Structural similarity based on time-span sub-trees

Masatoshi Hamanaka

Keiji Hirata

Satoshi Tojo

pp. 187-192

in: Tom Collins, David Mérédith, Anja Volk (eds), Mathematics and computation in music, Berlin, Springer, 2015

Abstract

We propose structural similarity of two melodies based on sub-trees from the time-span tree provided by the Generative Theory of Tonal Music. The structural distance of the tree was previously defined and called the "maximal time-span distance," and experimental results showed to some extent a correspondence between the maximal time-span distance and psychological similarity. However, there is a big problem in that almost all pairs of melodies are not similar on the basis of the maximal time-span distance because the definition of the similarity is too strict. Therefore, we attempt to express a melodic structural similarity by using the coincidence rate of time-span sub-trees to weaken the condition for calculating similarity. We have set up three experimental conditions and compared their results.