Entropy-based tuning of musical instruments

Hinrichsen, Haye

doi:10.1590/s1806-11172012000200004

Cited by 13 publications

(12 citation statements)

References 8 publications

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“…One approach involved calculating the sensory dissonances between tones and minimizing them [4]. Another unique approach was to minimize the Shannon entropy of all tones in a piano [7]. All these seem to produce quite good results.…”

Section: Introductionmentioning

confidence: 99%

Automatic Tuning of High Piano Tones

Shah

Välimäki

2020

Applied Sciences

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Piano tuning is known to be difficult because the stiffness of piano strings causes the tones produced to be inharmonic. Aural tuning is time consuming and requires the help of a professional. This motivates the question of whether this process can be automated. Attempts at automatic tuning are usually assessed by comparing the Railsback curve of the results with the curve of a professional tuner. In this paper we determine a simple and reliable rule for tuning the high tones of a piano with the help of a listening test. This rule consists of matching the two tones in an octave interval so that the first partial frequency of the upper tone becomes exactly the same as the second partial frequency of the lower tone. This rule was rated best among four tuning rules that were compared in the test. The results found are explained using a beat-based analysis, and are consistent with some previous studies. They are also tested against the existing method of using Railsback curves, and it is shown that comparison using Railsback curves is an unreliable method of assessing different tunings. The findings from this paper can be used to create a complete automatic tuner that could make the process of piano tuning quick and inexpensive.

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Section: Introductionmentioning

confidence: 99%

Automatic Tuning of High Piano Tones

Shah

Välimäki

2020

Applied Sciences

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“…In Ref. [10] we observed that the entropy of pure (harmonic) intervals is locally minimal since the entropy decreases when higher partials overlap. This suggests that the entropy of overlaid power spectra can be used as a measure of harmonicity.…”

Section: Introductionmentioning

confidence: 96%

Revising the musical equal temperament

Hinrichsen

2016

Rev. Bras. Ensino Fís.

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Western music is predominantly based on the equal temperament with a constant semitone frequency ratio of 2 1/12 . Although this temperament has been in use since the 19 th century and in spite of its high degree of symmetry, various musicians have repeatedly expressed their discomfort with the harmonicity of certain intervals. Recently it was suggested that this problem can be overcome by introducing a modified temperament with a constant but slightly increased frequency ratio. In this paper we confirm this conjecture quantitatively. Using entropy as a measure for harmonicity, we show numerically that the harmonic optimum is in fact obtained for frequency ratios slightly larger than 2 1/12 . This suggests that the equal temperament should be replaced by a harmonized stretched temperament as a new standard.

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“…Our work reflects to the cultures that show a clear tendency towards the optimization of consonance, for example the ancient Greek one [17], [18] which the Aulos corresponds to. Humans who are part of the aforementioned cultural groups consider a combination of sounds as pleasant, harmonic, or in tune when they perceive correlated spectra [19], [20]. Every tone consists of frequency partials, which include the fundamental and higher frequencies (overtones).…”

Section: Introductionmentioning

confidence: 99%

“…Thus, in both cases, tuning depends on aural feedback. Hinrichsen [19] proposed a method to simulate aural tuning by compromising the lack of coincidence of the partials and the deviation of fundamental frequencies according to a tuning system. An entropy-based optimizer constitutes the core module of ENTROTUNER's tuning approach.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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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.

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Entropy-based tuning of musical instruments

Cited by 13 publications

References 8 publications

Automatic Tuning of High Piano Tones

Automatic Tuning of High Piano Tones

Revising the musical equal temperament

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

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