Department of Communication Design Science, Faculty of Design
Associate Professor SAMEJIMA Toshiya
Our laboratory has been engaged in developing physical modeling sound synthesis of almost all kinds of musical instruments. The title above is a slogan for our activity. Through the activity, we hope that an answer to the essential question shown in Figure 1 could be revealed.
As an example, we would like to introduce physical modeling sound synthesis of cymbals. Since the essence of the cymbal is nonlinearity from a physical point of view, cymbals are also called nonlinear percussion instruments.
Figure 2 shows a physical model of a cymbal. The body of a cymbal is modeled as a shallow spherical shell. In addition, a washer, related to the support conditions of the cymbal, is modeled as a single-degree-of-freedom (SDOF) vibration system and involved in the physical model of the cymbal. Furthermore, a stick/mallet striking the cymbal is considered in the physical model. The mallet head is modeled as an SDOF system having a mass and nonlinear stiffness. The mallet stick is modeled as an Euler-Bernoulli beam and treated as a multi-degree-of-freedom (MDOF) system using the finite element method, and coupled with the cymbal vibration.
Figure 3 demonstrates that the difference of the method of holding the mallet stick has effect on the vibrational acceleration spectrogram. In both tight grip and loose grip, the spectrogram patterns show the growth at higher frequencies with time delay, which indicates the crash sound. In loose grip, the time delay of the crash sound becomes slightly longer than that in tight grip.
Movie 1 shows the time development of the deformation in the cymbal and mallet; the movie also includes the cymbal sound generated by the physical calculations. One can grasp changes of the vibrational state due to the difference of the condition of the washer and mallet stick.
Movie 1 Time evolution of the shapes of the mallet and cymbal: Loose grip and SDOF washer.
Through developing such a physical modeling sound synthesis, we could reveal how the timbre of musical instruments alters according to their forms and performance methods.