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arXiv:1203.5101physics.class-ph

Entropy-based Tuning of Musical Instruments

Haye Hinrichsen

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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.

arXiv comments
13 pages, 9 figures
Journal reference
Rev. Bras. Ens. Fis. 34(2) (2012), 2301
DOI
Subjects
physics.class-phClassical Physics cs.SDSound physics.pop-phPopular Physics

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Discussed in comments1 thread

  1. The Mathematics of Tuning Systems 1 comment

    • There is actually an interesting mathematical method for piano tuning that takes harmonics into account [1]. The core idea is to minimize the integral over the logarithm of the sum of all spectra. This basically favors spectra that are smeared out less. Instead of the logarithm…

      jankhgView on HNParent context

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