Harmonic inharmonicity: Eliminating beats with quantized harmonics

Abstract

Just intervals sound harmonious due to the absence of beats but cause mathematical problems when trying to define a tuning system with a fixed number of tones per octave. To address these problems, various different scales, microtonal intervals, and, more recently, algorithms for adaptive just intonation have been proposed, all with certain advantages but also downsides.In this work, we want to present a novel approach that aims to remove beats in equal temperament by quantizing the harmonics of a note. This results in a new class of tones that produces more even-sounding chords and can be easily integrated into existing synthesizers. To back up these claims, we performed a power spectrum analysis to investigate the effect of quantized harmonics on beats in equal temperament and performed a user study to examine the practical implications of this approach on human perception.In the future, we believe that the unique sound characteristics achieved by this approach could provide more even timbres in electronic or film music, for example.