JP3508976B2 - Interpolated tone color synthesis method - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an interpolated tone color synthesizing method by a physical model in which two perceptually different tone colors are used as both ends, and tone colors obtained by interpolating these two tone colors at arbitrary ratios are synthesized.

[0002]

2. Description of the Related Art In a conventional electronic musical instrument, a user adds various tones (1) preset by various methods such as PCM sound source and FM sound source, and (2) addition (sampling) by recording sound by the user. , (3) parameter synthesis represented by a model such as an FM sound source is re-synthesized by modifying and editing, (4) various filtering processes, processing by adding distortion and the like.

Further, continuous processing of timbre and subtle processing could be realized to some extent by processing such as filter processing and distortion addition. However, these are to destroy and transform a certain timbre, and to give a specific timbre as a target and interpolate towards that timbre.
More advanced timbre control was not possible.

[0004]

SUMMARY OF THE INVENTION An object of the present invention is to synthesize a tone color that is an arbitrary perceptual internal division point that includes both ends of two different tone colors. An object of the present invention is to provide an interpolated tone color synthesis method capable of realizing tone color synthesis that continuously changes the tone.

[0005]

As shown in FIG. 1, a tone color A sounding body and a tone color B sounding body are used by using a tone color A physical model and a tone color B physical model based on a tone color generating mechanism. Of the synthesis parameters including at least the physical constants of the interpolation parameters α according to the degree of the desired proximity to the timbres A and B.
, A new parameter Z is created by interpolation, and the new parameter Z is used to calculate the acoustic signal waveform at each time point based on the physical model based on the tone color generation mechanism to synthesize the interpolated tone color. .

[0006]

BEST MODE FOR CARRYING OUT THE INVENTION An embodiment in which the present invention is applied in the case of synthesizing a timbre emitted by a one-dimensional vibrating body excited by hitting or repelling (repelling) will be described. In this embodiment, the excitation model used is one that imitates plucking and plucking.
The vibrating body uses a rigid string model. First, the physical model used will be described. The behavior of the vibrating body is expressed by the following differential equation.

[0007]

[Equation 1] Here, y: displacement of the string, μ: linear density (density ρ × area S), 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. The first term on the right-hand side is the restoring force generated by the tension of the strings, the second term is the restoring force caused by the rigidity, and the third and fourth terms are the damping terms,
This attenuation term expresses a frequency-dependent attenuation rate d given by the following equation by the formulation.

D (ω) = b ₁ + b ₃ ω ² ω is the angular frequency. With respect to the external force term (excitation), the string striking by the piano hammer is modeled as the following equation. _MH d ² η / dt ² = −F _H (t) (2) F _H (t) = K | η (t) −y (x ₀ , t) | ^p , η (t) > y (x ₀ , T) = 0, η (t) <y (x ₀ , t) (3) η: Displacement of hammer, F _H (t): Force applied to string, M _H :
Hammer mass, K, p are constants determined experimentally. The relationship between f (x, x ₀ , t) and F _H (t) is given by the following equation.

F (x, x ₀ , t) = F _H (t) g (x, x ₀ ) / (μ∫g (x, x ₀ ) dx) (4) ∫ is from x ₀ −δx to x _0. Up to + δx, 2δx: width of hammer (exciter), g (x, x ₀ ): function that gives force distribution. Boundary conditions are given by the following equation in the case of both-end support.

Y (0, t) = y (L, t) = 0 (5) ∂ ² y (0, t) / ∂x ² = ∂ ² y (L, t) / ∂x ² = 0 (6 ) L: Length of the vibrating body. In addition, g as an initial condition
(X ₀ , x), excitation input position x ₀ , and initial velocity V _HO
give. Solve these equations using the finite difference method,
Then, a physical constant is designated as a synthesis parameter, and the displacement and the like are recursively calculated. Although a piano string model was used here, the vibration of the elastic body can be reduced by setting the tension of the vibration body parameter to 0 and using appropriate values for the other parameter values.
In other words, vibration can be simulated when a metal rod without tension is excited by a hammer.

For the above physical model, refer to the document A. Ch
Aigne et al., “Numerical Simulat”
ions of Piano Strings. I. A
physical model for a str
uck string using finishing d
difference methods "Journal
of the acoustic societ
y of America, Vol. 95, No. Two
Feb. 1994.

As a basic model of a sound such as a guitar sound excited by plucking a string, that is, a plucked string, there is one that gives an initial displacement and an initial velocity of 0 as initial conditions. There are some more complicated models that give a certain acceleration as the movement of the finger, and ones that consider the resistance of the finger, but no one that formulates the physical behavior of the string and plucked body has been proposed.

Therefore, in this embodiment, the plucking model shown in FIG. 2 is proposed. First, the plucked body 11 collides with the string 12 at a certain speed, and a displacement occurs from the equilibrium position while maintaining contact with the string 12. Upon contact, a repulsive force similar to that of the string striking model is generated. After a certain period of time, the plucked string 11 is moved to the string 12
Rebound from the string before the repulsive force from becomes 0. The frictional force generated while the plucked string 11 and the string 12 move while making contact with each other is ignored.

This plucking model can be expressed by the following equation. F _H (t) = K | η (t) −y (x ₀ , t) ^│p , η (t) ＞ y (x ₀ , t), t <t _p1 = 0, others (7) t _p1 : Contact time between plucked string 11 and string 12 (force duration)
This is an introduction of the force continuation length t _p1 into the string striking model of the equation (3), where t _p1 <ts, where ts is the force continuation length in the string striking model. As a result, the external force applied to the string 12 is rapidly attenuated at t = t _p1 and becomes 0 in a step function manner. In addition, p is considered to be different depending on the material of the plucked body 11,
A value different from the reference value for striking is used. In other words, it is considered that the fingertip at the time of plucking the string is softer than the piano hammer and the repulsive force generated is small, and p = 3.5 is set as the reference value in the plucking model. Further, the continuation length of the force is, for example, t _p1 = ts /
Set to 2. Here, when the duration t _p1 is kept sufficiently long, the exciter naturally separates from the string and the force becomes 0, which is a suspicion of string striking, and the duration at this time is ts. This model can represent both striking and plucking by manipulating the exponential coefficient p and the duration t _p1 and is an extension of the conventional model.

Using the finite difference method, equations (1), (2),
By solving the equations (4) to (7), the following recursive equation for obtaining the displacement is obtained. Where x = iΔx, t = ηΔ
replaced with t. Note that the recursive formula may be modified depending on the difference scheme used and the like, but in this embodiment, the C
Those shown in the literature such as haigne are described below.

[0016]

[Equation 2]

[0017]

[Equation 3]

[0018]

[Equation 4] n_p1Is the mode setting time.
Represent, n_s/ 2 (ts / 2) shows plucked sound
Forget The boundary condition can be expressed by the following equation. y (0, n) = y (N, n) = 0 y (−1, n) = − y (1, η), y (N + 1, n) =
-Y (N-1, n) n: time, i: position on the string Specify the following physical constants and others as parameters
By increasing the value of n from 1 by 1
The operations of (8) and equations (9) and (10) are performed alternately.
The synthetic sound waveform at each time point n at each position i is obtained by and
be able to.

For the vibrating body, T: tension, E: Young's modulus, ρ: density, a: radius, L: length, b ₁ : damping coefficient, b ₃ : damping coefficient, and for the exciter, M _H : mass, p: exponential coefficient, K: stiffness coefficient,
t _p1 : contact time, and others N: number of divisions of the length L of the vibrating body (length of one divided element is Δx), i ₀ : input position of excitation, i
_out : output position of displacement, g (i ₀ , i): distribution function of force, V _HO : initial velocity.

In the sounding mechanism model adopted in this embodiment, the parameters X and Y of the physical models A and B which generate two tone colors are obtained. Here, physical model parameter estimation is not performed, and parameters for obtaining two perceptually different synthesized sounds are used as parameters for both ends used for interpolation. These X and Y can be expressed as follows. X = (T _x , E _x , ρ _x , ...), Y = (T _Y , E _Y , ρ _Y , ...) (11) These parameters X and Y at both ends are given the interpolation rate. α
Is used to interpolate between the corresponding parameters to obtain a new parameter Z (α).

Z (α) = (T (α), E (α), ρ (α), ...) A specific example of the method of parameter interpolation processing will be described below. 1. When timbre synthesis is performed by using the sound of a string excited by striking and the sound of an elastic body excited by striking as both-end tones (Fig. 3) (1) As excitation parameters, M _H , K, p and continuation of force There is a length t _p1 . In this example, assuming that the string and the elastic body are both hit with the same hammer (exciter), M _H , K, p are
By fixing the same value to X and Y and making t _p1 sufficiently large, that is, the vibrating body is naturally separated from the exciter body by the repulsive force, the impact is simulated. Therefore, in this case, the formula (3) may be used instead of the formula (10) for the calculation of the synthesized tone color.

(2) Of the parameters of the vibrating body, the density,
The radius, length, and damping coefficient are fixed to appropriate values for X and Y, the Young's modulus E of the string is E _S = 0, and the tension of the elastic body is T _b = 0. (3) Tension T of the string from the fundamental frequency f _{1 of the} timbre to be generated
_S and Young's modulus E _b of the elastic body are calculated by the following equation.

F ₁ = (1 / 2L) √ (T _s / μ) = (1
/ 2La) √ (T _s / ρπ) f ₁ = (Kπ / 2L ² ) √ (E _b / ρ) = (Ka / 4L
² ) √ (E _b / ρ) (4) Give the interpolation rate (coefficient) α (0 <α <1), and (3)
Z (α) is obtained by linearly interpolating the T _s and E _b obtained in (1) by Z (α) = (E (α) = αE _b , T (α) = (1-α)
T _s ) 2. When synthesizing interpolated tones by using the plucked sound of guitar strings made of different materials as both-end timbre (Fig. 4) (1) Fix the excitation parameter to a value that imitates plucked string.

(2) For the parameters of the vibrating body (guitar string), the density, radius, length, and damping coefficient are linearly interpolated as follows at a given interpolation rate α. (Ρ (α), a (α), ...) = (αρ _X + (1-
α) ρ _Y ), αa _X + (1-α) a _Y , ...) (3) A constant B _i (i =
X, Y) are respectively obtained and are linearly interpolated by α according to the following equation.

B _i = π ³ a _i ⁴ E _i / 8L _i ² T _i , i = X, Y, B (α) = αB _X + (1-α) B _Y (12) (4) The fundamental frequency f ₁ to be generated is given, and the tension T (α) corresponding to this is determined. T (α) = (2L (α) a (α) f ₁ ) ² ρ (α) π (13) (5) Young's modulus E (α) is calculated from the following equation.

E (α) = B (α) 8L (α) ² T (α) / π ³ a (α) ⁴ (14) (6) (2), (3), (5) Using the parameters, n (n) is sequentially increased, and equation (8) is obtained for each n.
And the formulas (9) and (10) are alternately calculated, and F _H (n) =
The minimum n that becomes 0, that is, n _s is obtained. Continuation length ts at string striking obtained in this way 1/2 of (n _s )
Continuation length t _p1 (α) = ts (α) / 2 (n
Let _p1 (α) = n _s (α) / 2).

3. When interpolating timbre synthesis is performed with the string-sounding sound of the piano string and the string-plucking sound of the guitar string as both ends (FIG. 5) (1) Of the excitation parameters, M _H and K are the same values for the string-striking and plucking strings, and p , T _p1 are linearly interpolated between the reference values of striking and plucking with a given interpolation rate α by the following equation.

P (α) = αp _x + (1-α) p _Y t _p1 (α) = αts (α) + (1-α) ts (α) / 2 = (1 + α) ts (α) / 2 This ts (α) (n _s (α)) is obtained as obtained in (6) of 2 above. In this case, t _p1 (α) is a linear interpolation between the string striking duration ts (α) and the plucking string duration ts (α) / 2. As a result, the functional form of the external force recursively obtained is also interpolated.

(2) Regarding the parameters of the vibrating body, the density, radius, length and damping coefficient are linearly interpolated by α as follows. (Ρ (α), a (α), ...) = (αρ _X + (1-
_{α) ρ Y, αa X +} (1-α) a Y, ···) obtains the non-harmonic constants B by (3) (12), which linear interpolation.

(4) From equation (13), the tension T (α) to be the target fundamental frequency is determined. (5) The Young's modulus E (α) is calculated from the equation (14). As described above, various parameters are linearly interpolated according to the interpolation rate α, and the interpolated tone color is synthesized using the interpolated parameter Z (α). FIG. 6 shows the functional configuration of the tone color synthesis. The interpolated new parameter Z (α) is given the initial velocity V, mass _MH , rigidity K, p, and continuation length t among the parameters to the string striking / plucking model, and the tension T, Young's modulus E, density ρ , Radius a, length L, and damping coefficients b ₁ and b ₃ are set in the vibration body model, and the displacement y (i, n) of the vibration body at each time point is set.
And the parameters of the string-plucking / plucking model, the equations (9) and (10) or the equations (9) and (3) are calculated to obtain the external force F _H (n), and this F _H ( n) and the parameters of the vibrating body model, the equation (8) is calculated to obtain the displacement y (i, n + 1) of the vibrating body, and the equations (9) and (1
0) (or (9), (3)) and the equation (8) are alternately calculated at each time point. The displacement or vibration speed of the vibrating body at a certain point is output as a synthetic sound waveform Z (n).

In the above description, the interpolation coefficient (ratio) α is invariable with respect to the time of the synthesized tone color, but if it is changed in the process of calculating the synthesized tone color and each time point, the tone color can be changed with time. For example, when α is continuously changed from 0 to 1 with time, morphing can be performed in which the tone color at one end naturally changes to the tone color at the other end. Although the estimation of the model parameters when two original acoustic signals are given is not described above, the parameters may be estimated from the original sound by using a method such as a neural network. It is characterized by using it and interpolating the model parameter.

In the above-mentioned embodiment, the case of a one-dimensional vibrating body has been described, but the same can be realized in the case of a two-dimensional vibrating body. That is, once the model is constructed, tone color interpolation can be realized regardless of the dimension of the sounding body shape. The present invention can also be applied to a model of characteristics such as resonance and radiation. Further, by designating the fundamental frequency and adjusting the tension in the case of a string and the Young's modulus in the case of an elastic body, a synthetic sound having a desired fundamental frequency can be obtained. This is very important when considering its use as a musical instrument.

[0033]

As described above, according to the present invention, it is possible to interpolate different timbres such as string striking and plucking. Further, once the model is constructed, the timbre interpolation can be realized by interpolating the physical parameters. Therefore, there are few parameters to be controlled in the timbre interpolation, and the control is easy. If the two timbres have a common attribute, the interpolated timbre can also maintain it. This is different from tone color control in which there is no target, such as simply adding distortion, which allows synthesis of tone colors that are close to the tone colors at both ends to an arbitrary degree, increasing the degree of freedom in tone color control. This makes it possible to have a function as a new electronic musical instrument. Further, in computer graphics, continuous deformation of images is called morphing, which has already been put to practical use and is widely used, but sound morphing can be performed in combination with this image morphing.

Further, by using the equations (8), (9) and (10), especially (10), not only the striking string but also the synthetic sound waveform of the plucking string can be calculated using the physical parameters. Since the timbres are synthesized by calculation, not only the physical constants of the sounding body corresponding to those of a real musical instrument but also timbres that do not normally exist in reality, for example, assuming a remarkably long string, can be generated.

[Brief description of drawings]

FIG. 1 is a diagram showing a processing procedure of a method of the present invention.

FIG. 2 is a diagram showing the behavior of a plucked model.

FIG. 3 is a diagram showing an example of interpolation of parameters of a string striking sound and an elastic body sound excited by striking.

FIG. 4 is a diagram showing an example of parameter interpolation of plucked sound of guitar strings made of different materials.

FIG. 5 is a diagram showing an example of parameter interpolation of a striking sound and a plucking sound.

FIG. 6 is a diagram for explaining a synthetic sound generation calculation.

Claims (2)

(57) [Claims] 1. A method for synthesizing interpolated tones of two sounding mechanisms that are excited by hitting and repelling, wherein each sounding mechanism is represented by a parameter group, and the parameter group is a behavior of a sounding body. It defines a differential equation expressing the behavior of the exciter and the differential equation expressing, the differential equation expressing the behavior of the exciter is a function of the displacement of the exciter and the force applied to the sounding body, the sounding body If the displacement of the exciter is equal to or more than the displacement of the sounding body and the contact time between the exciter and the sounding body is less than the predetermined time, the applied force has a value according to the difference between the displacement of the exciter and the displacement of the sounding body. It is specified to be 0 when other than, the predetermined time is a parameter included in the parameter group, when the excitation is a hit, a sufficiently large value is designated as compared with the case where the excitation is repulsion, Hit and repel The two sets of parameter groups and the interpolation rate that respectively represent the two sounding mechanisms excited by are specified, and the two sets of parameter groups are interpolated according to the interpolation rate, and are defined by the interpolated parameter group. A method for synthesizing interpolated timbres of two sound producing mechanisms in which striking and repelling are excited by solving a differential equation. 2. The interpolated tone color sound synthesizing method according to claim 1, wherein the predetermined time when the excitation is repulsive is about half of the predetermined time when the excitation is batting.