An Empirically Derived Measure of Melodic Similarity

Abstract

Music software applications often require similarity-finding measures. In this study, we describe an empirically derived measure for determining similarity between two melodies with multiple-note changes. The derivation of our final model involved three stages. In Stage 1, eight standard melodies were systematically varied with respect to pitch distance, pitch direction, tonal stability, metric salience and melodic contour. Comparison melodies with a one-note change were presented in transposed and nontransposed conditions. For the nontransposed condition, predictors of explained variance in similarity ratings were pitch distance, pitch direction and melodic contour. For the transposed condition, predictors were tonal stability and melodic contour. In Stage 2, we added the effects of primacy and recency. In Stage 3, comparison melodies with two-note changes were introduced, which allowed us to derive a more generalizable model capable of accommodating multiple-note changes. In a follow-up experiment, we show that our empirically derived measure of melodic similarity yielded superior performance to the Mongeau and Sankoff similarity measure. An empirically derived measure, such as the one described here, has the potential to extend the domain of similarity-finding methods in music information retrieval, on the basis of psychological predictors.

Keywords:

• melodic similarity
• music cognition
• similarity-finding methods

Acknowledgements

We are grateful to Lucy McGarry, Lisa Liskovoi, Tristan Loria and James McGrath for assistance with data collection; and Glen Kappel for providing us with valuable comments and suggestions. We would like to thank Geraint Wiggins for providing us with useful insights on similarity-finding methods.

Notes

1 A preliminary version of Experiment 1 was reported in Vempala and Russo (2012).

2 Planned contrasts are a type of follow-up test that is planned rather than post hoc. The advantage of the planned contrast is that it controls the familywise error rate without the need to impose a correction (i.e. as in the Bonferroni adjustment). In addition to being more powerful than post-hoc tests, planned contrasts do not require that the omnibus F-test be significant. The requirements of the planned contrasts are that (a) they are truly planned, (b) the number of contrasts is no more than one less than the total number of means in the study, and (c) the contrasts are linearly independent of one another (Cohen & Lea, 2004).

Additional information

Funding

This research was supported by a MITACS Elevate postdoctoral fellowship awarded to Naresh N. Vempala, co-sponsored by MITACS and WaveDNA, Inc, and an NSERC Collaborative Research and Development grant awarded to Frank A. Russo, co-sponsored by NSERC and WaveDNA, Inc.