Quantifying the rationality of rhythmic signals

TL;DR

This paper introduces a novel measure based on log-frequency correlation to quantify the rationality and harmony of rhythmic signals, with applications in biological rhythms and voice analysis.

Contribution

It proposes a new spectral density correlation measure using analytic wavelets to analyze frequency ratios and introduces sonance as a metric for vocal harmony.

Findings

Demonstrated the measure on numerical sine signals and voice recordings.

Showed how sonance quantifies harmony between voices as a function of pitch transposition.

Provided insights into the rationality of biological and vocal rhythms.

Abstract

Rhythms and vibrations represent the quintessence of life, they are ubiquitous (systemic) in all living systems. Recognising, unfolding these rhythms is paramount in medicine, for example in the physiology of the heart, lung, hearing, speech, brain, the cellular and molecular processes involved in biological clocks. The importance of the commensurability of the frequencies in different rhythms has been thoroughly studied in music. We define a log-frequency correlation measure on spectral densities that gives the temporal evolution of the distribution of frequency ratios (rational or irrational) in between two signals, using analytic wavelets. We illustrate these concepts on numerical signals (sums of sine functions) and voice recordings from the Voice-Icar-Federico II database. Finally, with a second correlation operation from two of these ratio distributions (a reference one, the other from the voices) we introduce another quantity that we call \emph{sonance}, measuring the ``harmony'' (rationality) of two voices sung together as a function of a pitch transposition.