How do finger holes and keys change pitch on woodwind instruments?

On woodwind instruments, finger holes and keys change pitch by altering the effective sounding length of the instrument's air column.

When all finger holes are covered, the instrument produces its lowest fundamental pitch. By lifting fingers one by one—starting from the hole closest to the end of the tube—the player effectively shortens the vibrating air column, which raises the pitch. To produce chromatic notes, players use a technique called cross-fingering, where they close one or more holes located below an open hole to adjust the air column's resonance.

As instrument design evolved, additional keys were added to address limitations in fingering and intonation. These keys allow players to cover holes that are otherwise out of reach or to produce notes that cannot be achieved through standard finger hole configurations alone. Modern key systems, such as those refined by Theobald Boehm, further expanded these capabilities by allowing for the simultaneous closure of multiple holes, facilitating greater technical dexterity across all musical keys.1