Toussaint

AAWM JOURNAL VOL. 1 NO. 2 (2011)

Computational Models of Symbolic Rhythm Similarity:
Correlation with Human Judgments

Godfried T. Toussaint, Malcolm Campbell, and Naor Brown

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Abstract:

A novel approach to describing rhythmic relationships in music is introduced by means of three experiments designed to test computational measures of symbolic rhythm similarity against human judgments. The first experiment involves a group of six distinguished Afro-Cuban timelines that had previously been compared with respect to a variety of mathematical measures of rhythm similarity in the context of phylogenetic analysis of rhythms. The results support the hypothesis that the edit distance correlates better with human judgments, than does the swap distance. The second experiment concerns Mario Rey’s musicological classification of Afro-Cuban rhythms into two groups being derived from either the Habanera or the Contradanza. The phylogenetic analysis of these rhythms performed with the edit distance, as well as the human judgments, lend support to Rey’s two-group categorization. However, they do not suggest that the Habanera and Contradanza timelines play a unique ancestral evolutionary role in the generation of the two groups. Both of these experiments involved rhythms with identically sounding beats. The third experiment incorporated Middle Eastern and Mediterranean rhythms composed of beats with two different timbres (dum-tak rhythms), thus introducing the simplest form of melody possible into the comparisons. Incorporating the additional information provided by using different symbols for the two sounds (dum and tak) in the edit distance did not increase the correlation with human judgments. The results obtained here also uncover a novel quantitative approach to the study of a class of music prototypes, namely, the identification of those rhythms that minimize the sum of the edit distances to all the other rhythms in a category.

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Contributor Information:

Godfried Toussaint received a Ph.D. in 1972 from the University of British Columbia. Until 2009 he taught and did research at McGill University in the areas of information theory, pattern recognition, textile-pattern analysis and design, computational geometry, instance-based learning, music information retrieval, and computational music theory. Presently he is a research scholar in the Music Department at Harvard University. He is a recipient of numerous awards, a founder of several conferences and workshops, an editor of several journals, and has published more than 360 papers. In 2009 he was awarded a Radcliffe Fellowship by the Radcliffe Institute for Advanced Study at Harvard to do research on the phylogenetic analysis of musical rhythm.

Malcolm Campbell graduated from Harvard University with a Bachelors degree in Chemistry and Physics Summa cum laude in 2010, and earned a Masters degree in Jazz Piano Performance from the New England Conservatory in 2011.  He now works for the Kohane lab at Children’s Hospital Boston studying Autism genetics.

Naor Brown is an undergraduate at Harvard University studying Applied Mathematics with Computer Science and Economics. An avid guitarist, Naor is interested in mathematically modeling the qualitative and social sciences in his research.

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