A symmetry-oriented mathematical model of classical counterpoint and related neurophysiological investigations by depth EEG

G. Mazzola, H. G. Wieser, V. Brunner, D. Muzzulini

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Abstract

This work presents (1) a mathematical model of classical counterpoint, based on distinguished symmetries between consonant and dissonant musical intervals and derived local symmetries, together with (2) an investigation of the electrical activity (depth EEG) of the human brain in relation with consonant and dissonant musical stimuli. Presenting a musical test program to 13 patients with electrodes implanted within different brain areas [hippocampal formations of both sides, planum temporale (near Heschl's gyrus) and/ or placed epicortically at mediobasal limbic structures], we found that the reaction of depth EEG corresponds in a precise and quantified way to the postulates of mathematical counterpoint theory. The main results are: (1) The EEG of the hippocampus reflects the consonance-dissonance dichotomy for simultaneous intervals in a predominant way. (2) Within the right Heschl's gyrus, the EEG response to the distinguished symmetry between consonances and dissonances is significant. (3) The EEG of right hemispheric locations dominate the processing of music related to Gestalt perception in space-time (pitch/onset-time), in particular of successive intervals. (4) The geometrically distinguished pair of dichotomies (the consonance-dissonance dichotomy and dichotomy of proper tonal intervals from the major tonic) is reflected within the spectral density data of the classical θ-, α-, and β-frequency bands. These findings may help to understand the relation between music and emotion.

Original languageEnglish (US)
Pages (from-to)539-594
Number of pages56
JournalComputers and Mathematics with Applications
Volume17
Issue number4-6
DOIs
StatePublished - 1989

Bibliographical note

Funding Information:
Acknowledgement--This work was supported by Sehweizerischer Nationalfonds (3.087-084).

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