Major and minor. The formula of musical emotions

TL;DR

This paper proposes a mathematical formula based on information theory to quantify how musical chords evoke positive or negative emotions, linking pitch proportions to emotional responses.

Contribution

It introduces a novel formula connecting pitch ratios in chords to emotional valence using information theory principles, supported by experimental validation.

Findings

The formula accurately predicts emotional responses to major and minor chords.

Experimental checks support the applicability of the proposed formula.

The model clarifies the relationship between pitch proportions and emotional intensity.

Abstract

The new formulas, which determine sign and amplitude of utilitarian emotions, are proposed on the basis of the information theory of emotions. In area of perception of musical chords the force of emotions depends on the relative pitch of sounds of major and minor chords. Is advanced hypothesis that in the perception of a musical chord in the psyche caused by the subject value of some objective function L. This function is expressed directly through the proportion of the pitch of chord. Major chords are expressed as the straight proportions, which generate idea about an increase in the objective function (L>1) and are caused positive utilitarian emotions. Minor chords are expressed as the inverse proportion, which generate idea about the decrease of objective function (L<1) and are caused negative utilitarian emotions. The formula of musical emotions is advanced: Pwe = log(L) = (1/M)*log(n1*n2*n3* ... *nM), where M is a quantity of voices of chord, ni - integer number (or reciprocal fraction) from the pitch proportion, which corresponds to the i-th voice of chord. Confined experimental check is produced. The limits of the applicability of the formula of musical emotions are investigated. Keywords: sound, music, chord, major, minor, emotions, the formula of musical emotions, the information theory of emotions.