aKyushu Institute of Technology
The function of the register hole of the Clarinet can be basically explained from the common property of two delay systems (J. Phys. Soc. Jpn, Vol.83, 124003 (2014)). Namely, if the strength of a short time delay is sufficiently small but non-negligible, the third harmonic is well sustained over a wide range of the short delay time. This fact indicates that the register hole with a small radius raise the pitch of the first register notes in a wide range more than an octave to the second register notes by a twelfth (19 semitones). However, the reflection function has many delay peaks even when only the register hole is opened. That is, the clarinet should be characterized as a multi-delay system. In this paper, we focus on the effect of a very short time delay, which characterizes the reflection from the discontinuity in the mouthpiece. We numerically found that the function of register hole survives even for such a three delay system including the reflection from the mouthpiece.
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