Empirically testing <i>Tonnetz</i>, voice-leading, and spectral models of perceived triadic distance

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 – <i>Tonnetz</i> 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 <i>Tonnetz</i> 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 <i>Tonnetz</i>. The experimental data and the computational models are available in the Online Supplement (http://dx.doi.org/10.1080/17459737.2016.1152517).