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The vibration of a wrapped string has theoretically been treated as an ideal string with a uniform linear density, neglecting its naked parts at both ends of an actual piano string. This paper shows that (1) the inharmonicity of the vibration of the actual piano string is larger than that of the ideal string and (2) the increase of the inharmonicity (Δan) due to the naked parts is calculated by the following formula;Δan=1731 (ean-ea1), whereean=2/3n2π2 (1-ρ1/ρ2) (a/l) 31+2/5 (1+ρ1/ρ2) (nπa/l) 2/1+ (nπa/l) 2n; the number of the order of harmonicsl; the total length of the piano stringa; the length of each naked partsρ1; the linear density of the naked partsρ2; the linear density of the wrapped part

Inharmonicity of the Vibration of a Wrapped Piano String