The sawari is an instrumental mechanism of biwa and shamisen. Its physical structure involves a solid surface of very small size that the vibrating string touches dynamically, creating a peculiar timbre in the produced sound. This paper proposes a model of the sawari mechanism, which is a unilateral constraint on the displacement of a string, that is, a mechanism that is essentially nonlinear and time-dependent because of contact/separation phenomenon. Here, the key point of the model is the repelling force caused by the lateral elastic deformation of the string. The study is focused on the dynamic effect under an idealized problem setting so that the string vibrates at no loss of mechanical energy without any interaction with other objects such as a resonator that terminates the string in the real instrument. A numerical method is given for the computation of this problem. The numerical results show a gradual build-up of high-frequency oscillations that eventually prevail over the entire string motion. The short-term spectrum changes in a continuous way with time, maintaining a nearly harmonic structure on the fundamental frequency of the associated sawari-free problem.
Some drums have, typically, a hollow trunk (or a barrel) with a circular membrane at each of the two ends. In this type of drum structure, the two membranes interact with each other through the air between them inside the body. Even if the two membranes have an identical fundamental resonance frequency, the interaction results in two resonance frequencies. At the lower resonance, the two membranes vibrate in phase. Since the membranes must move the internal air, the frequency at the lower resonance is lower than that of the original resonance (without air loading). At the higher resonance, they vibrate out-of-phase, causing compression or expansion of the internal air simultaneously. The frequency at this resonance is higher than that of the original resonance since, in this case, the air works as a spring. In this paper, resonance frequencies and mode shapes of the coupled membranes are investigated using an analytical model. The membranes are assumed to be ideal (i.e., no bending stiffness) and the body is assumed to be ideally rigid. Since it is a common practice that the two membranes are slightly (intentionally) miss-tuned, the main interest of this paper is to simulate the effect of this miss-tuning on the resulting resonance frequencies and mode shapes. Numerical results for the case of a 48 cm diameter and 50 cm length Japanese drum are presented.
Sound quality (SQ) is a perceptual or subjective reaction to a sound and its concept becomes one of the important factors that improve the competitive power of a product. Through the various studies related to SQ by psycho-acoustic researchers, models for objective measures that substitute subjective evaluation, called SQ metrics, have been proposed which consider human auditory characteristics. Representative SQ metrics are loudness, sharpness, roughness, and fluctuation strength. For other SQ metrics except loudness, however, the calculation algorithms have not been standardized yet. The purpose of this study is to investigate whether there is difference among the commercial software for the calculation of SQ metrics and if any, how much difference exists among them. For this, three kinds of popular commercial software and one self-coded program were chosen and by applying them to some sample sounds, four representative SQ metrics were calculated and compared. As a result, it was confirmed that there are considerable differences among the calculated results of SQ metrics including loudness. This means that it is necessary to standardize SQ metrics as soon as possible before everything else and in addition, to mention used SQ software when an index that can predict SQ is developed or SQ database for any kind of product is created.