T he mathematician Srinivasa Ramanujan looked to create some of the most complex mathematical patterns of all time. We are all looking [listening]. The question is who can see [hear].” — Simon McBurney, Ensemble Complicite, ‘A Disappearing Number’, London, Barbican, 2007.
C ognitive phenomena do not always respect the ‘boundaries’ that are observed by textbooks and conferences in cognitive science. Consider the mirror neuron system—neurons in the premotor cortex that fire both when observing and performing an action. This discovery has challenged the assumed distinction between perception and action in the brain. While the human capacity to perceive opportunities for action (i.e., ‘affordances’; Gibson, 1979) has been extensively documented, it appears that even non-action-related judgments are in the ‘currency of action’... Cognitive phenomena do not always respect the boundaries that we draw between people either. Cognitive science has been concerned with the individual in isolation. But there have been striking insights into the brain’s sensitivity to social information and the way in which people think and act cooperatively [as exemplified in music].” — Kevin Shockley (Center for Cognition, Action and Perception, Univ Cincinnati), Daniel Richardson (Cognitive, Perceptual & Brain Sci, Univ College London), Rick Dale (Dept Psychology, Univ Memphis), Topics in Cognitive Science 2009; 1:305-19.
S peed for speed’s sake—or overly complex rhythmic structures, or insincere utilization of mathematical calculations as a performance or compositional device—can justly be criticized as aesthetically weak or contrived. Authenticity is threatened by throw-down theory. Virtuosic technic can only be redeemed by genuine feeling. The person in the street needs ‘ghazals’, not maths.
A nd yet... There are some musics whose rhythmic structure is unabashedly mathematical yet deeply moving. Tabla music, for example; and particularly performances by Ustad Zakir Hussain, or his father Ustad Alla Rakha who passed away in 2001. The mathematical design takes into account the length of each phrase, the duration of each pause that comes after the last DHA of each phrase, and the starting point of each tihai (see Gottlieb's book). There is a carefully worked-out, “composed” element, but there are necessarily the wonderful, small-scale human improvisational elements as well. [It's hard to conceive of anything less musical than a MIDI drum machine tabla executing mathematics-governed tabla rhythms. Gotta be “live”.] Here is link to a figure in Robert Gottlieb’s book on tabla, showing (left hand column) the rational-number relationships of tabla rhythms/metrical patterns.
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