How do valves change the pitch of a brass instrument?

Valves change the pitch of a brass instrument by altering the course of the air column. When a player depresses a valve, it deflects the airstream into an additional piece of metal tubing, known as a crook, which is permanently attached to the instrument.1234

By adding this extra tubing, the total length of the vibrating air column is increased, which lowers the fundamental pitch of the instrument. Conversely, less common ascending valves function by cutting off air from such tubing, thereby raising the pitch.31

Most brass instruments are equipped with three descending valves that can be used individually or in combination to lower the pitch by up to six semitones, enabling the player to produce notes outside the instrument's natural harmonic series and play a full chromatic scale. Because these valves open a fixed amount of tubing, players often use their embouchure or compensating slides to correct minor tuning discrepancies.341