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 ω
U and ω
L excited independently. The ω
± differ even if ω
U= ω
L. The normal effect of cross-fingering, i.e., pitch flattening, corresponds to excitation of the ω
--mode, which occurs when ω
L⪆ω
U 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 ω
L⪅ω
U 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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