On Duration and Developing Variation: The Intersection of Bergson’s Time and Free Will with Schoenberg’s Sechs kleine Klavierstücke Op. 19
Keith Salley, Shenandoah University

Abstract: Many authors have addressed Schoenberg’s philosophical influences, but few have addressed the philosophy of Henri Bergson. This presentation takes a close look at Bergson’s Time and Free Will (1889), a popular treatise owned by Schoenberg that introduces the concept of Duration. I present several analytical readings from op. 19, a collection written shortly after publication of that treatise’s German translation. These analyses show how Bergson’s Duration is reflected in op. 19, and support my claim that this reflection represents a significant innovation in developing variation.

Space, to Bergson, is a homogeneous medium where objects have discrete borders and measurable distances between them. Linear conceptions of time are misguided mappings of event successions onto spatial metaphors. Time—perceived by the subject—is intrinsically different from space, where “objects” of time are perceived in Duration as interpenetrating conscious states whose borders are fuzzy at best, and the intervals between them are ultimately immeasurable.

Taking Schoenberg’s and Frisch’s writings on developing variation as points of departure, I argue that Schoenberg’s interpenetrating motives and evocations of subjective time are significant innovations in developing variation, and furthermore, that Begson’s Duration helps us understand exactly how they are innovative. In this way, Bergson’s Duration enables us to conceptualize motivic transformations as subjective phenomena. We can therefore appreciate developing variation reflectively, understanding changes in a motive or gesture as different perspectives of the same moment of time—rather than objectively, regarding those changes in a teleological sense.

Ebb and Flow: Rhythm and Temporality in Unmetered Music by George Crumb
Kristina Knowles, Northwestern University

Abstract: Twentieth-century composers experimented not only with the organization of pitch structures, but also with rhythmic and metrical structures. Yet research exploring these latter elements is limited in scope. My paper aims to expand theories of rhythm and meter to explore the relationship between these musical elements and temporality in unmetered music. I define “unmetered” music as lacking both a consistently notated meter provided by the composer and a consistently present underlying pulse that can be perceived by the listener. This repertory allows the composer to manipulate the listener’s perceived passage of time through the organization of, and the relationship between, rhythmic and metrical elements.

I identify a set of mechanisms used by composers which contribute to fluctuations in the listener’s perceived passage of time. These mechanisms are grounded in psychological studies addressing influences on the perception of time passing. Through a set of analytical vignettes focusing on the work of George Crumb, I show how the repetition of certain rhythmic motives, the presence of competing pulse streams (Roeder 1994; 2001) and the occurrence of metrical emergence and dissolution (Horlacher 1995) can be used to manipulate the perceived passage of time within the music. By developing a theoretical framework that emphasizes the interaction between rhythmic and metrical elements and our perceptual experience of time, I demonstrate how composers can and do systematically manipulate time in unmetered music.

The Hunt for Form in Wolfgang Rihm’s String Quartet no. 9 “Quartettsatz”
Robert Baker, Catholic University of America

Abstract: Wolfgang Rihm’s ninth string quartet, “Quartettsatz” (1993), is a prime example of his compositional style of the past two decades, and represents a body of work that has gone largely unanalyzed. Joachim Brügge’s overview of the string quartets, and Richard McGregor’s writing on portions of the Chiffre-Zyklus (1982-88) offer a valuable beginning to understand Rihm’s work, but more detailed analysis is required to make a stronger correlation between techniques and formal properties evident in the score and Rihm’s own statements on his compositional philosophies and approaches, two of which most relevant to this study are: a sound following a different sound in time, truly transforms its predecessor; and, the act of composing is itself a hunt for the form.

In this paper I employ a quasi-paradigmatic analysis to show details in pitch and phrase structure in the first major section of Rihm’s ninth string quartet, “Quartettsatz” (1993). The results reveal a musical form that bears two principal features: one, a quasi-cyclical process of three principal elements that recur in varied form, suggesting alternate possible outcomes based on their newly transformed states; and two, a gradual abating of this cyclical process giving way to a rising dominance of a second musical idea. This reading draws a correlation between Rihm’s comments and his compositional techniques, revealing a decidedly unique musical form; one that appears to be constantly transforming and hunting for itself.

Pathways to Compositional Autonomy: The Emancipation of the “Triad” in Howard Hanson’s Symphony no. 6
Mark Parker, Bob Jones University

Abstract: More than fifty years have passed since the publication of Howard Hanson’s Harmonic Materials of Modern Music: Resources of the Tempered Scale in 1960, and until recently this comprehensive compendium of “sonorities” has received virtually no consideration by music theorists except as a footnote crediting it as a forerunner of the pitch-class systematizing of Allen Forte (1964, 1973 f.). However, misconceptions regarding the scope and content of Hanson’s work as a theorist have since been addressed (notably by Allen Cohen in Howard Hanson in Theory and Practice, Praeger, 2004) and, as a result, certain of Hanson’s notions have been recognized to be progenitors of ideas later developed by Forte, Rahn, Lewin, and Quinn.

Hanson’s classification of pitch material, while lacking the rigor and abstraction of a mathematically-based set theory, has a breadth and elegance of its own. Intended as a tool for composers, Hanson’s book perhaps is best appreciated in this light. If understood on its own terms, it provides insights into the compositional processes of Hanson and others through its elucidating of relationships that are readily accessible precisely because they are concretely stated. Hanson’s pathways of compositional discourse include: 1) a motivic usage of involutions (mirror inversions of pitch-class sets); 2) the expansion of basic sonorities through the projection of intervals; 3) a structural role of isomeric sonorities (Forte’s Z-related pairs). The idiosyncratic though not unique implementation of these and other techniques in Symphony No. 6 proclaims the compositional voice that is universally recognized to belong to Howard Hanson.

Crossing One’s Fingers: Gestural, Textural, and Rhetorical Chiasmi in Works for Violoncello
Daniel Stevens, University of Delaware

Abstract: Studies of musical embodiment and performance analysis tend to focus on piano music and its performance. This paper seeks to expand this focus by asking how the physical gestures associated with a non-keyboard instrument—specifically, the violoncello—may be thought of as compositionally generative. As a starting point, I take the crisis found in the Prelude of Bach’s First Suite for Violoncello in G Major involving a contrapuntal dissonance that cannot resolve properly due to the lower limit of the cello’s range. In context, this crisis results from a large-scale inversion of the opening tonic triad, and it frustrates a repetition of this opening’s upper neighbor prolongation. Importantly, these structural features fit naturally with the gestures employed while performing the Prelude. From the first measure, the changing angle of the bow as it moves across the upper three strings of the cello creates a composite “X” in space. The undulating rise and fall of the bow seem to motivate the pitch transfers and harmonic inversions that unfold across the piece.

Next, I examine textural and rhetorical chiasmi in works by Shostakovich (first Cello Concerto), Carter (Sonata for Violoncello and Piano), Sessions (“Berceuse” from Six Pieces for Cello), and Babbitt (Dual) to suggest avenues for future research. In the Shostakovich, Carter, and Babbitt, large-scale exchanges of material between cello and piano/orchestra are composed out in strikingly different manners and with different contextual significances. Sessions’s “Berceuse,” by contrast, invites us to consider the mimetic associations of the cellist’s gestures.

1:45–3:15

Schema and Prototype

The Second-Reprise Medial PAC and the Form of Bach’s Binary Dance Movements
Christopher Brody, Indiana University

Abstract: This paper argues for a complication of the two-phrase/three-phrase classification system for Bach’s binary dance movements proposed by Charles Rosen and Joel Lester. I show that an overwhelmingly pervasive feature of those movements (present in 85% of all examples) is a nontonic PAC midway through the second reprise (medial PAC). While in three-phrase binary movements this nontonic PAC divides the second reprise’s two phrases from each other, in two-phrase binary movements the medial PAC intrudes within a single rotational span, creating a generically mandatory disconnect between the movement’s cadential structure and its thematic design. Therefore, while the three phrases of a typical minuet may fairly closely track the thematic layout of the first reprise, the second reprise of a two-phrase movement unavoidably must be rewritten to accommodate a nontonic PAC about halfway through. In addition, the reprise-length and thematic-repetition criteria by which two- and three-phrase movements are distinguished from one another are at times inconclusive, as in the Menuet from Bach’s B-flat major Partita. Consequently, I argue that these classifications are less rigid categories than the endpoints of a spectrum along which pieces may be situated.

Chord Types as Metric Determinants, Syncopation as Surprise
Christopher White, University of North Carolina – Greensboro

Abstract: Meter, at least in the common practice, is often defined as a recurrence of some kind of accent.  Metric dissonance, as an extension of this idea, tends to be formulated as either a deformation (extension, diminution) of an underlying pattern, or the overlaying of a second pattern—a dissonant metric layer—against the fundamental consonant pattern In contrast, I will show that meter can be determined by observing the periodic rise and fall of musical probabilities (i.e., the likelihood of particular chords, scale-degree sets, rhythmic durations, etc. occurring in particular contexts) throughout a passage of music. Instead of focusing on predicting events occurring at all—i.e., being able to predict the periodicity of any event onset—I will argue that the corpus-derived probabilities of musical events recur with certain periodicities. I will propose a novel definition of meter: meter is not just the periodic and predictable recurrence of accented events such as louder attacks, pitch onsets, or harmonic changes, but rather is the recurrence of a series of higher and lower event probabilities at constant periodicities.

Based on this model, I will argue for a related definition of metric dissonance. Using new computational and psychological research, I will argue that metric dissonances occur when an event’s probability does not align with expectation. Unlike traditional music theories, my conception of meter considers events dissonant if they conflict with expectations of probability periodicity.  Such a theory not only brings a new subtlety to the idea of metric dissonance as it represents events as more or less dissonant using a sliding probabilistic scale, but also potentially formalizes the differences between types of dissonance (e.g., hemiola, displacement) from a corpus-based perspective.

Playing With Schemata
Janet Bourne, Northwestern University

Abstract: Agawu (1991) suggests that composers create “play” by placing topics (conventional signs; Monelle 2006) together. Regarding Beethoven’s use of horn fifths to begin Lebewohl, Caplin (2005) responds that the “play” comes from “specific musical parameters” and not the topic (122). Lebewohl also begins with a Mi-Re-Do schema (conventional voice-leading pattern; Gjerdingen 2007). Associated with ending formal function, the Mi-Re-Do as a beginning is marked (not the topic), creating “play.” Scholars analyze topics and schemata separately even though these patterns often co-occur in eighteenth-century music. Both patterns provide information; for example, schemata may provide topics with formal function and topics may provide schemata with extra-musical association. How do topics and schemata interact? When do topics include schemata and does this create different classes of topics?

I devise a continuum for: analyzing interactions between topics/schemata, sorting classes of topics, and implying when topics are troped and/or marked. On the continuum, the X axis reflects variation in musical parameters: musical passages based on primary parameters (pitch-melodic-rhythmic) on the left and passages based on secondary parameters (figuration-texture-timbre-etc.; Meyer 1989) on the right. Though topics are often defined by secondary parameter features, some topics, by definition, require voice-leading material, creating topic/schema combinations in the middle of the continuum. I use this methodology on three topics/schemata in Mozart, Haydn, and Beethoven: 1) horn fifths (horn-call topic and Mi-Re-Do schema), 2) lament bassline (descending bassline schema and lament topic), and 3) Stabat Mater Prinner (Prinner schema and church style). This research looks at how topics/schemata create “play.”

Pitch Centricity Without Pitch Centers
Stanley Kleppinger, University of Nebraska

Abstract: Pitch centricity is commonly understood as the effect of perceptual focus upon one pitch class above all others in a given musical context. From this vantage point, Western music of approximately the last century is often casually classified in two ways: either it projects no pitch center, or it engenders pitch centricity via continuation of common-practice techniques or new, divergent methods. But lost in this dichotomy is a third potential class of post-common-practice repertoire: music that coaxes the listener into associating the music with pitch centricity without fostering certainty about what its pitch center might be. Often in music by Copland, Bartók, and others, the question “What is the pitch center of this passage?” seems the right question to ask, yet consensus among listeners about the identity of that center is virtually impossible to reach. This scenario contrasts with non-pitch-centric musical contexts, where the question “What is the pitch center of this passage?” may seem irrelevant rather than only perplexing.

This paper speculates that certain common-practice tonal elements catalyze the “listen-for-pitch-centers” mechanism of the auditory process, even in those cases where identifying a certain pitch center is a difficult or impossible task. This line of thought highlights the importance of distinguishing between pitch-centric listening and pitch-center identification: the former may exist without the latter, and the gap between them is an essential stylistic feature for much music of the last century. This paper advocates recognizing that gap and its analytic consequences in several relevant excerpts.

Exploring Polyscalarity in the Music of Igor Stravinsky: Discerning Surface- and Deeper-Level Scalar Collections
Aaron Grant, Eastman School of Music

Abstract: Since Arthur Berger’s 1963 article “Problems of Pitch Organization in Stravinsky,” a host of studies has emerged concerning Stravinsky’s use of scalar collections. Most established analytical traditions view Stravinsky’s work entirely in terms of octatonic and diatonic interactions, often ignoring notes in order to fit the music into these two collections. Tymoczko’s 2002 study, however, revealed the ambiguity of affiliation that exists within any collection of pitches, showing that Stravinsky’s music is better understood as exhibiting polyscalarity, rather than simply diatonic and octatonic collections.

Although Tymoczko’s study brought about a reformed view of Stravinsky’s music, the theoretical underpinnings and analytical ramifications of polyscalarity remain unexplored. If a single pitch collection can project a variety of scales, under what conditions can the interaction of multiple collections project a single scale? Furthermore, what are the criteria for segmenting pitches on the musical surface into different scalar collections?

This study explores these questions in three parts. Part 1 establishes the theoretical backdrop for the study, examining how surface- and deeper-level scalar collections interact in polyscalar music. Part 2 provides analytical support, showing that this methodology not only allows for more nuanced interpretations of Stravinsky’s music than traditional methodologies, but also aids in connecting seemingly disparate passages. Finally, part 3 demonstrates how this theory aligns with Gretchen Horlacher’s theory of ordered succession.