Measuring musical rhythm similarity: Transformation versus feature-based methods

Background in musicology. A central problem in musicology is to develop classification algorithms that match the way human observers perceive musical rhythm similarity and pass on music forms as cultural knowledge. Rhythm similarity measures that have been investigated in the past fall into two categories: transformation methods and feature-based methods. In the former the similarity is measured by the amount of effort required to transform (morph, mutate) one rhythm into another. One of the most well know transformation measures is the edit distance, defined as the minimum number of mutations required to transform one rhythm to the other. The mutations here are insertions, deletions, and substitutions of symbols in a sequence. In the feature-based methods a set of pre-determined features is calculated for each rhythm, and similarity is measured by the degree to which the two sets of features match. Typical features measure properties of the inter-onset intervals present in a rhythm. For either approach, a measure of rhythm similarity is desired that is not only efficient to compute, but that agrees well with human perceptual judgments of rhythm similarity. Background in cultural evolutionary biology. Phylogenetic trees were originally conceived for the purposes of describing and visualizing evolutionary relationships that exist between members of a group of biological organisms. However, more recently they have been applied to cultural objects as well, language being an early prime example. Phylogenetic tree construction approaches fall into two main categories: distance-based methods and “character”based methods. Distance methods assume that a distance matrix is available containing the distance between every pair of objects being studied. In character-based methods the input data are sets of binary and/or multistate characters, and the final observed distribution of characters is modeled as resulting from a set of inferred transition probabilities. Aims. By combining phylogenetic tools from cultural evolutionary biology with the cognitive and computational study of measures of rhythm similarity from musicology and music theory, this project aims to create a synergistic bridge between these two domains of knowledge. Main contribution. A feature-based approach to rhythm similarity is compared to a frequently used transformation method, using a family of rhythms of equal length. Distance matrices calculated from the rhythms are compared with ‘dissimilarity’ matrices obtained from human judgments using Mantel tests. Two different phylogenetic analysis techniques are also compared: a distance based method and a Bayesian approach. The results provide evidence from the music domain that supports the hypothesis that transformation methods are superior to feature-based methods for modeling more general human similarity judgments. Implications. Our results highlight the difficulty of modeling rhythm similarity by means of purely structural features collected from musicology and music theory, and imply that more attention should be devoted to the study of transformation methods. The methods explored here, standard in evolutionary biology and anthropology, provide novel tools for musicology and music theory that complement traditional historical and ethnographic accounts.