Harmony perception by periodicity detection

Abstract

The perception of consonance/dissonance of musical harmonies is strongly correlated with their periodicity. This is shown in this article by consistently applying recent results from psychophysics and neuroacoustics, namely that the just noticeable difference between two pitches for humans is about 1% for the musically important low frequency range and that periodicities of complex chords can be detected in the human brain. Based thereon, the concepts of relative and logarithmic periodicity with smoothing are introduced as powerful measures of harmoniousness. The presented results correlate significantly with empirical investigations on the perception of chords. Even for scales, plausible results are obtained. For example, all classical church modes appear in the front ranks of all theoretically possible seven-tone scales.

Keywords:

• consonance/dissonance
• harmony perception
• periodicity
• dyads, triads, chords, and scales

Acknowledgements

This article is a completely revised and extended version of previous work (Stolzenburg 2009, 2010, 2012, 2014). I would like to thank Wolfgang Bibel, Peter A. Cariani, Norman D. Cook, Martin Ebeling, Thomas Fiore, Adrian Foltyn, Sergey Gaponenko, Ludger J. Hofmann-Engl, Phil N. Johnson-Laird, Gerald Langner, Florian Ruh, Tilla Schade, and – last but not least – Marek Žabka, as well as several anonymous referees for helpful discussions, hints, and comments on this article or earlier versions thereof.