ピアノ絃と響板の連成振動のINHARMONICITY

抄録

This paper describes inharmonicities of a piano string vibration. Inharmonicities δ_on are first measured with a soundboard fixed and then inharmonicities δ_n with a soundboard unfixed. The latter are larger in a bass section than the former, and in mediant and treble sections there is no difference between the two. The vibration of a piano string is not interpreted as independent vibration, but as coupled vibration. Theoretical treatment of coupled vibration of a string with the soundboard leads to the following solution.
δ_n-δ_on=1200 log₂(1+ε_n-ε₁)
_??_1731(ε_n-ε₁) [cent]
and ε_n_??_(n²π²M/ρl-kl/T)^-1
where M ; the equivalent mass of a soundboard
k ; the spring constant of a soundboard
ρ; the linear density of the spring
T ; the tension of the string l; the speaking length of the string,
The above experimental facts are well explained by these theoretical calculations.