This is the report about the consideration on the stochastic properties of the level fluctuation by the various kinds of the disk played music. The time series of sound levels which are obtained by three sampling methods, are investigated in terms of well fitting probability density functions. Three sampling methods are as follows: a) level sampling at every 0. 1 seconds, b) sampling by equivalent sound levels averaged during every one second, c) level sampling at hearing peaks of loudness. The following results are obtained. 1) The well fitting probability density functions are the Declined-Beta distribution by the linear combination of Beta distribution and the straight line distribution using the suitable parameters. 2) The well fitting transition probability density functions are the joined functions by the Declined-Beta distribution and the binomial distribution using the suitable parameters.
This is the report about the quantization method of the rhythm and fluctuation of tempo in the musical performance, and about these results. The method of analysis is as follows. The time intervals between the successive peaks of played tone of a melody are measured. The power spectrum of these time intervals is calculated by the Fourier analysis. The rhythm and the fluctuation of tempo in "Romance" used as the test melody are analysed. They are played on the guitar by different 10 players. The results obtained are as follows. 1) It is observed that the fluctuation of rhythm at low frequency components in power spectrum is dominant, and the high frequency components in power spectrum are comparatively small. However, there are few examples which the power of each component has no relation with the frequency. 2) The component which has the period same as the duration of three beats of the melody, is dominant in almost results. However, there are following two types as to this property of rhythm. a) The time duration of the 1st and the 2nd beat are short, and the 3rd one is long. b) The time duration of the 1st and the 3rd beat are long, and the 2nd ones is short.
In a water-filled shock tube with rectangular cross section, it is shown that the propagation velocity of pressure wave in degassed water is around 200 m/s. The propagation velocities of a pressure wave in bubbly water are also determined as a parameter of void fraction, and it is clarified that the propagation velocity is affected by the shape of cross section and the elastic property of the tube materials and that the results are estimated by a modeling consideration of "water hammer" theory. Moreover, for one or two slug bubbles in a rectangular water filled shock tube the following facts are ascertained; (1) Its oscillation period by a pressure wave and the pressure change in it can be qualitatively shown by mean of a springs-masses model of slug bubble train, in spite of large deformation, such as water jet generation, of the bubbles. (2) The velocity of water jet, formed at the top or bottom surface of the slug bubble, is around 10m/s.
High-frequency sound fields in a deep ocean symmetrical duct with source and observation points on a duct axis are investigated by three methods: (1) discrete mode and continuous spectrum representation, (2) acoustical ray and trapped mode representation, and (3) near field perturbation representation. The accuracy and applicable ranges of these alternative representations are discussed from numerical comparisons for a specific example. Acoustical ray and trapped mode representation is found to be most convenient from the viewpoints of numerical evaluation and physical interpretation. Error criteria due to the truncation of ray or mode series are also discussed. Sound fields for deep ocean duct are analyzed as parameters of frequency, duct width and velocity change ratio in duct.
The critical masking interval, the time period during which wideband noise is effective in masking a brief signal (click), is investigated. Both the click and the noise are low-pass filtered so that the power spectra of signal and noise have similar shape. In the first experiment, a click is presented in the temporal center of the masker and the masked threshold is measured as the duration of the masker is varied from 2ms to 400ms. The result shows that the critical masking interval is 12 to 20ms. In the second experiment, the simultaneously masked threshold of a click is measured in various temporal locations relative to the noise burst whose duration varies. That is, the interval T_1 between the onset of the noise and the click, or the interval T_2 between the click and the offset of the noise is varied. The results are as follows: (1) The masked threshold is not greatly affected by changing the duration T_1 from 1ms to 100ms when the duration T_2 is fixed at 100ms. Inversely, the threshold increases as the duration T_2 is varied from 1ms to 10ms for T_1=100ms. (2) When the click is located at the onset of the masker (T_1=0ms) or at the offset (T_2=0ms), the threshold increases with T_2(T_1) at the rate of 10dB/decade for T_2(T_1) less than 10ms. (3) Overshoot, the increase in masking for intermediate noise durations occurs under the condition of T_1=T_2≠0 or T_1=0 or T_2=0. Next, it is shown that the overshoot phenomenon can be interpreted by a running average model if it is assumed that subjects adopt two different criteria in detecting of the click for short-maskers and for long-maskers. Finally, if it is assumed that internal response to the masker in the auditory system persist, gradually decaying, after its physical termination, the above results (1) and (2) imply that the threshold is greatly affected by the internal response following the click and the effective time interval in masking is about 10ms.