Entropy-based Tuning of Musical Instruments

TL;DR

This paper proposes an entropy-based method for tuning musical instruments by minimizing Shannon entropy of Fourier spectra, aligning with human perception of harmony and reproducing high-quality tuning characteristics.

Contribution

It introduces a novel entropy minimization approach for instrument tuning that correlates with human auditory perception and achieves accurate and natural-sounding results.

Findings

Reproduces correct stretch curve in tuning

Matches pitch fluctuations of high-quality aural tuning

Validates entropy minimization as effective tuning method

Abstract

The human sense of hearing perceives a combination of sounds 'in tune' if the corresponding harmonic spectra are correlated, meaning that the neuronal excitation pattern in the inner ear exhibits some kind of order. Based on this observation it is suggested that musical instruments such as pianos can be tuned by minimizing the Shannon entropy of suitably preprocessed Fourier spectra. This method reproduces not only the correct stretch curve but also similar pitch fluctuations as in the case of high-quality aural tuning.