Sunday morning, November 15, 11–11:50 CST

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John Y. Lawrence (University of Chicago), Chair

Chord Spacing and Quality: Lessons from Timbre Research

Matt Chiu (Eastman School of Music)

Matt Chiu is a Ph.D. student at the Eastman School of Music. Prior to Eastman, Matt received degrees from Boston University (MM) and the University of Connecticut (BM). His recent interests connect computational models to perception, drawing on the interdisciplinary aid of natural language processing, audio engineering, and machine learning.

Noah Kahrs (Eastman School of Music)


In describing the opening of Debussy’s La Cathédrale engloutie as “an open fifth,” one strips the chord of its distinct character; although octave equivalence may seem innocuous, listeners often notice spacing more than PC content. To quantify this seemingly intangible quality, this paper extends the Discrete Fourier Transform (DFT) theory of chord quality from PCsets to Psets. The DFT has several common musical uses. Applied to audio, it identifies pitches, but a second DFT can be applied to this spectrum, yielding the “cepstrum” engineers use to describe timbre. In music theory, the DFT measures interval content in PCsets. This paper’s model, the pitch-DFT (P-DFT) lies between these approaches, considering note data without octave equivalence. By identifying regularities in P-space, the P-DFT analyzes quality in terms of chord spacing.

This paper has two primary sections: (1) introduction to the DFT and contextualization of its uses in both music theory and engineering; and (2) an analytical vignette of La Cathédrale engloutie, demonstrating that an approach using the P-DFT may more closely resemble our perceptual experience. In taking up Hasegawa’s (2019) call to “bring concepts from the world of timbre to the study of harmony,” this example shows that even basic tonal sonorities can be productively analyzed with methodologies used most often in other domains. By fusing music theory’s PCset analysis and timbre research’s cepstral methods, the P-DFT succeeds in examining chord spacing, which lies between pitch-class and timbre.

Janáček’s Virtual Viola d’Amore

Ethan Edl (Yale University)

Ethan Edl is a PhD candidate in Music Theory at Yale University. His dissertation, titled "Leoš Janáček and the Aesthetics of Attention," proposes fresh analytic perspectives on Janáček's music by contextualizing the composer's music and thought within early 20th-century discourses of attention, psychoacoustics, and the phenomenology of time.


Leoš Janáček frequently wrote for the viola d’amore, yet his music demonstrates a dubious understanding of the instrument’s unique affordances. What maintained the composer’s fixation on this archaic instrument, since none of Janáček’s works were performed with a viola d’amore in his lifetime? While existing scholarship generally begins (and ends) with the instrument’s name and the imagery it evokes, I explore some more tangible sources that might shed light on Janáček’s use of the viola d’amore, specifically the organ stop of the same name, and the suggestive correlations between the instrument’s construction and the composer’s idiosyncratic theories of harmony. Close readings of several musical examples reveal a consistent cluster of sonic effects which amplify or exaggerate certain aspects of the instrument, even as the viola d’amore part is paradoxically ill-suited for performance on the instrument itself. Recent scholarship has trained a critical lens on how instrumental technics inform compositional practice (De Souza 2017). As a case study, Janáček’s viola d’amore motivates an inquiry into the many forms of knowledge that might structure an encounter with an instrument one does not play. To address the gap between the “viola d’amore” in the composer’s scores and the viola d’amore as a sounding instrument, I propose thinking of Janáček’s viola d’amore as a qualified kind of virtual instrument, in the literal sense of emphasizing certain virtues of the instrument. This formulation invites us to attend to the gaps in knowledge and productive (mis)readings made possible by naïve encounters with musical instruments.

The Acoustic Properties of Tanya Tagaq’s Vocal Sounds as Situated on Timbral Continua

Kristi Hardman (The Graduate Center, CUNY)

Kristi Hardman is a Ph.D. candidate in music theory at the Graduate Center, City University of New York. She holds bachelor’s degrees in music and education from the University of Manitoba and a master’s degree in music theory from the University of British Columbia.

Currently, she teaches music theory at Hunter College in New York. Kristi also serves as an associate editor for the Analytical Approaches to World Music journal. She has presented her research at numerous conferences, including the Society for Ethnomusicology, Analytical Approaches to World Music, the College Music Society, and IASPM. Her research interests include Indigenous music made in North America, popular music, computational analysis, timbre, rhythm and meter, text/music relations, and issues of transcription, all of which she is working to incorporate into her dissertation.


Tanya Tagaq is an experimental vocalist originally from Cambridge Bay, Nunavut, who regularly employs Inuit katajjaq (throat singing), as well as screams, moans, cries and whispers. Tagaq describes katajjaq sounds in two ways: (1) by inhalation or exhalation, and (2) as a low, deep growl or a high, pure pitch. Her description focuses on sound qualities, indicating an importance of timbre in her music. In contrast to the oppositional way that Tagaq categorizes these sounds and the timbral opposition charts of Cogan (1984), this paper suggests that the acoustic properties of Tanya Tagaq’s vocal sounds are best situated on a continua of relative values for various acoustic properties, allowing for a more in-depth comparison of the sounds.

Computer-assisted acoustic measurements show noticeable differences between all sounds used by Tagaq. First, I analyze recordings of Tagaq’s solo singing with Sonic Visualiser plugins for RMS energy (loudness), periodicity (noisiness), and spectral centroid (brightness). From this data, I establish the central tendency values for Tagaq’s sounds using descriptive statistical analysis. Based on this analysis, I construct continua of the acoustic properties of these sounds—a continuum of loudness, of noisiness, and of brightness. These continua provide a nuanced way of describing the subtle, but important, differences between Tagaq’s sounds. This exploratory method of analyzing the acoustic properties of musical sounds is not only useful for Tagaq’s vocal style but could also be applied to any other music using “extended” techniques where timbre plays a significant role.