Dependence of Tuning of Wind Instruments on Temperature Available to Purchase

Observations by Pottle on the change of tuning of musical wind instruments with ambient temperature are here summarized by a single coefficient representing each instrument tested. The largest effect was observed on the BB♭ sousaphone where the increase with ambient temperature occurred at the rate of 2.6 cents/°C. This is equivalent to a fractional frequency coefficient of $1.6 × 10−3/°C$⁠. The cent is a logarithmic unit of frequency ratio such that 1200 cents equals one octave. A theory is developed by which the average temperature (and thus the velocity of sound) of the air within a wind instrument may be inferred from the empirically determined dependence of equilibrium tuning on ambient temperature. The theory also provides a qualitative estimate of the change in tuning which occurs while the instrument is first being warmed by the player's breath.