ENTROTUNER: A Computational Method Adopting the Musician’s Interaction With the Instrument to Estimate its Tuning

Archeomusicologists commonly use methods based on the physical properties and the relative tuning system of a musical instrument in order to estimate its tones. However, because the musician often alters the tones' frequency, for example, while playing in wind instruments by means of embouchure or by stressing the string in string instruments, the current methods that neglect the musician's interaction with the instrument cannot provide solid results. In this work, we introduce ENTROTUNER, a computational method, based on mathematical optimization, to more accurately estimate the generated tones by considering: the instrument as a sound production mechanism, the relevant musical scale(s), and the musician's interaction with the instrument. We simulate this interaction as a system that, by following tuning rules, aims to maximize the partials' overlap (harmonicity), coded as entropy's minimization of the aggregated tones' spectrum. Last, we put ENTROTUNER into practice for the ancient Greek wind instrument Aulos. The results reveal that, compared with the traditional methods, ENTROTUNER highlights increased harmonicity (entropy decreased by 0.341bits), eleven additional consonant intervals, as well as 47.8% more tuning quality for the musical instrument.