Pitch value in temperature variations

The pitch of musical instruments is closely related to air temperature.
As regards wind instruments, the pitch rises as the temperature grows and it decreases as the air becomes colder.

At a first glance you could think that this kind of change depends on dimensional variations of the instruments (expansion or contraction of wood or brass). Actually that kind of dimensional variations are quite insignificant for the change of pitch. Instead the change of pitch depends mostly on the density of the air where the sound wave is generated. In other words the pitch variations depends not on the “container” (the musical instrument), but on the “contents” (the air moved).

The air density increases as the temperature decreases otherwise the air rarefies as the temperature rises, this process influences directly the speed of sound and, as a consequence, the pitch.
All wind instruments are designed, manufactured and sold to play at a certain pitch. That pitch depends on the maker choice, on the musician request and on the time period. The unit of measure for the pitch is the Hertz (Hz) of the A above middle C and it can be set at 392Hz, 415Hz, 440Hz, 442Hz and many more.
The maker will specify it.

However a second factor is essential for pitch specification: the air temperature. A common standard for the wind instruments intonation is a room temperature of 68 °F. If the temperature changes also the pitch of the instrument will change.

So we present here a simple chart to calculate the pitch/temperature variations and, in that way, we hope to give an help to musicians who wants to understand and handle better theirs wind instruments.