Empirically testing Tonnetz, voice-leading, and spectral models of perceived triadic distance. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Milne, Andrew J.; Holland, Simon
• Is Part Of: Journal of mathematics and music. Volume 10:Issue 1(2016)
• Page Start: 59
• Page End: 85
• Publication Date: 2016-01-02
• Subjects: spectral pitch-class distance -- voice-leading distance -- Tonnetz -- similarity -- fit -- harmony; 15A04 -- 15A06 -- 65C20; applied computing -- arts and humanities -- sound and music computing; Music theory -- Periodicals; Music -- Mathematical models -- Periodicals; Music -- Mathematics -- Periodicals; 781.2
• DOI: 10.1080/17459737.2016.1152517
• Languages: English
• ISSNs: 1745-9737

Abstract

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 distance 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 triadic distance and its music theory representation, the Tonnetz . The experimental data and the computational models are available in the Online Supplement (http://dx.doi.org/10.1080/17459737.2016.1152517 ).