The wave equation for stiff strings and piano tuning
ثبت نشده
چکیده
ENG) 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 note and its fifth by minimizing their beats.
منابع مشابه
A Parametric Model of Piano Tuning
A parametric model of aural tuning of acoustic pianos is presented in this paper. From a few parameters, a whole tessitura model is obtained, that can be applied to any kind of pianos. Because the tuning of piano is strongly linked to the inharmonicity of its strings, a 2-parameter model for the inharmonicity coefficient along the keyboard is introduced. Constrained by piano string design consi...
متن کاملA laboratory investigation on the potential of computational intelligence approaches to estimate the discharge coefficient of piano key weir
The piano key weir (PKW) is a type of nonlinear control structure that can be used to increase unit discharge over linear overflow weir geometries, particularly when the weir footprint area is restricted To predict the outflow passing over a piano key weir, the discharge coefficient in the general equation of weir needs to be known. This paper presents the results of laboratory model testing of...
متن کاملPiano Hammer-String Interaction
A hammer-string interaction for bass notes is investigated and the problem what can cause the hammer to rebound is clarified. For a linear elastic hammer interacting with a long flexible string the exact solution of the equation describing the hammer motion is derived. It was shown that in some cases no reflected wave is needed to assist the hammer for going away from the string. The numerical ...
متن کاملWhen stationary modes aren’t stationary: Coupling of modes and adiabatic processes in dynamic eigenproblems
Many physical and mathematical problems involve the study of harmonic modes, solutions which oscillate sinusoidally in time. For example, the vibrations of a drum or a piano string (acoustic waves), the propagation of light (an electromagnetic wave) in a medium or down an optical fiber, and the allowed energies of an electron bound to a nucleus (a quantum probability wave), are all described by...
متن کاملTuning of fuzzy logic controller using an improved black hole algorithm for maximizing power capture of ocean wave energy converters
Seas and oceans are the most important sources of renewable energy in the world. The main purpose of this paper is to use an appropriate control strategy to improve the performance of point absorbers. In this scheme, considering the high uncertainty in the parameters of the power take-off system in different atmospheric conditions, a new improved black hole algorithm is introduced to tune fuzzy...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016