The wave equation for stiff strings and piano tuning

Authors

  • Xavier Gràcia Universitat Politècnica de Catalunya
  • Tomás Sanz-Perela Universitat Politècnica de Catalunya

Keywords:

wave equation, vibrating string, stiffness, inharmonic spectrum, musical scale, dissonance

Abstract

We study the wave equation for a string with stiffness. We solve the equation and provide a uniqueness theorem with suitable boundary conditions. For a pinned string we compute the spectrum, which is slightly inharmonic. Therefore, the widespread scale of 12 equal divisions of the just octave is not the best choice to tune instruments like the piano. Basing in the theory of dissonance, we provide a way to tune the piano in order to improve its consonance. A good solution is obtained by tuning a note and its fifth by minimizing their beats.

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Published

2018-09-27

How to Cite

Gràcia, X., & Sanz-Perela, T. (2018). The wave equation for stiff strings and piano tuning. Reports@SCM, 3(1), 1–16. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/139742

Issue

Vol. 3 No. 1 (2017)

Section

Articles

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