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The wave equation for stiff strings and piano tuning

Autor
Gràcia, Xavier; Tomás Sanz-Perela
Tipus d'activitat
Document cientificotècnic
Data
2016
Codi
arXiv:1603.05516
DOI
10.2436/20.2002.02.11
URL
http://arxiv.org/abs/1603.05516 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 ...
Paraules clau
Wave Equation, Vibrating String, Stiffness, Inharmonic Spectrum, Musical Scale, Dissonance
Grup de recerca
DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions

Participants