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Salons 5–7 • Saturday morning, 9:00–12:00

Poster Session

Philip Duker (University of Delaware), Chair

Alexander Amato (Stephen F. Austin State University)

Hindemith’s Harmonic Fluctuation and Obscured Tonality in Satie’s Nocturnes

André Brégégère (Queensborough Community College, CUNY)

Some Thoughts on Maximally-Smooth Voice Leading Among Pcsets and Set Classes

Niels Chr. Hansen (The Ohio State University)

Twirling Triplets: What Makes Music Spin?

David Kant and Larry Polansky (University of California Santa Cruz)

The Shape and Structure of Musical Contour Space

Jeremy M. Robins (Florida State University)

Defining Phrases in Popular Music

Nicholas J. Shea (The Ohio State University)

Meter in French and Italian Opera, 1809–1859

Abstracts

Hindemith’s Harmonic Fluctuation and Obscured Tonality in Satie’s Nocturnes

Alexander Amato (Stephen F. Austin State University)

To accommodate the elaborations of harmony and tonality that characterized many twentieth-century musical styles, Paul Hindemith (1895-1963) stated that it is not the scalar context of chord roots that initiate tonality, but rather the juxtaposition of the chords’ constituent intervals (Hindemith 1942). As part of his compositional practice, he devised a system of measuring dissonance and tonal force in harmonies, classifying them by intervallic content into six groups of graduating dissonance while discounting the scalar context of the chords’ roots. He coined the term harmonic fluctuation for varying levels of dissonance between adjacent harmonies. Recent analyses employing harmonic fluctuation (Harrison 2016) show that it can be an important component, if not the main component in the analysis of many post-tonal styles, being adaptable to many musical contexts.

Intervals also played a key role in Erik Satie’s composition of his Nocturnes (1919) for solo piano. Satie departed from his practice of parodying earlier styles and shifted to a more serious compositional style in the Nocturnes by largely abandoning functional harmony and systematically using intervals as the basis for his harmonic language, and this is evident in the works’ sketches. Taking into account the favoring of intervals in both Hindemith’s and Satie’s construction methods, this study will trace the evolution of Satie’s use of chromaticism and obscured tonality in his Nocturnes by utilizing harmonic fluctuation.

Some Thoughts on Maximally-Smooth Voice Leading Among Pcsets and Set Classes

André Brégégère (Queensborough Community College, CUNY)

The study of voice-leading among pitch sets and pitch-class sets has been a prominent topic of music theory in the past twenty years. A variety of approaches, focused on harmonic similarity, transformational networks, or parsimonious voice-leading, have more recently been subsumed under a geometrical model based on a mapping of pitch or pc sets onto dimensional coordinates using the semitone as a metric. These developments have led to some early attempts to establish a general typology of voice-leading sets (vlset) and voice-leading classes (vlclass), as a higher-level analog to the pc-set and set-class typologies.

My paper examines vlsets and vlclasses from a purposely narrowed perspective, limited to instances of Maximally-Smooth (MS) voice leading—i.e., wherein motion between pcs is limited to one semitone. I show that there exist, for each cardinality, only a relatively limited number of MS-vlsets, and an even smaller number of MS-vlclasses. Focusing initially on pcsets and set-classes of cardinality two and three (including multisets), I examine the properties MS- vlsets and vlclasses, corresponding to various types of relations (T/I, K-net isographies, constant sums), and explore the various geometrical features of the resulting voice-leading spaces. I then extend these observations to other cardinalities, and conclude with suggestions for a unified, systematic typology of MS-vlsets and vlclasses for all cardinalities.

Twirling Triplets: What Makes Music Spin?

Niels Chr. Hansen (The Ohio State University)

While music scholars have long noted that triplets evoke sensations of spinning or rotation in listeners (Jankélévitch, 1961; Mellers, 1954), this topic has not been subject to theoretical development or empirical scrutiny.

Addressing this question, we first solicited musical examples “connoting spinning, rotating, twirling, or swirling” using SMT Discuss. Analysis revealed a prominence of fast, repeated, isochronous patterns employing stepwise pitch movement and compound meters.

To explain these associations, we devised an Ecological Theory of Rotating Sounds (ETRoS) inspired by ecological acoustics (Gibson, 1979). Specifically, listeners acquire sensitivity to continuous fluctuations in location, pitch, and dynamics emitted by rotating sound sources. Whereas immobile musical instruments producing discrete pitches render location and pitch cues largely unavailable, loudness changes remain pertinent. ETRoS posits that stress patterns for binary (strong-weak) and ternary (e.g., strong-weak-weak) rhythms are consistent with a spinning trajectory, unlike archetypal quaternary or quinary patterns (e.g. strong-weak-medium-weak, strong-weak-medium-weak-weak). For binary rhythms, however, ecologically simpler, pendular representations may be cognitively preferred (Chater & Vitányi, 2003).

Two perceptual experiments tested ETRoS. Participants in Experiment 1 rated how much binary, ternary, quaternary, and quinary figures evoked sensations of rotation. Experiment 2 used a two-alternative forced-choice paradigm pitting ecological quaternary stimuli (strong-medium-weak-medium) against unecological ones containing the strong-weak-medium-weak pattern more typical of Western music. Our results show greater perceived rotation for ecological patterns, for faster tempi, and for ternary/quaternary/quinary compared to binary stimuli.

In conclusion, ecological acoustics provides a plausible explanation for the musical qualia of rotation, potentially explaining why composers resort to triplet/compound rhythms.

The Shape and Structure of Musical Contour Space

David Kant and Larry Polansky (University of California Santa Cruz)

Musical contour remains an active topic in music analysis, ethnomusicology, music cognition, and composition. Different strains of contour theory have employed various formulations and tools to categorize and measure contour. Contour is succinctly described as the sequence of ups and downs, or changes in direction rather than the magnitude of those changes, in some musical feature: melody, rhythm, or even sound spectra, from the shortest gesture to larger forms.

Our work examines the structure of contour space, using new mathematical and computational tools. We refigure contour as a quotient space, introducing a general definition of contour as equivalence class on the space of possible contours. This representation unifies various contour representations, presents a generalized mathematical model, and suggests new tools for understanding contour.

We develop a geometric interpretation of contour space and its enumeration that reveals combinatorial contour as a highly structured lower-dimensional subspace of linear contour space. Through a change-of-basis, we construct a coordinate system specific to combinatorial contour, which allows us to work directly with and only with combinatorial contours. Continuing, we offer a comparative analysis of existing contour definitions by representing them as quotient spaces, and we examine their relation to other mathematical measures. We find that most contour metrics (Morris’ and Marvin and LaPrade’s CSIM, Quinn’s C+SIM, Polansky’s OCD) correlate closely to cosine (angular) distance. This leads to a formulation of contour in terms of polar coordinates, where angle expresses difference in shape and magnitude difference in scale, creating a theory that unifies magnitude and contour.

Defining Phrases in Popular Music

Jeremy M. Robins (Florida State University)

Phrases in common-practice music are traditionally defined by harmonic processes, particularly goal-directed progressions to tonic. In popular music, however, harmonic motion toward a tonic is not always present, making traditional approaches to phrase segmentation problematic. This paper presents a methodology for phrase segmentation using melodic activity that can be applied to a broad spectrum of popular music.

Inconsistency in methodology between scholars highlights the analytical challenge of phrase segmentation in popular music. Applying the three primary criteria cited by scholars–unified melodic activity, goal-directed motion, and vocal breath/rest–can result in conflicting segmentations for the same musical excerpt. My methodology delineates phrases by melodic activity, specifically repetition and contrast between subphrases, and is modeled after phrase-structure research by Caplin (1998), Callahan (2013), and Richards (2016). Resulting common phrase paradigms include various sentence types, repeated subphrases, and rotated subphrases. Composite structures include periods, double periods, repeated phrases, modified repeated phrases, and rotated phrases.

The primary goal of this research is to provide a systematic method that lacks ambiguity or ad hoc parameters for phrase segmentation. This approach provides consistent results, is applicable to music featuring recurring chord loops, allows for a detailed consideration of phrase structures across the variety of popular music styles, and opens the door to research into the interaction of phrase structure and large formal units.

Meter in French and Italian Opera, 1809–1859

Nicholas J. Shea (The Ohio State University)

Current and historical methods of metric analysis often assume that the first beat of a metric group is stronger than the second. This, however, is not the case in all repertoires. For example, a study by William Rothstein (2011) demonstrates that Verdi’s midcentury operas often place emphasis on even-numbered beats. This paper shows this metric trend to be even more prevalent in a corpus of 200 nineteenth-century operatic excerpts, (1809-1859).

I present a formal model that classifies phrases according to anacrusis length and prosodic accent, showing where large-scale metric accents fall within a phrase. This model produces three metric types which align with Rosthstein’s (2011) previous work. Compositional and historical features (e.g., language, premiere date, librettist, etc.) were tracked alongside type in order to determine whether preferences for certain metric forms were more prevalent in certain contexts. This indeed was the case. For instance, use of even-emphasis meter increases over time, even though odd emphasis meter remains most common. Individual composers also show a significantly distinguishable preference toward each type of meter. These results not only confirm that the highest concentration of even-emphasis meter occurs in Verdi’s midcentury operas (Rothstein 2011), but that Verdi is the primary user of this type overall. I also demonstrate that language and composer nationality do not significantly affect an excerpt's metric type; only Verdi shows distinction in these areas. With this finding, I argue against using nationalist language to identify metric types and instead propose suggestions that better reflect an updated understanding of nineteenth-century metric conventions.