Analyzing Complex Rhythms

This paper analyzes the interplay of motivic shape and context in Guinean Malinke dance drumming, arguing that it is not only the melo-rhythmic shape of motives, but also their relationships to contextualizing temporal cycles, that give them meaning. Temporal organization in this genre is governed by a combination of temporal cycles that interact as the music unfolds, allowing encultured performers, dancers, and listeners to actively engage with the sounds through entrained prediction. As I will demonstrate, metrical complexity in this genre is heightened in two specific ways: by the inclusion of an asymmetrical timeline as one of the temporal cycles, and by the co-importance of both the quarter and dotted quarter cycles in compound time. This non-nesting of metrical cycles ensures that motives on the musical surface may be heard in multiple contexts simultaneously.

The music under study is a corpus of traditional pieces of the Malinke of Guinea, as disseminated by master drummers Mamady Keita and Fara Tolno. The pieces utilize nine parts, played by a combination of hand drums, stick drums, and bells. To analyze Guinean Malinke drum motives in terms of their temporal placement, I apply a methodology I call momentum vectors. Pairs of musical attacks are analyzed as moving TO, FROM, or remaining NEUTRAL, relative to points on the different metrical cycles contextualizing the music. The non-nesting of metrical cycles ensures that there are often multiple directions for the same pair of notes, imparting depth and complexity to this music.

Like other late Nancarrow works intended to be performed by live musicians, Piece No. 2 for Small Orchestra (1988) is written “in one”: each bar can be simultaneously divided into multiple subdivisions of 4, 5, 6, or 7. While this notation makes it possible to perform the work with a single conductor, it can disguise some polymetrical relationships, while privileging others. With the aid of rewritten passages, we find Nancarrow working with two kinds of rhythm, presented in contrasting timbres and tempo streams: 6/8 hemiola and odd-meter aksak rhythms. Earlier instances of these rhythmic combinations are found in Nancarrow’s Study No. 7 and elsewhere. These polytempic streams, each articulated by different polymeters, represent potent yet contrasting ways to create rhythmic complexity.

Although identifying a song’s primary pulse rate, more commonly called the beat, is a fundamental musical skill, it has generated varied theories and analyses throughout history and across disciplines. Popular music has been a rewarding repertoire to which to apply and refine traditional approaches as well as to develop new, style-specific theories. Rather than adopting any single definition, this presentation introduces a three-part conception of beat for popular music analysis which better characterizes the temporal phenomenon’s multi-dimensional, interactive, and interpretive attributes. The first half of the presentation outlines the three facets of beat, each identifying a song’s primary pulse rate according to a different musical parameter. The drum pattern rate (DPR) prioritizes the drumset rhythm, aligning with the bass-snare alternation or the four-on-the-floor bass drum rhythm. The absolute time rate (ATR) privileges a prescribed tempo, identifying the layer closest to 120 beats-per-minute. And the preferred pulse rate (PPR) models listener preferences, allowing individuals to treat any pulse rate as primary. The second half of the presentation shifts to analytical application. For example, while it is common for the DPR, ATR, and PPR to identify the same pulse rate as primary, there are at least three types of musical passages that show the more dynamic and varied ways these distinct conceptions can interact: different tempi, changing grooves, and ambiguity.