Abstract
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.
Highlights
Archaeomusicological research primarily focuses on the findings of excavated ancient musical instruments and on relevant evidence, both iconographic and textual
CASE STUDY: AULOS OF LOUVRE Table 3 presents the optimal set of fundamentals derived by ENTROTUNER and Hagel’s method [24] (referred to as Physical Model Based Method (PMBM))
In order for the reader to get an intuition regarding the physical meaning of the entropy values, we present two examples: A) the entropy of the aggregate spectrum of a diatonic scale tuned in just intonation is 0.025bits less than the one tuned in 12-tone equal temperament, B) the entropy of the spectrum of two tones forming the perfect fifth is 0.137bits less than the dissonant tritone (64/45)
Summary
Archaeomusicological research primarily focuses on the findings of excavated ancient musical instruments and on relevant evidence, both iconographic and textual. Scholars conclude regarding the ancient musical sound, which, according to modern anthropological studies, have played an important-functional role at certain activities of the members of ancient communities Missing parts of excavated musical instruments and lack of concrete evidence on the ancient playing techniques (i.e., the players’ interaction with them) lead us to ambiguities regarding their function and relation to specific tuning systems and practices [2]. An ancient musical instrument is not an apparatus detached from the cultural practices of that era but rather an item whose study can reveal unknown aspects of prior civilizations.
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