Beats of the Musical Sound of a Cantilever-Electro-Piano
Takeshi Yanagisawa, Mikio MORIOKA, Kijuro NAKANURA · Journal of the Japan Society of Precision Engineering · 1972
The musical sound in each key of a cantilever-electro-piano is produced from the vibration of respective cantilever-top. But the sound is composed of many strong over-tones whose frequencies are integer multiples of their fundamental. The cause of the beats sensation of the sound in the bass section is explained in this paper. The beats appear in the harmonics, when (1) the vibration of the cantilever-top is a higher-order-beat oscillation, represented by the equation y=cos ωt+acos (nω+ε) t, where a is amplitude ratio, n is 79, and ω, ε (ω>>|ε|) are frequencies, and (2) the vibro-electro-trans-ducer is non-linear.