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The wave equation for stiff strings and piano tuning

Autor
Gràcia, Xavier; Sanz-Perela, T.
Tipus d'activitat
Article en revista
Revista
Reports@SCM
Data de publicació
2017
Volum
3
Número
1
Pàgina inicial
1
Pàgina final
16
Repositori
http://hdl.handle.net/2117/101752 Obrir en finestra nova
URL
http://revistes.iec.cat/index.php/reports/article/view/142136 Obrir en finestra nova
Resum
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 ...
Citació
Gràcia, Xavier, Sanz, T. The wave equation for stiff strings and piano tuning. "Reports@SCM", 2017, vol. 3, núm. 1, p. 1-16.
Paraules clau
dissonance, inharmonic spectrum, musical scale, stiffness, vibrating string, wave equation
Grup de recerca
EDP - Equacions en Derivades Parcials i Aplicacions
GEOMVAP - Geometria de Varietats i Aplicacions

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