Acoustical Science and Technology
Online ISSN : 1347-5177
Print ISSN : 1346-3969
ISSN-L : 0369-4232
Resonance modes of a flute with one open tone hole
Seiji Adachi
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2017 Volume 38 Issue 1 Pages 14-22


A minimal model explaining intonation anomaly, or pitch sharpening, which can sometimes be found in baroque flutes, recorders, shakuhachis etc. played with cross-fingering, is presented. In this model, two bores above and below an open tone hole are coupled through the hole. This coupled system has two resonance frequencies ω±, which are respectively higher and lower than those of the upper and lower bores ωU and ωL excited independently. The ω± differ even if ωU= ωL. The normal effect of cross-fingering, i.e., pitch flattening, corresponds to excitation of the ω--mode, which occurs when ωL⪆ωU and the admittance peak of the ω--mode is higher than or as high as that of the ω+-mode. Excitation of the ω+-mode yields intonation anomaly. This occurs when ωL⪅ωU and the peak of the ω+-mode becomes sufficiently high. With an extended model having three degrees of freedom, pitch bending of the recorder played with cross-fingering in the second register has been reasonably explained.

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© 2017 by The Acoustical Society of Japan
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