Abstract
Acoustical differences between normal and cross fingerings of the shakuhachi with five tone holes are investigated on the basis of the pressure standing wave along the bore and the input admittance. Cross fingerings in the shakuhachi often yield pitch sharpening in the second register, which is contrary to our conventional understanding of pitch flattening by cross fingerings and is called intonation anomaly. It is essential to identify and discriminate the input admittance spectra between the upper and lower bores on the basis of the standing-wave patterns. Spectrum (or mode) switching between both types of bores is a clue to the cause of the intonation anomaly. This is illustrated by considering stepwise shifts of tone holes while keeping the hole-to-hole distances fixed and by comparing the resulting switches in input admittance spectra. When spectrum switching occurs, docking of the upper and lower bores makes up a higher resonance mode throughout the whole bore and then leads to the intonation anomaly. This spectrum switching on the cross fingering is generalized as the diabatic transition (the Landau–Zener effect) in physics.
