Rhythm complexity measures: A comparison of mathematical models of human perception and performance

Thirty two measures of rhythm complexity are compared using three widely different rhythm data sets. Twenty-two of these measures have been investigated in a limited context in the past, and ten new measures are explored here. Some of these measures are mathematically inspired, some were designed to measure syncopation, some were intended to predict various measures of human performance, some are based on constructs from music theory, such as Pressing's cognitive complexity, and others are direct measures of different aspects of human performance, such as perceptual complexity, meter complexity, and performance complexity. In each data set the rhythms are ranked either according to increasing complexity using the judgements of human subjects, or using calculations with the computational models. Spearman rank correlation coefficients are computed between all pairs of rhythm rankings. Then phylogenetic trees are used to visualize and cluster the correlation coefficients. Among the many conclusions evident from the results, there are several observations common to all three data sets that are worthy of note. The syncopation measures form a tight cluster far from other clusters. The human performance measures fall in the same cluster as the syncopation measures. The complexity measures based on statistical properties of the inter-onset-interval histograms are poor predictors of syncopation or human performance complexity. Finally, this research suggests several open problems.