Pitch sharpening in woodwinds

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 and amenable to numerical calculation. Yet pitch sharpening has gotten little attention. Now Seiji Adachi at the Fraunhofer Institute for Building Physics in Stuttgart, Germany, offers an explanation of the effect by modeling a minimal system—a flute with one open tone hole—as a system of coupled oscillators. Closed tone holes below the open hole essentially create a downstream pipe of adjustable length. The upper and lower flute sections will have their own resonant frequencies, but since the sections interact, the resonances shift—some higher, some lower. Moreover, some of the coupled modes are more easily excited than others. By extending his model to include an additional resonant mode in the upper bore, Adachi could quantitatively account for both pitch flattening and pitch sharpening in an actual recorder. (S. Adachi, Acoust. Sci. Tech. 38, 14, 2017, doi:10.1250/ast.38.14 .)