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The wave equation for stiff strings and piano tuning

Author
Gràcia, Xavier; Sanz, T.
Type of activity
Journal article
Journal
Reports@SCM
Date of publication
2017
Volume
3
Number
1
First page
1
Last page
16
Repository
http://hdl.handle.net/2117/101752 Open in new window
URL
http://revistes.iec.cat/index.php/reports/article/view/142136 Open in new window
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 on 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 ...
Citation
Gràcia, Xavier, Sanz, T. The wave equation for stiff strings and piano tuning. "Reports@SCM", 2017, vol. 3, núm. 1, p. 1-16.
Keywords
dissonance, inharmonic spectrum, musical scale, stiffness, vibrating string, wave equation
Group of research
EDP - Partial Differential Equations and Applications
GEOMVAP - Geometry of Manifolds and Applications

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