Supercomputer simulation reveals how the reed vibrations are controlled in single-reed instruments

Tsukasa Yoshinaga – yoshinaga@me.tut.ac.jp
Hiroshi Yokoyama – h-yokoyama@me.tut.ac.jp
Akiyoshi Iida – iida@me.tut.ac.jp
Toyohashi University of Technology
1-1 Hibarigaoka, Tempaku, Toyohashi 441-8580 Japan

Tetsuro Shoji – tetsuro.shoji@music.yamaha.com
Akira Miki – akira.miki@music.yamaha.com
Yamaha Corporation
10-1 Nakazawacho, Nakaku, Hamamatsu 430-8650 Japan

Popular version of paper 2aMU1

Presented 9:35-9:50 morning, June 9, 2021

180th ASA Meeting, Acoustics in Focus

Single-reed instruments, like clarinet, produce sounds with reed vibrations induced by airflow and pressure in the player’s mouth. This reed vibration is also affected by the sound propagation in the instrument so that the player can change the musical tones by controlling the tone holes. Therefore, to analyze the single-reed instrument, it is important to consider the interactions among the reed vibration, sound propagation, and airflow in the instrument. In particular, the airflow passing through a gap between the reed tip and mouthpiece becomes turbulent, and it has been difficult to investigate the details of the interactions in the single-reed instruments.

In this study, we conducted a numerical simulation of sound generation in a single-reed instrument called Saxonett which has a clarinet mouthpiece and recorder-like straight resonator.  In the simulation, airflow and sound generation were predicted by solving the compressible Navier-Stokes equations, while the reed vibration was predicted by calculating the one-dimensional beam equation. To accurately predict the turbulent flow in the mouthpiece, computational grids were needed to be smaller than the turbulent vortices in the airflow (approximately 160 million grid points were constructed). In contrast, the simulation time became larger than the usual flow simulation because the frequency of musical tone was relatively low (approximately 150 Hz). Therefore, the supercomputer was needed to simulate the turbulent flow and sound generation associated with the reed vibration.

By setting a mouth-like pressure chamber around the mouthpiece in the simulation and inserting the airflow, the reed started vibrating and the sound was produced from the instrument. Moreover, amplitudes of the reed oscillation as well as the sound generation were changed by adding the lip force on the reed. Then, by controlling the lip force, a stable reed vibration was achieved. As a result, the reed waveform and sound propagated from the instrument well agreed with the experimental measurements.

With this simulation technology, we could observe the details of airflow and acoustic characteristics inside the instrument while the player is playing the single-reed instrument. By applying the simulation to various designs of the instruments, we can clarify how the sound is produced differently in each model and contribute to the improvement of the sound quality as well as the player’s feeling.

 

Numerical simulation of the single-reed instrument. Blue to red color shows the pressure amplitude whereas the rainbow color vectors indicate the flow velocity.

 

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