It is customary to think of quintuple and septuple time as being divided asymmetrically, with beats of unequal divisions: {2, 3} or {2, 2, 3}, respectively. Yet certain grooves in popular music feature a steady pulse layer underneath these grooves that threatens to undermine their asymmetricality. From a headbanging standpoint, these slower steady pulses, not the asymmetrical guitar riff, become the most comfortable beat layer.

In this presentation, I analyze these "steady asymmetries," in which a steady pulse is provided in one instrument layer, undermining an asymmetrical quintuple or septuple meter heard in another layer. For example, in the signature groove from “Bows and Arrows” by Canon Blue, the violin plays an asymmetrical melody in septuple time with divisions at 184 BPM, while the drums project a slower steady pulse with quarter-note kicks at 92 BPM. Similarly, in Slayer’s “Killing Fields,” Kerry King’s blistering 5/8 guitar riff, with its 2+3 grouping at 310 BPM, becomes undercut by Dave Lombardo’s slow hi-hats and even slower kick and snare groove projecting a 155-BPM 5/4 feel.

The juxtaposition of these two layers reveals a kinship between steady asymmetries and grouping dissonances. Grouping dissonances can be described as x against y, where two layers alternate states of being in phase and out-of-phase. While complex or embedded grouping dissonances can take quite a long time to “resolve,” in the simplest grouping dissonances such as 3 vs. 2, the in-phase state (e.g. sharing a downbeat) alternates with an out-of-phase state in which the y-layer bisects the x-layer. This happens in both the Slayer and Canon Blue examples, where the asymmetrical meter and steady pulse line up in odd-numbered bars, with the asymmetrical meter bisecting the steady pulse in even-numbered bars. In this sense, you could hear the 7/8 Canon Blue melody against the kick drum in 7/4, the 5/8 Slayer guitar riff against the drum set groove in 5/4. Throughout my presentation, I draw attention to the ways in which these and other steady asymmetries might suggest new strategies for rethinking concepts such as beat, asymmetrical meter, entrainment, and grouping dissonance.

The Armenian-born pianist Tigran Hamasyan has developed a unique style that fuses aspects of folk musics, jazz, and metal. Chief among his music’s characteristics is a metric and rhythmic complexity that involves non-isochronous meters, polyrhythms, fast subdivisions, and what Schumann 2021 terms developmental cycles, in which a rhythmic ostinato that is typically introduced at the beginning of a piece returns later “with a different metric identity.”

In a recent interview (Leal 2022), Hamasyan discusses the development of his rhythmic style, at one point offering “There were a lot of ways that I practiced—I made playlists of nothing but songs in seven, for example, and wrote down ideas that I wanted to try within that seven.” His solo piece “Nairian Odyssey” (An Ancient Observer, 2017) seems to be an exemplar in its tour-de-force exploration of 7s. Perhaps unexpectedly, the 7s correspond mainly to a fast subdivision level, with an IOI of about 125ms. As a result, they are nearly out of perceptual reach, given the commonly accepted pulse floor of 100ms (London 2012).

As a result, and probably by design, the track begins with a folk-like theme in what initially sounds like an “expressively timed” compound quadruple. Repeated listening and the context of the rest of the composition reveal that each beat is actually subdivided into an isochronous-but-odd 7. The piece explores many ways of dividing up its 28-subdivision measures, varying beat-cycle cardinality and subdivision structure in its exploration of different motivic ideas. At the midpoint of the piece, in a striking passage that Bruce 2019 has detailed, Hamasyan steps up the number of subdivisions per measure by 25%—from 28 to 35—thereby hitting the perceptual wall of 100ms. The denoument from this subdivisional climax involves a progressive splitting of and evening out at the beat-cycle level followed by a step-down back to 28 subdivisions per measure.

In addition to unpacking the details of Hamasyan’s thoroughgoing investigation of 7 in this piece, my paper also highlights Hamasyan’s implicit pedagogy, as suggested by compositional details, performance nuances, and his public music theory persona.

This paper is an exploration of the concept of polymeter in Afro-Cuban batá drumming. Meter has blossomed into a contentious topic in the last few decades, as traditional “western” frameworks have often been deemed inadequate in analysis of “non-western” folkloric genres (Benadon 2020; Stover 2009). Yet the use and design of new rhythmic concepts, equally detached from emic performer perspectives, have at times been critiqued as overcorrection (Agawu 2003). I aim to maneuver around this friction in looking into the existence of polymeter in the Cuban religious drumming practice of batá, one associated with the religion colloquially known as Santería.

To conceptualize the possibility of polymeter in this sacred practice, I will first define meter from perspectives in relation to hierarchy and duration, drawing on past scholarship (Benadon 2020; Cohn 2019). Polymeter, much like Chris Stover’s theory of “beat spans,” exists as a tension or multiplicity of feels instead of a singular division of time (Stover 2009). This tension is elucidated further in master drummer Michael Spiro’s theory of “In-Fix” playing, in which batá rhythms are often situated equally, almost dialectically, in between 12/8 and 4/4 meters (Spiro 2015). Examples of batá rhythms are analyzed that live in a polymetric space, such as the dance rhythm Chachalokpfun. Analyses are also done of specific players such as Regino Jiménez and Manley “Piri” López in regards to how polymetric feeling has developed over time.

Spiro’s “In-Fix” helps us conceptualize the liminal “edge-like” nature of meter in batá practice and performance, but also aligns with clave as a polymetric device. Contrasting beat-divisions live inside of both isochronous pulses and asynchronous patterns (clave) concurrently. While my focus will be on the existence of polymeter in batá music, I will touch on performer and audience rhythmic entrainment and the idea of clave, as an asynchronous pattern that functions as meter. Ultimately, I argue that in the context of batá music the isochronous pulse is by far the most important, but control of clave, contrasting meters, and abstract beat spans within and between the meters is a necessary component of playing the music idiomatically.