Godfried Toussaint - Measuring the Complexity of Musical Rhythm Duration Patterns

Описание: Godfried Toussaint - Measuring the Complexity of Musical Rhythm Duration Patterns
NYUAD
The Rhythm Project (2014)

A mathematical measure of pattern complexity based on sub-symmetries possessed by the pattern, originally proposed by C. Alexander and S. Carey (1968), and shown by them to correlate highly with empirically derived measures of cognitive complexity in the visual domain, is found to also correlate significantly with empirically derived complexity measures of perception and production of auditory temporal and musical rhythmic patterns. A sub-symmetry in a sequence is a subset of contiguous (connected) elements of the sequence that exhibits mirror symmetry. Not only does the sub-symmetry measure correlate highly with the difficulty of reproducing the rhythms by tapping after listening to them, but the empirical measures exhibit similar behaviour, for both the visual and auditory patterns, as a function of the relative number of sub-symmetries present in the patterns. This simple measure is also compared to the measures of complexity, homogeneity, order, and symmetry proposed subsequently by F. Papentin & M. Krüger (1983) to approximate upper bounds on the Kolmogorov complexity in a computationally feasible manner.