Major and minor. The formula of musical emotions

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(n1n2n3 … *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.

💡 Research Summary

The paper proposes a novel quantitative model linking the emotional response to musical chords with the information‑theoretic concept of a “utility function” L. The author argues that when a chord is heard, the brain assigns a value L to the pitch relationships among its constituent tones. If L > 1 the chord is interpreted as an increase in the objective function and elicits a positive utilitarian emotion; if L < 1 the opposite occurs, producing a negative utilitarian emotion. The core formula is

 Pwe = log L = (1/M)·log (∏ ni),

where M is the number of voices in the chord and each ni is an integer (or its reciprocal) representing the pitch proportion of the i‑th voice. In this framework, major chords correspond to “direct” integer ratios (e.g., 4 : 5 : 6), yielding L > 1, while minor chords correspond to the reciprocal ratios (e.g., 1/6 : 1/5 : 1/4), giving L < 1. The sign of Pwe therefore predicts the emotional valence, and its magnitude predicts emotional intensity.

The manuscript reviews basic acoustics (Fourier decomposition of tones), the traditional concepts of consonance and dissonance, and introduces the idea that three‑tone chords create a “monolithic” proportion that can be expressed either directly or inversely. It claims that the brain extracts these proportions as information, preferring the representation with the smaller product of its constituent numbers; this preference supposedly underlies the major/minor distinction.

A limited experimental test is described: participants listened to a set of major and minor triads built from pure tones with simple integer ratios, and they rated their emotional response on a Likert scale. The author reports that positive ratings correlated with positive Pwe values and negative ratings with negative Pwe values, and that larger absolute Pwe values corresponded to stronger reported emotions. However, the paper provides no details on sample size, stimulus presentation, control of timbre, loudness, or statistical analysis, and the data are not shown.

The discussion acknowledges that the model works best for chords whose pitch ratios involve small integers (1–6) and breaks down for more complex or irrational ratios. It also notes that dyadic intervals (two‑tone chords) do not produce the utilitarian emotional component, which only emerges when three or more tones are combined. The author suggests that the “information” contained in the main proportion of a chord is the source of its emotional character, whereas other aspects such as timbre or overall loudness are irrelevant for the major/minor effect.

In conclusion, the paper presents an intriguing hypothesis that major/minor emotional qualities can be derived from a simple logarithmic function of pitch ratios, framing the phenomenon in terms of information theory. Nonetheless, the theoretical justification for mapping pitch ratios onto a utility function is speculative, the definition of “direct” versus “inverse” proportions is ambiguous, and the empirical validation is insufficiently documented. The work would benefit from a rigorous neuro‑cognitive grounding, a well‑controlled psychophysical experiment with adequate statistical analysis, and a comparison with established models of musical emotion that incorporate expectancy, cultural learning, and affective semantics. As it stands, the proposal remains a hypothesis awaiting robust testing.