How temperature affects the speed of sound and therefore the pitch of wind instruments, and why brass instruments are more susceptible than woodwinds.

The pitch produced by a wind instrument is determined by the resonant frequencies of its air column. Those frequencies depend on the speed of sound, which in turn depends on the temperature of the air. The relationship is:

v = 331.3 × √(T/273.15) m/s

where T is the temperature of the air column in Kelvin. Since frequency equals the speed of sound divided by the wavelength — and the wavelength is fixed by the tube length — pitch rises as temperature rises and falls as temperature falls.

The deviation in cents between two temperatures can be calculated as:

Δcents = 600 × log₂(T2/T1)

where T1 and T2 are in Kelvin. A 20°F increase from 70°F to 90°F shifts the pitch approximately 32 cents sharp. The difference between a 30°F outdoor performance and a 70°F indoor environment represents a shift of nearly 70 cents — close to a semitone.

It is the temperature of the air column specifically that determines pitch, not the temperature of the instrument body. However, the instrument body is in constant contact with the air column, and its thermal properties strongly influence how quickly the air column temperature changes.

Thermal conductivity — measured in watts per meter-kelvin W/(m·K) — describes how readily a material transfers heat. Brass conducts heat at approximately 109 W/(m·K). Wood, such as the grenadilla commonly used for clarinets, conducts at roughly 0.7 W/(m·K). Hard rubber and plastic fall in a similar range, around 0.16–0.17 W/(m·K). Brass conducts heat roughly 150 times faster than wood and around 600 times faster than plastic.

This difference has significant consequences for intonation stability. A brass instrument equilibrates rapidly with whatever air is passing through it, making the air column temperature — and therefore the pitch — highly sensitive to ambient conditions. A wooden or plastic instrument changes temperature much more slowly, buffering the air column against rapid shifts.

For smaller woodwind instruments this effect is compounded by their smaller air column volume. A clarinet, for example, has both low thermal conductivity and a relatively small air column — the player's warm breath warms and maintains the air column temperature quickly, and the insulative body does not rapidly draw that heat away. The result is that clarinets are substantially more stable against temperature-driven intonation changes than brass instruments.

Larger brass instruments face the greatest challenge. A tuba presents a large metal surface area in contact with the air column, conducts heat readily in both directions, and requires a large volume of air to fill. These factors combine to make the air column temperature — and therefore the pitch — more difficult to stabilize and more responsive to changes in the surrounding environment.

A warm stage under performance lighting and a cold outdoor marching performance represent two ends of this spectrum. In both cases the pitch of the ensemble shifts with the temperature of the air columns inside the instruments, and that shift is predictable from the formula above.

String instruments are affected by temperature through an entirely different mechanism — thermal expansion of the strings and body rather than the speed of sound in an air column. As temperature rises, strings expand and go flat; as temperature drops they contract and go sharp. This is the inverse of wind instruments. In a warming concert hall, winds go sharp while strings go flat, pulling the two sections in opposite directions simultaneously.