JP2000081887A - Plucked sound synthesizing method, and device and program storing medium therefor - Google Patents

Abstract

PROBLEM TO BE SOLVED: To synthesize more natural tone of stringed instrument. SOLUTION: A characteristic expressing friction between a string and an exciting body is given, and the friction Efr(n) is determined by inputting a speed VE according to the control of a user and a displacement y(i0, n) of the string, and using the friction characteristic based on the sound-generating mechanism, and a force F(n) applied to the string at the time of plucking string is calculated by summing Ffr(n) and F0 nΔt. And, the physical conditions regarding the string are given, and a displacement y(n+1) is calculated by inputting F(n) and using a differential equation based on the sound-generating mechanism, and the calculations of F(n) and y(n+1) are repeated predetermined times.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention synthesizes the timbre of a stringed musical instrument by using a string-plucking sound synthesizing method characterized in that the user's action on the sounding body and the frictional force associated with the movement represent the excited state of the sounding body. , A pluck sound synthesis method, an apparatus, and a recording medium.

[0002]

2. Description of the Related Art In a conventional electronic musical instrument, a user plays a plucked instrument sound such as a violin and a plucked instrument sound such as a guitar.
(1) Preset by various methods such as PCM sound source, FM sound source, etc. (2) Addition (sampling) by user recording sound, (3) Re-edit and edit the parameter expression by FM sound source model It has been created by methods such as synthesis, (4) various filtering processes, processing by adding distortion, and the like.

Further, continuous processing and subtle processing of timbre can be realized to some extent by processing such as filtering and adding distortion. However, many of these lack realism in terms of the vividness of instrument sounds, and the only way to create more realistic sounds was to use recorded sounds. In addition, the timbre of the musical instrument can be variously changed depending on the playing method. It is not practical to record variously changing timbres in advance, since it is necessary to record infinitely many sounds.

[0004]

SUMMARY OF THE INVENTION It is an object of the present invention to provide a method of synthesizing a plucked string sound which synthesizes a more natural tone of a stringed musical instrument and realizes a change in the tone color by a playing method, an apparatus therefor, and a recording medium. It is in.

[0005]

According to the present invention, a vibration of a string is represented by a differential equation as a model based on a sound generating mechanism, and the acoustic signal waveform is calculated for each time point by solving this numerically. In particular, in this model, the excited state of the string is expressed by the physical constant of the string, the action (excitation force) on the string by the player, and the frictional force associated with the action.

[0006]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 shows an outline of a functional configuration of a pluck sound color synthesizer according to the method of the present invention. Using a method of synthesizing a plucked sound, wherein the action on the sounding body by the user and the frictional force associated with the movement represent the excited state of the sounding body,
By giving an appropriate value to this model parameter,
The synthesized timbre waveform is completely represented.

An embodiment in which this apparatus is specifically applied to the "problem of synthesizing the timbre of a guitar sound generated by plucking a string with a normal finger" will be described. In this embodiment, a rigid string model is used as the vibrator. First, a physical model of a string to be used will be described. The behavior of the vibrating body is represented by the following differential equation.

[0008]

(Equation 1) Here, x: a value in the length direction of the string, y: displacement of the string, ρ: density, T: tension, E: Young's modulus (representing rigidity), κ: gyration radius, S: string cross-sectional area, f (X, x ₀ ,
t): external force density, x ₀ : string striking position, b ₁ , b ₃ : viscous resistance. The first term on the right side is the recovery force generated by the string tension,
The second term is the restoring force caused by having rigidity. Also,
The third and fourth terms are attenuation terms, and represent a frequency-dependent attenuation rate d given by the following equation by this formulation.

[0009]

(Equation 2) ω: angular frequency. The excitation model is the subject of the present invention and will be described later. The external force F (t) applied to the string is calculated by the excitation model. The relationship between _{f (x, x 0, t} ) and F (t) is given by the following equation.

[0010]

(Equation 3) 2δx: width of the excited body, g (x, x ₀ ): function that gives a distribution of force. The boundary condition in the case of both ends support is given by the following equation.

[0011]

(Equation 4) Here, L is the length of the vibrating body. Other initial conditions include g (x ₀ , x), the input position x _{0 of the} excitation, and the initial velocity _VE.
give. Solve these equations using the finite difference method,
Specify synthesis parameters and calculate displacements recursively. For the above oscillator model, see A. Chaigne et al.
“Numerical simulationsof piano strings. IA physi
cal model for a struck string using finite differe
nce methods, “Journal of the Acoustical Society o
f America, Vol.95, No.2, Fed.1994.

Next, the excitation model will be described. In plucking the strings, the strings are displaced more greatly than in the case of striking a piano or striking a violin. The greater the displacement, the greater the recovery force from the strings, and thus it is considered that a greater force is required to maintain the displacement of the strings. Therefore, it is assumed that a force F ₀ t in the form of a ramp function that increases in proportion to time and increases at a constant rate is applied to the string. Then, in order to simulate the occurrence of friction between the finger and the finger, the following relational expression, which is conventionally used for simulating a bowed string, is used. Friction force F
_fr (t) is given by the following equation.

[0013]

(Equation 5) Here, μ _d and μ _s are the kinetic friction coefficient and the static friction coefficient, P is the pressure of the exciter on the string, υ _R is the relative speed between the string and the exciter, and υ _C is the critical velocity. This friction characteristic is shown in FIG. This frictional characteristic is generally used for modeling the oscillation mechanism of a violin. For example, the literature bank, "Calculation of rise time of bowed string vibration by simulation method", Musical Acoustics Research Society, MA95-22, pp65-72, 199
It is shown in FIG.

In this equation, the applied frictional force is determined by the relative speed between the string and the exciter. Therefore, it is assumed that the excitation body is a uniform motion at a velocity V _E. Using the model of the frictional force, a force F applied to the strings at the time of plucking the strings is determined as follows.

[0015]

(Equation 6) Here, t _d is the time length of the force. By controlling the parameter relating to the frictional force and F ₀ , it is possible to control the noise and intensity of the waveform resulting from the friction. When a difference equation is derived using the finite difference method and equations (1) to (5) are simultaneously solved, the following recursive equation for obtaining displacement is obtained. Here, x = iΔx and t = nΔt. The recursive formula for the strings can be modified due to a difference in the difference scheme used (method of replacing the differential equation with a differential equation). In this embodiment, the one shown in the above-mentioned Chaigne et al. Document is described below.

[0016]

(Equation 7) The boundary conditions (Equations (3) and (4)) are represented by the following equations.

[0017]

(Equation 8) By specifying the following physical constants and other parameters as parameters, Equation (7), Equation (8), and Equation (9) are alternately performed while sequentially increasing n from n = 0, so that each position i A synthesized sound waveform for each time point n can be determined. However, it is necessary to partially correct the equation (7) for n = 0,1. That is, when n = 0 or n = 1 is substituted into, for example, y (i, n−2) in the equation (7), n
-2 is a negative value. In this case, y (i, n-2) is set to 0
And make corrections.

Regarding the vibrator, T: tension, E: Young's modulus, ρ: density, a: radius, L: length
Say, b₁: Damping coefficient, b _Three: Damping coefficient, excitable, F₀: Constant of ramp function force, V_E: Excited body velocity, μ
_d: Dynamic friction coefficient, μ_s: Static friction coefficient, P: For strings of excited body
Pressure, υ_C: Critical velocity, t_d: Time length of force Others: N: Number of divided vibrating bodies (the length of one divided element is Δx
F)_s: Sampling frequency, i₀: Excitation input position
Place, i_out: Displacement output position, g (i₀, I): Minute of power
This is a cloth function.

FIGS. 3 and 4 show an example of the displacement of one point on the chord calculated using the above model and its FFT spectrum. FIG. 3 shows the result when the friction term F _fr (t) is not considered as the force F applied to the string at the time of plucking the string. This results in a periodic waveform corresponding to the fundamental period of the string. FIG. 4 shows the result when the friction term is considered. It can be seen that a noise-like waveform is generated by the introduction of the friction term.

FIG. 5 shows the first 40 ms portion of a recorded sound waveform generated by an actual musical instrument and its FFT spectrum. From this, it can be seen that the signal power exists in a wide band and is noise-like. Also, it can be seen that peaks and valleys exist in a certain frequency band on the spectrum. This is considered to represent the characteristics of the resonance cylinder and radiation. Therefore, the spectrum envelope of the musical tone of the actual musical instrument is extracted in advance, and the spectrum envelope is applied to the synthesized string waveform, that is, the frequency envelope filtering shown in FIG. 1 is performed to simulate the recorded sound. L for extracting the spectral envelope
PC analysis was used.

FIGS. 6 (40 ms at the beginning) and FIGS.
(200 ms). FIG. 6 is about 100H compared to FIG.
It is very similar that the oscillation of z is not major, but the power is noise over a wide band. Further, the power ratio between the initial portion and the free vibration portion following the initial portion is about 30 dB. As a result of hearing comparison with the recorded sound, it was possible to realize a so-called rubbing sound when the guitar was plucked.

The above-described method of synthesizing a plucked sound according to the present invention is summarized as follows. That given characteristic representing the friction between the string and the excitation member, enter the displacement y of the velocity V _E and the chord corresponding to the control of the user (i _0, n), using a friction characteristic which puts sounding mechanism with obtaining the frictional force F _fr (n) Te, a first step of calculating the force applied to the chord F (n) by adding the F ₀ n.DELTA.t and F _fr (n) during repellent strings, given the physical conditions relating to the strings A second process of inputting the force F (n) and calculating a displacement y (n + 1) using a vibrating body model represented by a differential equation based on a sound generating mechanism; a first process and a second process; Is repeated until n reaches a predetermined value, and for the displacement y (n), the spectral envelope of the musical sound of the corresponding musical instrument determined in advance is filtered.

In this embodiment, the respective synthesis parameters are described as being invariant with respect to the time of the synthesized sound. However, for example, the pressure P of the exciter is changed in the process of calculating the synthesized sound at each point in time. Realistic control is possible. Also,
The "unnatural" control of the parameters can lead to new acoustic effects not available in real performance. Further, since the present invention relates to an excitation model, a vibrator other than a one-dimensional string may be used. For example, the present invention can be applied to a problem such as making a sound by rubbing an edge of a wine glass or a saw.

In this embodiment, the problem of estimating model parameters when an original sound signal is given is not described. However, parameters may be estimated from original sound using a method such as a neural network. It is characterized in that the model parameters are operated by using.

[0025]

As described above, in the present invention, a player expresses a model in consideration of the action on the strings and the friction accompanying the action. In particular, a friction sound that could not be expressed conventionally can be expressed by considering friction. Therefore, a tone with higher naturalness can be synthesized as compared with the conventional tone synthesis method.

In this model, the sound generation mechanism can be characterized by a small number of variables. Therefore, if these variables are changed continuously, the timbre can be easily and continuously controlled. In particular, by controlling the ratio of the fricative sound, the degree of freedom for obtaining a desired tone is increased.

[Brief description of the drawings]

FIG. 1 is a schematic diagram of the configuration of a string sound color synthesis apparatus according to the method of the present invention.

FIG. 2 is a graph showing friction characteristics (speed-friction force characteristics) used in the present invention.

FIG. 3 is a comparison of a string displacement result calculated when a string-plucked tone color synthesizing apparatus realizing the method of the present invention is applied to “a problem of synthesizing a tone of a guitar sound generated by a string plucked by a normal finger”. FIG. 7 is a diagram showing a chord displacement (40 ms at the beginning) and an FET spectrum calculated without considering friction for the sake of clarity.

FIG. 4 is a diagram illustrating a string displacement (40 ms at the beginning) calculated when a string-plucked tone color synthesizing apparatus realizing the method of the present invention is applied to a “problem of synthesizing a tone of a guitar sound generated by a string plucked by a normal finger”. ) And FFT spectrum.

Fig. 5 Recorded sound guitar waveform (first 40 ms) and FFT
The figure which shows a spectrum.

FIG. 6 is a synthesized sound waveform (first 40 ms) obtained by applying the plucking tone color synthesizer that realizes the method of the present invention to “a problem of synthesizing the tone color of a guitar sound generated by plucking a string with a normal finger”. And FIG.

FIG. 7 is a synthetic sound waveform (200 ms at the beginning) obtained by applying the plucking tone color synthesizing apparatus realizing the method of the present invention to “a problem of synthesizing the tone color of a guitar sound generated by plucking a string with a normal finger”. And FIG.

Claims (3)

[Claims] 1. A method for calculating an acoustic signal waveform at each time point using a model based on a sounding mechanism, wherein the model represents a physical condition of a sounding body by a differential equation, and the model includes: A musical tone synthesizing method characterized in that the sound signal waveform is obtained by numerically solving the differential equation using a physical constant of a sounding body or a variable according to an operation performed by the user on the sounding body. Is a string in a stringed musical instrument, wherein a user's action on the sounding body and a frictional force associated with the movement represent an excited state of the sounding body, wherein 2. A method for calculating a sound signal waveform at each time point using a model based on a sounding mechanism, wherein the model represents a physical condition of a sounding body by a differential equation, and the model includes: A musical sound synthesizer characterized in that the sound signal waveform is obtained by numerically solving the differential equation using a physical constant of a sounding body or a variable according to an operation performed by the user on the sounding body. Is a string in a stringed musical instrument, and a user's action on the sounding body and a frictional force associated with the movement represent an excited state of the sounding body, wherein 3. A method of calculating a sound signal waveform at each time point using a model based on a sounding mechanism, wherein the model represents a physical condition of a sounding body by a differential equation, and the model includes: In the musical sound synthesis processing, the sound signal waveform is obtained by numerically solving the differential equation using a physical constant of a sounding body or a variable according to an operation performed by the user on the sounding body. Is a string in a stringed musical instrument, and a program for executing a plucking sound synthesis process, wherein a user's action on the sounding body and a frictional force associated with the operation represent an excited state of the sounding body, are stored. Medium.