Saturday morning, November 7, 10–10:50 CST

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Meter and Time Poster Session

Rebecca Jemian (University of Louisville), Chair

Connoted Semibreves in Pre-Franconian Theory

Kaho Inoue (Tokyo University of the Arts)


Most pre-Franconian works deal with semibreves ambiguously despite their stress on longs and breves, although two forms of semibreves, the minor and the major, were proposed by Lambertus (c. 1270) and disseminated by Franco of Cologne (c. 1280). However, this does not mean that pre-Franconian theory ignores semibreves; it instead tends to explain this note value without explicitly using the term “semibreve.” This presentation therefore aims at clarifying concepts and functions of these “connoted” semibreves in pre-Franconian treatises.

Connoted semibreves are found mainly in two forms: opposita proprietas and the “reduction to a three-note ligature.” Johannes de Garlandia (c. 1260) defines that within a ligature of opposita proprietas, regardless of how many preceding notes are juxtaposed before a long, the whole length of them is equivalent to one breve. Here, the preceding notes imply semibreves. Additionally, several pre-Franconian treatises, including Garlandia and Anonymous VII (c. 1270), observe the rule of the reduction to a three-note ligature. Particularly according to Garlandia, the length of the preceding notes––except the penultimate and ultimate notes––in a more-than-three-note ligature corresponds to the first note in a three-note ligature, namely, a long. Here again, the preceding notes can be breves or semibreves. In both principles, the connoted semibreves have flexibility in that their duration is changeable according to the number of preceding notes within a ligature. I also argue that this flexibility might have been inherited by Petronian notation (after 1280), in which three and more semibreves are placed for one breve.

Generative Meter and Phrase-Rhythmic Multivalence in Three Slavic Folk Tunes

Grant Sawatzky (University of British Columbia)


Using three Slavic folk tunes, I demonstrate an analytical approach for irregular phrase-rhythmic structures that involves anti-metrical motivic parallelisms and aperiodicities. The three generative analyses illustrate how melodic, harmonic, and rhythmic groupings interact to create phrase-rhythm, regardless of whether the structures involved are periodic enough to establish hypermeter, or idiomatic enough to invite comparison to normative phrase lengths. The music theory literature has addressed issues of rhythmic/metric irregularity, including well-known accounts of irregular rhythm in Stravinsky (for whom Slavic folk tunes were a source material). Analyzing rhythmic irregularity in Stravinsky’s music, theorists have described the unique time-sense engendered by aperiodic structures using concepts such as Van den Toorn’s “strong-weak reversal” or Horlacher’s “metric reinterpretation.” Both concepts involve analyzing phrase-rhythmic irregularity with reference to how a passage conforms to some a priori regular metric structure; i.e. irregular tunes are described in terms of what they distort rather than in terms of what they create. I describe irregularity in positive terms by conceiving of meter and phrase-type as generative rather than conformational schemas (Bonds, 1991). The generative view I endorse does not take alternate possibilities to be in conflict (e.g. Krebs’ “metrical dissonance”), nor as an ambiguity to be clarified by the performer (e.g. London’s “metric malleability”). Instead, I propose that co-present grouping structures mutually inform one another and establish phrase-rhythmic multivalences, imbuing these short and repetitive game-songs with their characteristic playfulness. In this way, their phrase-rhythmic whole is greater than the sum of its parts.

Temporal Techniques in the Serial Music of Roberto Gerhard

Rachel Mann (University of Texas Rio Grande Valley)

Rachel Mann is an assistant professor of music theory at the University of Texas Rio Grande Valley and has held appointments at the University of Illinois, the University of North Texas, and University at Albany-SUNY. She is a Question Leader for the AP Music Theory Exam, serves as the Vice President of the Association for Technology for Music Instruction (ATMI), and has received a quarter-million-dollar NSF grant to develop the part-writing and analysis app, Harmonia. Her Gerhard research has been published by Ashgate, Cambridge Scholars Press, and Routledge, and next summer, she will host a conference on the composer Roberto Gerhard at the University of Huddersfield funded by a grant from the British Academy. In her “free” time, she plays horn and Alphorn in a local RGV German Club polka band, sings with the Brownsville Festival Chorus, and plays electric guitar in the UTRGV faculty rock band, The Minör Revisiöns.


While best known as a student of Arnold Schoenberg, Catalan composer Roberto Gerhard (1896–1970) composed works covering a broad range of styles and genres and was a pioneer of electronic music in England. His position as a student in Schoenberg’s inner circle is reason enough to examine his writings on the twelve-tone method and serialism, but Gerhard also held close associations with the European avant-garde through his active involvement in the International Society for Contemporary Music and developed connections with the American musical community in the 1960s, earning commissions from prominent ensembles and teaching appointments at the University of Michigan and Tanglewood.

In an examination of his two published string quartets, Symphony no. 2 (Metamorphoses), and Hymnody, I will show how Gerhard serialized temporal elements in a way that clearly differed from his contemporaries. Gerhard used time series to govern both pitch durations as well as the number of beats per bar (offering compositional freedom to use pitches of any duration). Additionally, by dividing a time series into time sets, Gerhard added together each time set’s pcs to generate proportions for governing elements such as tempo markings, phrase lengths and rotations, and large-scale formal sections. While these few examples show some of the numerous ways Gerhard serialized time and space, a closer examination of his compositions, essays, notes, and lectures—particularly those written between 1945–1970—reveals a body of music and scholarship that, as Meirion Bowen claims, is essential to the modern repertoire.

Rhythmic Cycles and Ostinati as Formal Process in the Music of Tigran Hamasyan

Scott C. Schumann (Central Michigan University)

Scott Schumann is currently an Assistant Professor of Music Theory at Central Michigan University, and also currently works as a content developer for Picardy, an online interactive platform for developing theory and musicianship skills. His primary research interests include music of the 20th- and 21st- centuries, and theories of expressive meaning in music, including topic theory, musical semiotics, musical gesture, and intertextuality in the music of Stravinsky. However, his poster today represents a new area of research interest, focusing on rhythm and meter in pop music, specifically the music of Tigran Hamasyan.


Gretchen Horlacher’s work on cycles in Stravinsky’s music analyzes the rhythmic and contrapuntal interactions between ostinati, suggesting that these cycles create “a sense of progression among events,” and “produce a formal framework through the joint completion among strata of a contrapuntal pattern” (1992, 173). While there are a number of styles used in the music of pianist and composer Tigran Hamasyan (Armenian folk music, jazz, prog rock, etc.), the analyses in this poster focus on the use of asymmetrical meter, ostinati, and cycles throughout his compositional output. Three types of cycles (phrase, structural, and evolutionary) are defined and discussed using several transcribed examples of Hamasyan’s compositions.

Analyzing Drum Patterns and Drum Pattern Changes in Twenty-First Century Mainstream Pop

David Geary (Wake Forest University)

David Geary is an Assistant Professor of Music at Wake Forest University where he teaches music theory and music history. A recent graduate of Indiana University, his dissertation presents new techniques for analyzing drum parts in popular music and examines eight unique definitions of the word “beat” and their application in popular music analysis. David has published research on post- tonal aural skills in the Journal of Music Theory Pedagogy and The Routledge Companion to Music Theory Pedagogy. His other research interests include Renaissance counterpoint and Verdi operas, which have been presented at meetings of the Society for Music Theory and various regional conferences. Prior to joining the faculty at Wake Forest, David was a Visiting Instructor of Music Theory at Oberlin Conservatory.


In many genres of popular music, the drums perform a fixed rhythmic layer called a drum pattern. Further, most analytical methods either compare specific drum patterns to more generalized rhythmic structures or treat the drums as a backdrop for evaluating rhythmic variability in other parts. In twenty-first century mainstream pop, however, the drums alone provide both fixed and variable elements. A close study of Billboard’s top fifty pop songs from 2018 shows that individual tracks have an average of four drum patterns and eight drum pattern changes—the action of moving between adjacent drum patterns—and as many as nine and eighteen. The first goal of this presentation is to outline the three musical characteristics that vary most regularly amongst a song’s multiple drum patterns: number of layers, rhythm, and instrumentation. This corpus also shows that patterns typically match the rhetorical function of formal areas. The second goal is to define two types of drum pattern changes: drum buildups and drum decays. Both of these musical processes can create a sense of trajectory across different spans of musical material as well as for different expressive effects—and the two are regularly combined in individual tracks. Together, analyzing drum patterns and drum pattern changes can be a new way to highlight expressive variability in this repertoire, and it can also be used to refine other types of popular music analysis.