to surround the issue, particularly in the work of James Hepokoski and Warren Darcy, and William E. Caplin. In short, the problem is that no matter how powerful a single rule may be, none per se is able to identify all those places that, for one reason or another, strike analysts as the beginning of the second- theme group. I therefore recognize six factors that contribute to the expression of a second-theme beginning (assuming a prior first theme and transition): (1) preparation by a phrase-ending dominant chord (in any key); (2) Hepokoski and Darcy’s medial caesura; (3) a phrase structure with discernible beginning and end functions in the manner of one of Caplin’s theme types; (4) presence of tonic harmony of the new key (in root position or first inversion) at some point in the new phrase; (5) a change in texture at the new phrase; and (6) characteristic melodic material at the start of the new phrase. This paper will examine some challenging pieces in which the combination of factors helps to decide between (a) multiple second-theme candidates in a movement, as in Beethoven’s Eroica Symphony, and (b) a continuous or two-part exposition, as in Mozart’s “Hunt” Quartet.

This paper proceeds with Edward Cone’s idea that musical lines can often be heard as embodying a virtual persona. Such personae are especially salient when established by lines like melodies and counter-melodies, which occupy what might be called the musical foreground. I argue that in first-movement expositions of Classical and early Romantic string quartets, these foreground personae are often deployed according to a particular archetypal plan, which corresponds closely to the exposition’s tonal and thematic structure. While the first theme features only one foreground persona, the transition introduces a second, and this second persona remains present for the rest of the exposition. The paper presents empirical evidence, derived from a corpus of these expositions, that such a hearing is often plausible. The results indicate that first themes, compared to subsequent sections, tend to contain fewer concurrent lines that would elicit a foreground persona. They also show that the lines of first themes tend to have lower information content, which, as previous research suggests, might make them less likely to establish foreground personae.

Formal analyses of Dmitri Shostakovich’s sonata-form movements often focus on the idea of “sonata arch” or “reverse recapitulation” structures, wherein the primary- and secondary-zone themes return in reverse order after the development. Using methodology from Hepokoski and Darcy’s Elements of Sonata Theory (2006), this paper examines such structures through the lens of rotational form, describing Shostakovich’s “reverse recapitulations” as a unique blend of double- and triple-rotational sonata-form characteristics.

I begin by outlining double- and triple-rotational sonata structures, respective layouts corresponding to Hepokoski and Darcy’s Type 2 and Type 3 sonata forms. Rotational form frames the referential thematic pattern—first established as an ordered succession at the piece’s onset—as a rhetorical principle rather than a tonal one. A return of the primary theme in the coda, considered a hallmark of the “reverse recapitulation”, actually underscores the ordered rotational structures and is equally common in double- and triple-rotational sonatas. Next, analyses from Shostakovich’s fourth and fifth symphonies illustrate his techniques of blurring the lines between double- and triple-rotational constructions. Finally, further examples consider coda presentations of the P-theme, a regular feature of Shostakovich’s work. Examination of Symphony No. 5’s delayed ESC and inverted P-theme and Symphony No. 4’s unaltered P-theme explores the theoretical and hermeneutical ramifications of each coda’s thematic return.

In his book Fantasy Pieces, Harald Krebs presents a methodology for describing passages involving metric dissonance. One of his categories of metric dissonance is displacement dissonance, which he defines as "a conflict between a metrical layer and an antimetrical layer.”In this paper, I examine passages that involve instances of low-­level displacement dissonance—those whose unit of displacement is less than half the value of the beat. I present an alternative approach to understanding such passages that replaces Krebs’s perpetually-nonaligned metrical layers with a theory of flexibly-linked metric streams.

In Krebs’s definition, the dissonant relationship between conflicting metrical layers permits no intersection—the two layers can never meet. But in many instances of low-level displacement, a more flexible performance interpretation may be intended, since some composers used syncopation as a notational shorthand for the effects of classical rubato, wherein two voices may move subtly into and out of alignment with each other. This flexible relationship can be more effectively modeled with metric streams.

Metric streams can drift out of alignment with each other in performance, but they essentially communicate the same underlying meter, rather than two wholly separate meters. The events in coordinated metric streams are separated by only a very small amount of time, in such a way that the listener feels that the nonaligned streams could move back together easily at any time—that they can indeed meet.

Temporal manipulations in works from the classical period may have a surprising, comic, or dramatic effect, yet they often give the impression to be logically motivated. It is this latter, and frequently overlooked, aspect of music temporality that this paper seeks to address. To this end, this paper introduces the concept of motivic temporality, which attempts to capture the notion that in some musical works temporal manipulations are associated with a particular musical idea or set of ideas. This paper develops the concept of motivic temporality and its implications of temporal coherence through an analysis of Haydn’s Piano Sonata, XVI: 50, I. By drawing on historical and contemporary approaches to rhythm, meter, and temporality in general, I argue that many of the moments of temporal interest in this movement are seeded in the seemingly simple opening phase. In particular, I propose that the temporal manipulations in this movement generally involve a slowing down of the musical flow, and that these manipulations are associated with upward melodic impulses frequently accompanied by a reaching-over gesture, and, to a lesser extent, with the tone Ab. Thus, the various forms of temporal manipulation throughout this movement may be heard not as arbitrary foreground anomalies but as expressions of the work’s unique temporal and motivic integrity.

György Ligeti’s fourth piano étude, Fanfares, opens with remarkable clarity and balance. Its two-voice texture, an ostinato and an accompanying dyadic melody, is readily apparent and inverts at the end of each phrase. Yet almost from the outset, the piece commences a long, slow process of metric and motivic disintegration, one fraught with dissolution and fragmentation, but speckled with moments of motivic crystallization. Previous analyses have capitalized on the ostinato’s potential for suggesting listening strategies (Duker, SMT 2010), exotic elements of the asymmetrical rhythms (Bouliane, 1989), or postmodern implications of the triadic harmonies (Drott, 2003). These approaches fail, however, to capture the work’s essential struggle between order, disorder and the traditional basis of its formal organization.

In this paper, I adapt Gretchen Horlacher’s polymetric cycle (Horlacher, 1992) to study the rhythmic and metric interaction between the ostinato and the dyadic voice and the thematic potential of the relationship between voices. I examine the metric placement of the dyadic voice relative to beats in the ostinato and use phrase expansions, contractions, and various metric displacements to show a variety of recurring metric structures that occur at formally significant junctures. Many metric themes have strong ties to conventional phrase and formal structures, including the sentence and the antecedent-consequent construction and, more globally, the departure-return model. I show how Ligeti carefully changes and subtly develops each metric theme in the second half of the piece, creating continuity and closure in a piece that forges its own blend of tradition and innovation.

Schoenberg was less than candid about his own use of musical form. On the one hand, he often contextualized his own work as the obvious outgrowth of the music of the past, and thus employed earlier forms in new ways. On the other, he sometimes responded to critics, who claimed that his music was not progressive enough, by distancing himself from the same common- practice forms. Schoenberg’s paradoxical stance creates a problem for the listener, who cannot necessarily take Schoenberg’s own formal designations at face value, even when they are written directly into the score. The little-known Variations on a Recitative for organ (Op. 40) presents a prime example of this problem, as it is surprisingly difficult to follow the form as Schoenberg apparently intended. Hepokoski’s notion of dialogic form provides a useful lens for examining Op. 40 through which we can examine the ways in which the piece enters into a “…dialogue with culturally pre-established generic expectations within the craft.” (Hepokoski 2010, 19). The exploration of ambiguity in this composition will reveal how form is not necessarily something inherent in “the music itself,” but rather results from an unending trialogue of composer, performer, and listener, as well as a dialogue with the established genre of theme and variations.

Variations in nineteenth-century sets—represented here by Brahms’s Variations on a Theme by Robert Schumann—do not as a rule merely decorate a pre-established theme (as in many classical-period sets) but rather substantially interpret it. In fact, insofar as they bring to light otherwise obscure or imperceptible features of the theme—or rather, hypostatize them as features—such variations can reasonably be said to constitute the theme, to bring it into being. In these sets, in other words, what the theme is cannot be separated out from how it is varied. I propose that Brahms actualizes latent thematic features in one of two ways: first, a variation may render a latent feature of the theme more explicit—more audible, repetitive, and salient; second, a variation may afford such a feature greater structural significance, as when the variation composes it out. In short, a variation concretizes an otherwise obscure thematic feature by rendering it either more perceptible in the foreground or more structurally consequential in the middleground. In this paper, I uncover instances of both techniques within a close reading of Brahms’s piece.

The lack of close analytical study of melodic invention in guitar-based blues music may be explained in part by music theory’s preference for essentialist theories of harmony and form, which can distort or reduce otherwise complex phenomena. Blues harmonies are easily reduced to a progression of three chords and its melodies to a blues or pentatonic scale. However, much of the interest in guitar-based blues melodies lies not in the harmonic material or the scalar collections, but rather in the creative employment of stock motives.

Many blues melodies are constructed from certain characteristic motives, or “licks,” and this is particularly true for the guitar solos of B.B. King. This present study more thoroughly defines King’s characteristic guitar licks as schemas, using the work of Robert Gjerdingen and his galant schemata as a model. Through a corpus study, I have identified four schemas as indicative of King’s classic 1950s and 1960s style. The manner in which King’s schemas manifest themselves on the guitar fretboard is an essential feature of the theory. These licks are instantiations of the same physical schemata on the guitar—physical schemata that King discusses in his own guitar method book. Their currency might be then attributed to their related physical gesture involved in playing the licks. A fuller analysis of the opening solo from his song “Worry, Worry” from the 1965 album Live at the Regal will be discussed in depth, showing how King uses many of these schemas as the foundation for his melodic invention.

American hardcore punk rock is a subgenre of punk, and first emerged in the late 1970s with bands such as Black Flag and Bad Brains. Although hardcore is characterized by its fast tempos and concise song forms many descriptions of the genre focus on the energy and intensity in its performance. For instance, Stevie Chick (2009) states that Black Flag’s songs “reveled in the pure rush delivered by riffs that, in their ascendant and descendent simplicity, packed an almost physical punch, thanks not least to the lurching rhythms” (51). My own reactions to hardcore are similar: while I hear pitches and rhythms I also feel the physical gestures with which they are performed. In order to highlight this process of understanding, I examine guitar riffs as a series of lateral motions along a fretboard. When taken together these performative actions often reflect a structural basis in what I call “riff schemes”: organizing patterns of physical repetition and change. There are four main types: (1) riffs that begin with a repeated gesture before undergoing change; (2) riffs that begin with a repeated gesture before undergoing a change that creates an extension; (3) riffs that follow a pattern of statement and varied repetition; and (4) riffs in which an initial gesture is subject to transposition. In addition to serving an organizational purpose riff schemes are often used to create tension and climax, and I conclude the paper with an analysis of Minor Threat’s “Straight Edge,” a song that demonstrates this use.

Before the later nineteenth century, the principle governing nearly all earlier tonal composition was monotonality. Some composers (notably Schubert) allow two or more keys to co-exist within the same composition, each salient enough to render a monotonal understanding of the composition problematic. Such tonal structures exhibit what is known as polyfocal tonality, also known as directional tonality. Schubert often pairs polyfocal tonality with the topic of distance, frequently ending such songs a third from where they began. In some polyfocal songs, Schubert enhances the feeling of distance by juxtaposing more remote keys.

To better understand the tonal relationships in polyfocal structures, I have developed a method of analysis that combines Schenkerian analysis with interpretive approaches derived from the work of Edward T.Cone, Harald Krebs, and Patrick McCreless. Polyfocal analyses of select Schubert songs will be presented to show how he represents distance with polyfocal tonality; in particular, extreme tonal distances will be examined in songs such as Ganymed (D. 544), Der Jüngling und der Tod (D. 545), and Orest auf Tauris (D. 548).

Tonal ambiguity is a topic rich in possibilities for discussing the music of Chopin, the mazurkas in particular. This paper shows how Chopin’s way of writing in some of the mazurkas can require alternative interpretations, as ambiguities organize entire works in this genre. The paper begins with some general observations on tonality and ambiguity, distinguishing ambiguity from tonal incompleteness (as might occur when a piece ends on an unexpected harmony) or vagueness (a lack of clarity). It then turns to several Chopin mazurkas that exhibit different kinds of multiple meanings. In Opp. 41/1 and 24/2, momentary ambiguity featuring an initial tonal uncertainty colors an entire piece that proves to be monotonal. Opp. 7/5 and 30/2 prove to be terminally ambiguous as the initial tonic and the closing one share equal importance so that either could be primary. In each of the mazurkas discussed in this paper, Chopin deploys tonal ambiguity in such a way that two different hearings are defensible. In none of these cases are we dealing with a lack of tonal clarity or uncertainty; rather, a sensitive listener must contemplate the multiple meanings of a passage and the implication of those meanings for interpreting the piece as a whole, embracing alternative readings when they become appropriate.

While few doubt the expressive potential of jazz music, this topic has not been well explored by music theorists. While many musicians and authors talk about “creating a story” with jazz improvisations, the question of expression in original jazz composition is simply overlooked. Building on Robert Hatten’s theories of markedness and musical agency along with Garrett Michaelsen’s topical approach to jazz “grooves,” I use Thelonious Monk’s “Crepuscule with Nellie” as a case study for the examination of expressive meaning in jazz composition.

“Crepuscule with Nellie” provides an ideal case study for this type of inquiry. Monk wrote the piece in May of 1957 while his wife, Nellie, was in the hospital having her thyroid removed. It is a unique piece in Monk’s output (and unusual for jazz in general) in that it was never played with any improvisation; the piece was simply the “head” of the tune, with no solos. Monk felt that the composition should stand alone, as a kind of concerto written for his wife. This paper asks the obvious question: What is it about this work that makes it somehow too intimate to be commented on, by Monk or anyone else? A thorough analysis of this work helps to illuminate how a consideration of musical meaning can enhance our understanding of both Monk’s unique style and, more generally, the art of jazz expression.

The suspension as contrapuntal technique is underutilized in jazz music. Henry Martin notes, “rarely [are suspensions] prepared and resolved [in jazz music] as in common-practice theory” (Martin 1996, 14). While true in much jazz music, Brad Mehldau’s Sehnsucht, from the 1998 album Art of the Trio, Volume 3: Songs, features numerous examples of suspensions prepared and resolved in a traditional way. This technique lies in distinct contrast to the way jazz composers normally incorporate a “sus” chord. I will demonstrate how contrapuntal norms are at work, the suspension among the most indicative, in Sehnsucht. I will argue, further, that the suspension creates the effect of musical motion and goal-orientation. Together, these characteristics promote the perception of beginning–middle–end that is essential to tonal principles in music of the common practice. Sehnsucht, which generally means yearning or longing, serves as the impetus for this piece’s notable tonal ambiguity. While Schenkerian voice leading analysis will help to clarify this ambiguity, it is the suspension that draws attention to this trademark German Romantic emotional state.

Putnam Aldrich (1966) understands the early baroque corrente in terms of rhythmic grouping and physicality: four-bar phrases in a fast triple meter, and some corresponding series of arsic and thesic dance steps. More abstractly, Lawrence Zbikowski (2008) calls dance a “dynamic process” that may be represented “through patterned sound” by a sonic analogue—especially dance music. Applying these conceptions to the Corrente of J. S. Bach’s keyboard Partita in E Minor, BWV 830 (1730), we find similar agreement between grouping and dance; however, the dance comes not from a dancer, but from the Klavierspieler’s physical actions in performance. But there’s a twist: Bach almost never suggested fingerings for—never “choreographed”—his keyboard pieces. Any individual performance therefore only articulates one of several possible “choreographies,” whether the performer’s own, or that of a third-party editor. Heinrich Schenker (1925), not explicitly addressing physical actions, staunchly opposes third-party interpretations, advocating faithful adherence to the composer’s original notation, which ideally allows the piece’s middleground to emerge autonomously. Leslie Blasius (1996) regards this middleground as a kind of “presence,” calling it the interior performance, which emanates from inside the score through a faithful performance and thereby “binds composer and performer.” This paper seeks within this corrente a similar “presence,” but expands Blasius’ interior performance to include the performer’s physical actions: the interior choreography. Rather than emanating from the score, we find that the interior choreography arises from the performer’s physical potential, the “voice” within every performer’s—your, my, Bach’s—physical body.

Conventionally, tonal structure in Bach’s binary dance movements is described as a first reprise modulating from I to V (or i to v for minor-key pieces), followed by a second reprise modulating from V to I. As this paper demonstrates via a comprehensive survey, that stereotype is mistaken with respect to the tonal structure of second reprises, which, in fact, normally do not begin in a non-tonic key at all. Instead, second reprises usually begin with what I term the V–I paradigm, in which the reprise begins on an active dominant in the tonic key, which then proceeds without overt cadential rhetoric to a tonic chord. Only after this reiteration of dominant-to-tonic harmonic motion, which occurs in about 70% of Bach’s binary dances whose first reprises end in the key of V, does the second reprise proceed with the tonicization of a secondary key area and an eventual cadence in tonic. Because the V–I paradigm occurs in a variety of prolongational contexts, I argue that it functions as a schema in the sense recently popularized by Robert O. Gjerdingen (2007). The V–I paradigm also serves as the structural underpinning for the subjects of certain fugues: those in the second reprises of binary gigues in Bach’s keyboard suites. As such, the V–I paradigm allows us to construct a supplement to the otherwise exhaustive categorization of subjects and exposition patterns described by William Renwick (1995).

Many scholars have argued that the act of performance, as a “reading” of a musical text, can serve as a form of analysis. This paper argues that the act of transcribing a musical text for a different group of instruments also constitutes a “reading,” and that both processes of translation will inevitably shed light on certain features of a work while obscuring others. To illustrate, the paper considers transcriptions of Bach’s chorale “Wachet auf” by Leopold Stokowski, Sir Granville Bantock, and Ottorino Respighi, and demonstrates that these translations represent three very different readings and interpretations of Bach’s text that collectively shed light on the work’s meaning.

Each transcription proposes a different reading of the relationship between Nicolai’s tune and Bach’s setting. Stokowski casts Bach’s contrapuntal setting as an ornamentation of Nicolai’s original chorale melody, which he regards as the work’s centrepiece; Bantock treats the chorale melody as merely a foundation upon which to build a new musical edifice, adding his own newly composed counterpoint to Bach’s setting; and Respighi undertakes a more holistic reading of the work, acknowledging both Nicolai’s and Bach’s contributions while focussing on Bach’s setting as a whole. These three transcribers also illuminate different aspects of the work’s form. Whereas Bantock and Respighi adhere to the bipartite form of Bach’s setting, albeit with subtle and compelling modifications by Respighi, Stokowski reveals a latent tripartite form; by omitting the repeat of the opening A section, he proposes a minor-mode B section followed by a modified recapitulation.

In American folk and popular music, dissonance frequently functions in ways that cannot be explained by conventional tonal theory. Two types of dissonance—dropping and hanging thirds—function outside of classical norms, and within the framework of a mode built around the tonic triad. They lie most frequently around ^1 and also frequently around ^5. The mode either transposes or remains in place during changes of harmony. When it transposes to IV or V—the most common non-tonic harmonies—the root and fifth of those harmonies may have dropping and hanging thirds. When the mode remains in place, a shift to non-tonic harmony renders certain members of the tonic triad temporarily unstable. Over IV, ^5 and ^3 are temporarily unstable, and their tendency in this context is to resolve to ^1. Over V, only ^5 remains stable, but the tendency of ^3 and ^1 is not to resolve to ^5, but rather to ^1 over tonic harmony. Thus, when the tonic mode remains over V, melodic resolution requires a shift back to I. The interaction between the mode and harmony influences the large-scale structure of a strophe or other section and the perception of its tension and resolution. When the mode transposes, dissonance derives mostly from shifts to non-tonic harmonies, which create large-scale harmonic dissonance with tonic harmony; when the tonic mode remains in place, further dissonance derives from the interaction between the tonic mode and the non-tonic harmonies, creating more compulsion to resolve.

Fiona Apple’s song “Extraordinary Machine,” from the 2005 album with the same title, charms listeners with playful timbres created by bells, woodwinds, and pizzicato strings, an “oom-pah” feel, and the vocalist’s graceful, seemingly effortless sliding and use of “blue notes.” In contrast, the lyrics have a much more serious tone, reflecting how the singer will overcome adversity, even though she feels underestimated by those around her. This same clash between playfulness and seriousness can be found in harmonic aspects of the song, as well; the lighthearted exterior masks the complexity and ambiguity that arise through mixture, enharmonic spelling issues, and remote modulations. Therefore, despite its outward appearance of simplicity, “Extraordinary Machine” warrants a close examination through the lens of chromatic tonal theory.

In this paper, I will trace a series of enharmonic events that coincide with pivotal formal and lyrical moments in the song. I will argue that these events set up the song’s highpoint that takes place at the end of the bridge. At this point, as she sings the words “everything will be just fine” while gracefully sliding and sounding nonchalant, she makes a remote modulation and an enharmonic shift seamless and almost imperceptible through her manner of performing a pitch that has been set up to be enharmonically paradoxical (C-natural/B-sharp). My analysis of this popular song reveals an underlying harmonic narrative that enriches the understanding of the performance and the story unfolding in the lyrics.

Yuri Kholopov (1932-2003) defines “hemitonicism” as “a half-step system in which each separate note is an independent unit (in contrast, for example, to the chromatic tonal system, in which each separate note belongs to a larger unit, the chord).” He continues, “Its first consistent use was by Anton Webern…and it was subsequently used by many composers in the 1950s through the 1970s, namely Stockhausen, Boulez, Denisov, and Schnittke.” With respect to Webern specifically, Kholopov says, “Pitch organization in Webern’s music is mainly represented by hemitonicism.”

After a brief look at precedents for this type of analysis, I will examine Kholopov’s hemitonic analytical system with respect to Webern’s atonal music. Kholopov discusses two manifestations of hemitonicism: hemitonic “fields” and hemitonic “groups.” A field is “the continuous filling in, by halfsteps, of some portion of the chromatic scale along the vertical, horizontal, and diagonal dimensions.” He says that groups are “of three or four notes formed by joining any interval with one or two halfsteps.” Specifically, there are five trichordal and five tetrachordal hemitonic groups.

Kholopov’s system invites comparisons with pitch-class set analysis, which I will briefly explore in this paper. Hemitonicism is self-contained and reflective of sets that are aurally comprehensible. Kholopov concludes: “Hemitonicism is the positive name that is implied by the so-called ‘atonality’ of Webern and that perhaps replaces that negative designation, which satisfied neither Schoenberg nor Webern, nor any composers or theorists of that time.”

Alfred Schnittke is well-known for his concept of polystylism, the blending of different musical styles in a single work. Scholars have misinterpreted this concept, in part because in Schnittke’s writings on the topic, he uses the terms quotation and allusion in idiosyncratic ways. This paper refines our understanding of polystylism by drawing critical attention to two facets of the Suite in the Old Style (1971, for violin and piano). First, the work appears to be written in the Baroque style, without irony. Schnittke claims that there is an unstylistic “smudge” in every movement, although I argue against this. Second, music from the Suite itself reappears in the cacophonous Symphony No. 1 (1972). Although the symphony contains several quotations of well- known musical works, I do not agree that the Suite music fulfills the same function, as has been suggested. Rather, I argue that this alleged “self-quotation” is meant to refer not to an earlier composition of Schnittke’s but to the Baroque style in general. In this case, Schnittke uses newly composed Baroque-sounding music instead of excerpting a specific eighteenth-century composition. This practice corresponds to Schnittke’s conception of quotation as the reappropriation of an earlier style, not an earlier work. I propose the Suite as a collection of “monostylistic” practice pieces in earlier styles, documenting Schnittke’s efforts to write convincing old-style music that can be quoted polystylistically. The Suite is thus crucial to the development of polystylism in Schnittke’s music.

Early in his career, many critics hailed composer Per Nørgård (b. 1932) as the mantle bearer of Danish nationalism after Carl Nielsen. But the political and cultural changes that followed World War II motivated Nørgård to travel beyond Europe for musical inspiration. Some of his early experiments dealt with the avant-garde and minimalism, but he soon began developing compositional styles and techniques of his own, which continued to change and evolve over the last half-century. The one compositional development that has arguably had the most influence on Nørgård’s musical output is his Uendelighedsrækken or the “infinity series” which he discovered in 1959. A mathematical sequence with fractal properties used as a way to create pitch material for his compositions, this music draws upon his experiences with Eastern cultures, philosophies, and music, including travels to Bali from 1975–1980. Interestingly, Nørgård’s infinity series predated mathematician Benoît Mandelbrot’s work with fractals in his chaos theories of the nineteen-eighties. The rhythmic incarnation of the infinity series, which Nørgård calls “Sun and Moon” music, is the basis for much of Nørgård’s percussion writing.

In this paper, I will demonstrate how the infinity series is constructed through an integer model of mathematical operations, how fractal properties permeate the series, and how transposed and inverted iterations of the series can be generated. I will then demonstrate how Nørgård employs the infinity series in musically creative and intriguing ways to create structure, energy and drama in music.

Lawrence Kramer writes that “sooner or later … the songs of Schubert’s errant subjects venture into a border area where something—a structural oddity, a textual twist, an expressive gesture—potentially transforms the observance of normative discipline into a deviation from it.” (1998) Schubert’s Atlas is one of these errant subjects. This errancy is concretely embodied in our inability to absolutely illuminate a Schenkerian third divider for the song. Clearly beginning and ending in G minor, “Der Atlas” (1828) nonetheless veers off course in ms. 20 and slips into B minor, a move that coincides with the last lines of the first strophe. In this paper, I propose that we hear B[nat] as a potential Schenkerian third divider. Potential because the triad to which it belongs, G major, is never fully realized at the background. Ultimately, the piece returns to G minor, and B[flat] seemingly assumes its “correct” position as the third divider. But this reading of B[flat]-as-third divider is highly problematic. B[nat] is articulated in such a way as to suggest that it should eventually be subsumed within a G major Bassbrechung. However, this potential Bassbrechung is in direct contrast to the very obvious and confident descent through B[flat] in the Urlinie. The song forcefully detaches B major from its composing-out of the background before obsessively reinforcing G minor. By positing an absolute conflict between the composing-out of two distinct triads, this analysis suggests that our inability to reconcile these two reflects Atlas’s inability to assimilate the lyrical “Ich” and “Du.”

This paper explores the conceptual and pedagogical advantages of conceiving harmonic motion in diatonic third-space. Clough 1994 examines this space as a subset of the mod7 diatonic. Tymozcko 2009a begins to suggest how a thirds-based model of syntax might substitute for the traditional fifths-based one; a later survey of tonal literature leads him to declare that thirds- space offers an "accurate, if approximate view of functional harmony, one that is largely independent of contrapuntal considerations". His theory is bolstered here by a new speculative investigation that considers both third-space's essential characteristics and some implications for abstract voice-leading.

I first establish an ad hoc priority of third-space over step- and fifth-spaces for describing harmonic motion. Musicians routinely employ all spaces when, for example, they recognize that motion from A-C-E to C-E-G can occur by root motion up two steps or down three fifths, or transformatively via voice-leading. Since all three spaces are equivalent under multiplication, this change in perspective simply reshuffles which root motions and voice-leadings appear smallest. I delineate three basic transformations on triads in this space, SHIFT, HINGE, and LEAP, encompassing all possible mod7 root motions. These correspond to accepted formalizations of diatonic movement (Kochavi 2008); however, I further establish for each essential voice-leading, harmonic, and melodic characters, respectively. SHIFT, HINGE, and LEAP are last shown to aid in the classification and pedagogy of harmonic sequences, specifically by virtue of how these transformations manifest on the diatonic tonnetz.

This paper reports on the first acoustical study of a peculiarly “musical” form of speech, which has been mentioned frequently, though casually, throughout both the musicological and linguistic literature. The “stylized interjection” is a brief, attention- getting, but endearing (and, occasionally, mock-endearing) exclamation, encompassing: calls (Yoo-hoo); infant-directed speech (Peek-a-boo) and certain adult-directed derivatives (Bye-bye); playground taunts (Nya-nya); ad hoc group chants (Air-ball); and other playful exchanges (Uh oh). Equivalents of these speech patterns have been identified in several languages by linguists whose accounts typically invoke a particular musical concept: the interval of the minor third. The minor third has therefore come to be thought of as a “very natural interval” (Liberman 1979: 30). Leonard Bernstein concludes “these are two very special notes” (1976: 16-17), and Peter van der Merwe similarly muses, “one of the great puzzles of music is the mysteriously satisfying quality of the minor third” (1992: 120)—sentiments that were anticipated by Brailoiu (1953), Sachs (1943), and Szabolcsi (1943).

In this paper, I will: review the provocative but rather irresponsible literature on the topic; present results from laboratory studies that both confirm and refine previous writers’ intuitions concerning the minor third (and a number of other acoustic features); consequently propose an interpretation of the stylized interjection as a form of “sung speech,” in a way that helps to explain the idiosyncratic relationship between (acoustical) form and (linguistic) function; and assess the anthropological/ethnomusicological ramifications of these findings.

Recent work on metric theory by Christopher Hasty, Harold Krebs, Justin London, and others has shifted focus towards phenomenal aspects of meter rather than the categorization of metric types. Admirably, these authors emphasize meter’s emergent properties, yet even these recent approaches understate the distinctions between rhythmic notation (“musical time”) and performed durations (“real time”). In this presentation, I will engage performed durations in a novel way through a discussion of entrainment, the synchronization of a listener to (real) periodicities in the environment. Because entrainment facilitates cooperative behavior and reduces mental processing demands, enabling or resisting entrainment can be a powerful expressive tool for performers and composers. The presentation will focus on a rendition of the phrase of Chopin’s Mazurka in G major, Op. 50, no. 1, wherein the alternation between metrically entrainable and disorienting presentations of musical material create a kind of narrative in an opening that might appear metrically unremarkable.

By attending to the durations of performed renditions, rather than notated proportional representations, I hope to demonstrate that the contrast between entrainment and disorientation (i.e. “metric dissonance”) is a feature not of exceptional pieces by certain composers, but rather an affordance of the unique durations of events in individual renditions. Recent decades of music scholarship have seen a broad move towards accepting performers as co-producers of musical meaning and in this presentation I hope to continue that trend by formulating more precisely how and when performers afford metrical experience.

Is there something wrong with the finale of Schubert’s Wanderer Fantasy? There is considerable scholarly consensus that finale is not sufficient to “close the deal.” Dunsby points to its many disassociated elements (2005:47), while Adorno views the finale’s shortcomings as symptomatic of a larger problem in Schubert’s output. (1928/2005:12) Newbould goes even further, suggesting that Schubert had a “finale problem.” (1997:183) Tovey, writing of the Liszt solo piano transcription of the finale, amazingly describes it as “more Schubert than Schubert,” as if Liszt’s recomposition succeeded in fulfilling Schubert’s poorly- executed conception. (1946:57) The Liszt edition of the Wanderer, published in 1868, presents an exceptional case of compositional criticism—a solo piano transcription of a solo piano piece. The finale is presented in two complete and separate versions, the first entirely by Schubert, the second recomposed by Liszt. Was Liszt merely adapting the movement to his innovative pianistic aesthetic, or was he trying to “fix” it?

After a comparison of both finales, I briefly examine a similar, but more recent case, Busoni’s transcription of Schoenberg’s Klavierstück, op. 11 no. 2. Schoenberg’s response to Busoni’s transcription was that the “overly flattering” variety of piano textures obscured the clarity of his musical ideas (Beaumont, 1987:386). One can imagine Schubert responding similarly to Liszt, who may indeed have been trying to fix the finale’s textural awkwardness. Lastly, I demonstrate, through live performance, the great success of Schubert’s Wanderer finale. My aim is to offer insight into how we may better understand Schubert’s completion strategies, particularly in his late works.

In 1861, Liszt left Weimar, center of the New German School, for Rome, a largely musically underdeveloped city. This marked a significant turning point in his compositional style as experiments in form and genre were replaced by experiments in harmony and tonality. Many of these late works remained unpublished until the Liszt Society Publications (1950-1978). A first wave of scholarship followed, emphasizing radical surface features. A second wave of scholarship included methodologies as diverse as dissonant prolongation, pitch-class set analysis, Schenkerian analysis, and Neo-Riemannian modeling. These diverse approaches often focus on a small subset of the repertoire and foster the misconception that there is one experimental type progressing from tonality to atonality. In reality, Liszt’s “experimental style” is difficult to define due primarily to a variety of harmonic languages. There appears to be no chronological progression from tonality to atonality.

This paper offers an approach to understanding the stylistic diversity and tonal anomaly of Liszt’s late experimentation by proposing five categories based on chord inventory and functional weakness. Category 1 is characterized by functionally weakened local cadences, Category 2 by globally-weakened tonic functions, Category 3 by globally-weakened dominant functions, Category 4 by globally weakened tonic and dominant functions, and Category 5 by non-tertian sonorities. The five categories are unified through shared weakening devices, structural deviations from Common-Practice norms that create tonal anomalies. These include chord rotation, rhythmic displacement, transference of the Urlinie to the bass voice, and “centralized cadences,” structural cadences placed near the exact center of a piece.