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Jazz: Improvisation/Polyrhythm

Keith Waters (University of Colorado Boulder), Chair

Composition, Improvisation, and Macroharmony in Henry Threadgill’s Sixfivetwo

Guy Capuzzo (University of North Carolina Greensboro)

bio for Guy Capuzzo

Guy Capuzzo (Ph.D., Eastman School of Music) is Professor of Music Theory and the author of the book Elliott Carter’s What Next?: Communication, Cooperation, and Separation (University of Rochester Press, 2012). He is a former associate editor of Music Theory Spectrum and an editor of Elliott Carter Studies Online. His writings appear in Journal of Music Theory Pedagogy, Music Theory Spectrum, Journal of Music Theory, Music Theory Online, Intégral, Theory and Practice, Tempo, and Guitar Review. Capuzzo’s talks include presentations to the Society for Music Theory and invited lectures at Yale University, the University of South Carolina, the University of Minnesota, and Youngstown State University. Active as an electric guitarist, he performs and records with the Lorena Guillén Tango Ensemble.


The music of Henry Threadgill (b. 1944), African-American composer/performer and 2016 Pulitzer Prize winner, strikes an innovative balance between composed and improvised elements. His influences include his activities with the Association for the Advancement of Creative Musicians (AACM), and the music of Varèse, and Carter. Threadgill’s music raises an interesting question about the coexistence of African-American and European traditions in 21st-century music: What methods might analysts use to describe the interaction between harmonic organization and improvisation in non-tonal settings? Building on work by Chad Taylor, Gareth Keany Hill, and Matthew Forker, I contend that attention to macroharmony will begin to answer this question. I use the discrete Fourier transform (DFT) to interpret macroharmonies and their harmonic qualities in Sixfivetwo (2018) for string quartet.

The picture that emerges from the paper’s analytic examples is one of striking coordinations between improvisation and composed harmonic structure. Macroharmony and the DFT offer a way to probe the interaction of harmonic organization and improvisation in Sixfivetwo. The results may lead to a deeper understanding of the music of a composer/performer described by the Pulitzer committee as “among the most important artists in jazz.” More broadly, the results may improve our understanding of other nontonal music in which composition, improvisation, European elements, and African-American elements play equal roles, particularly that of other AACM luminaries such as Anthony Braxton and George Lewis.

Supplementary Material(s)

Salience, Triads, and Transformational Counterpoint in Robert Glasper’s Improvisation on “North Portland”

Rich Pellegrin (University of Florida)

bio for Rich Pellegrin

Rich Pellegrin is Assistant Professor of Music Theory at the University of Florida and Affiliate Assistant Professor in the Center for Arts, Migration, and Entrepreneurship. His work has been published in Jazz Perspectives, Engaging Students, the Journal of Schenkerian Studies, and in volumes by Cambridge Scholars Publishing and KFU Publishing House. Active as a jazz pianist and composer, Dr. Pellegrin’s fifth album for Origin Records will be released in April.


This presentation examines the relationship between salience and stability in a performance by Robert Glasper. Triadic voicings such as slash chords, upper structures, and “So What” chords are highly idiomatic in jazz. The triads are salient in these voicings due to their placement in the upper register, but are usually unstable, being composed mostly or entirely of upper chord tones. Triads may be used similarly in melodic improvisation, where they are more salient than comping chords or rhythm section accompaniment. Because there are so many varieties of triadic voicings, a given triad may be used to realize numerous harmonies. When triadic voicings are used successively, they may form transformational pathways that are worthy of study in their own right. Moreover, such transformations may counterpoint those of the stable, lower chord tones in significant ways. 

“North Portland” is a typical Glasper composition in its lack of a clear tonal center, its avoidance of dominant harmonies, its tertian melodic structures, and its emphasis on S and LP/PL transformations. Glasper’s improvisation on the tune is replete with triadic transformations in the right-hand melodic line that interact compellingly with those of the underlying form, exemplifying the concept of transformational counterpoint. The metric counterpoint between the salient and stable levels is also explored.

Supplementary Material(s)

“Pulling Apart” and “Floating Above”: Cross-Rhythmic Metric Divergence in Jazz Improvisation

Sean R. Smither (The Juilliard School)

bio for Sean R. Smither

Sean R. Smither received his Ph.D. in music theory from Rutgers University and also holds an M.A. from Rutgers and a B.F.A. in jazz drumming from the New School for Jazz and Contemporary Music. His research interests include jazz analysis, improvisation, transformational theory, and music cognition. His dissertation, “Conceptualizing Tunes: Avant-Textes , Referents, and the Analysis of Musical Structure in Jazz,” explores the ways in which jazz improvisers conceptualize musical structure. His research has been published in Music Theory Online , Theory and Practice, and Jazz Perspectives, and he has presented his work at conferences throughout North America. He teaches jazz theory at the Juilliard School and theory and analysis courses at Rutgers University.


Theorists have long been fascinated by the rhythmic and metric particularities of jazz improvisers. Much of this fascination has centered around those aspects of rhythm that are not easily notatable, especially expressive microtiming, rubato, and cross-rhythm. Among the chief distinctions that can be made between such techniques is whether they occur at or below the syntactical level. While participatory discrepancies—slight deviations from an idealized prototypical tactus that compound when musicians play together—mostly fall below the level of musical syntax, microtiming can also inflect larger utterances on the syntactical level, creating gestures that stimulate group interaction.

In this paper, I examine the relationship between jazz interaction and two expressive metric devices,  “pulling apart,” and “floating above”, both of which involve the simultaneous sounding of two conflicting pulse streams. “Pulling apart” refers to moments when improvisers’ delays or anticipations suggest a slowing or quickening of tempo that conflicts with the prevailing tempo, resulting in a temporary disconnect that produces microrhythmic ambiguity before eventually resolving. “Floating above” occurs when an improviser’s utterance is untethered from the groove projected by the rest of the ensemble. I argue that such utterances arise from the interactional matrix of jazz improvisation and are therefore best analyzed using theories of improvisational interaction. As irreducibly interactive gestures, instances of metric divergence are a product of the Afrological orientation of jazz improvisation; by considering these metric techniques to be fundamentally dialogic, I seek to highlight the symbiotic relationship between elements of metric divergence and cultural aesthetics.