Empirically testing Tonnetz, voice-leading, and spectral models of perceived triadic distance

Milne, Andrew J. and Holland, Simon (2016). Empirically testing Tonnetz, voice-leading, and spectral models of perceived triadic distance. Journal of Mathematics and Music: Mathematical and Comptational Approaches to Music Theory, Analysis, Composition and Performance, 10(1) pp. 59–85.

DOI: https://doi.org/10.1080/17459737.2016.1152517

Abstract

We compare three contrasting models of the perceived distance between root-position major and minor chords and test them against new empirical data. The models include a recent psychoacoustic model called spectral pitch class distance, and two well-established music theoretical models – Tonnetz distance and voice-leading distance. To allow a principled challenge, in the context of these data, of the assumptions behind each of the models, we compare them with a simple “benchmark” model that simply counts the number of common tones between chords. Spectral pitch class and Tonnetz have the highest correlations with the experimental data and each other, and perform significantly better than the benchmark. The voice-leading model performs worse than the benchmark. We suggest that spectral pitch class distance provides a psychoacoustic explanation for perceived harmonic distance and its music theory representation, the Tonnetz. Scores and MIDI files of the stimuli, the experimental data, and the computational models are available in the online supplement.

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