Harmony Perception, Periodicity Detection, and Neural Transformation

Frieder Stolzenburg

The perception of consonance/dissonance of musical harmonies is strongly correlated with their periodicity. This can be shown by consistently applying results from psychophysics and neuroacoustics, namely that the just noticeable difference between 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 measures of harmoniousness. The presented results correlate significantly with empirical investigations on harmony perception. 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. By comparing the frequency spectrum of an input stimulus and its response spectrum in the auditory brainstem, the periodicity pitch frequency - which is not present in the input spectrum - occurs in addition. To explain this, it will be argued that the most important factor during the neural processing is the highly non-linear transformation of the input signal into pulse trains (spikes) whose maximal amplitude is limited by a uniform value. This is can be demonstrated by a simple artificial neural network model.

Talk

Harmony Perception, Periodicity Detection, and Neural Transformation (Cognitive Neuroscience Department, Maastricht University, Netherlands, 2018)

Material

Publications

Frieder Stolzenburg. Periodicity detection by neural transformation. In Edith Van Dyck, editor, ESCOM 2017 -- 25th Anniversary Conference of the European Society for the Cognitive Sciences of Music, pages 159--162, Ghent, Belgium, 2017. IPEM, Ghent University. Proceedings. [ .pdf ]

Frieder Stolzenburg. Harmony perception by periodicity detection. Journal of Mathematics and Music: Mathematical and Computational Approaches to Music Theory, Analysis, Composition and Performance, 9(3):215--238, 2015. [ http ]

Frieder Stolzenburg. Harmony perception by periodicity detection. In Moo Kyoung Song, editor, Proceedings of the ICMPC-APSCOM 2014 Joint Conference: 13th International Conference on Music Perception and Cognition and 5th Conference of the Asian-Pacific Society for the Cognitive Sciences of Music, pages 27--31, Seoul, South Korea, 2014. College of Music, Yonsei University. [ .pdf ]

Frieder Stolzenburg. Harmony perception by periodicity detection. CoRR -- Computing Research Repository abs/1306.6458, Cornell University Library, 2013. Extended, revised, and corrected version 2016. [ http ]

Frieder Stolzenburg. Harmony perception by periodicity and granularity detection. In Emilios Cambouropolos, Costas Tsougras, Panayotis Mavromatis, and Konstantinos Pastiadis, editors, Proceedings of 12th International Conference on Music Perception and Cognition and 8th Triennial Conference of the European Society for the Cognitive Sciences of Music, pages 958--959, Thessaloniki, Greece, 2012. [ .pdf ]

Frieder Stolzenburg. A periodicity-based approach on harmony perception including non-western scales. In Steven M. Demorest, Steven J. Morrison, and Patricia Sheehan Campbell, editors, Proceedings of 11th International Conference on Music Perception and Cognition, pages 683--687, Seattle, Washington, USA, 2010. [ .pdf ]

Frieder Stolzenburg. A periodicity-based theory for harmony perception and scales. In Keiji Hirata, George Tzanetakis, and Kazuyoshi Yoshii, editors, Proceedings of 10th International Society for Music Information Retrieval Conference, pages 87--92, Kobe, Japan, 2009. [ .pdf ]