Binary meets ternary

It is well known that in certain African and African-diasporic styles of music, binary and ternary subdivision can be co-present without creating permanent rhythmic tension. In other styles of the same cultural sphere, ternary and quaternary subdivisions can be combined and nonetheless host coherent ensemble grooves.

Polak 2010 suggested, and Polak and London 2014 showed in detail, that in Malian drumming, such co-presence can be achieved by nesting one swung subdivision level into another one. I propose that this does not represent an instance of so-called polymeter. Rather, the temporal nesting allows for the perception of the binary and ternary subdivision levels as two distinct layers in a coherent metric hierarchy.

Schematic tree- and dot- representation of 4-beat meter with  nested LS and SML sub- divisions. In the dot- representation, hori- zontal distance alludes to temporal proportions. From Polak (in review).



Screenshot of the binary accompaniment (top) and ternary lead part (bottom) in a 4-beat-cycle of the Khasonka piece "Bire." Green dots mark alignment of strokes, red dots mark lead part strokes nested into the binary accompaniment. From Polak/London 2014, Fig. 6.2.

Here is an example how a lead drummer nests ternary embellishments into an only lightly swung binary rhythm. Jeli Madi Kuyate (first jembe, center), Drissa Kone (second jembe, right) and Madu Jakite (dundun, left) play Woloso-Dòn (Bamako 2006).

To summarize, the non-isochrony of swing timing patterns can recur across two distinct metric subdivision levels.  In some pieces and given slow tempo, such non-isochrony can even extend across three subdivision layers. In these cases, the emergent stability of swing timing patterns at one level indicates that the neigboring (also swung) level is used as a primary reference structure, not as an expressive deviation. The hypothesis of underlying isochrony appears implausible in view of this swing-based metric hierarchy.