Abstract
Study of analyzing methods of musical instrument tone decay is made. One of the method is spectrogram which is often used to analyze decay rate of musical instrument tone. And the other is reverberation decay curves which are often used to analyze decay characteristics of room reverberation. In this paper, the reverberation decay curves are considered to apply to musical instrument tone. The reverberation decay curves characterize energy held in the musical instrument while the spectrogram characterizes sound power of the instrument. If the sound output is given as analytic signal, the spectrogram indicates same gradient as the reverberation decay curve. But in general, same figure can't be indicated.
Three ideal systems are examined, including system containing single or multiple resonance, and system with resonance vibration which is started or stopped in the midst of time scope. It is shown that reverberation decay curves calculated using Wigner distributions are the most resemblant to expected figure among three known methods of reverberation calculation, because uneven component of overall curve and interference component of narrow band curve can be eliminated by the Wigner method. Still more, reverberation decay curves by the Wigner method are less influenced by window length than the spectrogram.
Reverberation decay curves, as well as spectrogram, are applied to musical instrument tones. Reverberation decay curves by the Wigner method can characterize the tone decay rate while the spectrogram is afflicted with interference. It is shown that piano tone decay can be characterized as two or four step decay figure in higher partial tone by the reverberation decay curves.
