Inharmonicity of Coupled Vibration of a Piano String and a Soundboard

This paper describes inharmonicities of a piano string vibration. Inharmonicities δon are first measured with a soundboard fixed and then inharmonicities δn 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. δn-δon=1200 log2(1+εn-ε1) _??_1731(εn-ε1) [cent] and εn_??_(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.