Psychology-based rhythmic transformations

The psychology-based rhythmic analysis of McLachlan in 'A Spatial Theory of Rhythmic Resolution', on music from the African and Javanese musical traditions using Gestalt theory and mathematical group theory, to include ternarizations and other timespans, is generalized. McLachlan used Gestalt psychology principles to define rhythmic transformations from a 12-pulse rhythm to a 16-pulse rhythm. The superposition of two groups of 3 pulses over two groups of 4 pulses is sufficient to generate a 12-pulse rhythm. The 12-pulse rhythm is snapped to the 16-pulse rhythm using the nearest neighbor rule but the snapping of the rhythm to pulses numbered 0, 3, 4, 6, 8, 10, 12, and 13 are restricted. The results show that the original rhythm has many onsets in common with the salient positions in the construction of McLachlan showing an efficient binarization.