Today’s concert woodwinds feature as many as two dozen tone holes and a bevy of levers, called keys, that put the full chromatic scale over multiple octaves at a player’s fingertips. Yet even on keyless instruments, like the recorder, bagpipe chanter, and the Japanese shakuhachi, a player can use so-called cross-fingering to fill in the chromatic gaps: Covering one or more tone holes below the first open hole usually lowers, or flattens, the pitch by a semitone. But in what’s known as an intonation anomaly or pitch sharpening, cross-fingering can, in some circumstances, raise the pitch.
The flute is often presented as an example for understanding wave resonances: The open hole closest to the player’s mouth sets the effective length, which in turn determines the resonant frequencies and thus the notes produced. Although the actual pitch details aren’t quite that simple, the behavior is for the most part well understood...
