Using transportation distances for measuring melodic similarity

Most of the existing methods for measuring melodic similarity use one-dimensional textual representations of music notation, so that melodic similarity can be measured by calculating editing distances. We view notes as weighted points in a two-dimensional space, with the coordinates of the points reflecting the pitch and onset time of notes and the weights of points depending on the corresponding notes’ duration and importance. This enables us to measure similarity by using the Earth Mover’s Distance (EMD) and the Proportional Transportation Distance (PTD), a pseudometric for weighted point sets which is based on the EMD. A comparison of our experiment results with earlier work shows that by using weighted point sets and the EMD/PTD instead of Howard’s method (1998) using the DARMS encoding for determining melodic similarity, it is possible to group together about twice as many known occurrences of a melody within the RISM A/II collection. Also, the percentage of successfully identified authors of anonymous incipits can almost be doubled by comparing weighted point sets instead of looking for identical representations in Plaine & Easie encoding as Schlichte did in 1990.