JPH03140999A - Musical tone synthesizing device - Google Patents

Abstract

PURPOSE:To allow the diversified sound creation based on the physical structure of a natural musical instrument by expressing the musical instrument with the parameters approximated by prescribed discrete elements based on a finite- element method operating the parameter data, and thereby forming the musical tone waveform data changing with time. CONSTITUTION:A parameter setting means 1 sets the parameter data approximated by the finite field of sets of the discrete elements coupled by discrete nodes with the musical instrument to synthesize the musical tone based on the finite-element method. The means sets the conditions of the displacement, speed and/or acceleration corresponding to the touch of the performance operator of the electronic musical instrument as initial conditions. An arithmetic means 3 calculates the solution of the equation of motion by using the after- touch data of the electronic musical instrument or the external data including press data together with the parameter data and initial conditions thereby forming the musical tone waveform data 4 changing with time. The diversified sound creation based on the physical structure of the natural musical instrument is possible in this way.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a musical tone synthesizer, and more particularly to a musical tone synthesizer that synthesizes musical tones using the so-called finite element method.

[Prior Art] Traditionally, the methods of musical tone synthesis in electronic musical instruments can be roughly divided into:
It is classified into ■harmonic synthesis method, ■waveform readout method, ■formant method, etc.

Here, ■ the harmonic synthesis method uses the desired musical sound waveform F (t
) is expressed as a Fourier series 1. First, for each harmonic component, a sample value is calculated for each scheduled time interval of a sine wave with a frequency equal to that harmonic, and this value is used as the amplitude value of that harmonic component. This is a method of multiplying corresponding constants and then adding and synthesizing them (for example, Japanese Patent Laid-Open No. 48-90217).

(2) The waveform readout method is a method in which a waveform that is the basis of a musical sound waveform to be generated is stored in advance in a memory, and this stored waveform is read out at a desired readout speed (for example, US Pat. No. 3,515,792).

The formant method extracts and synthesizes various frequency components from a rectangular wave using a filter.

In addition, there is also a musical tone generating device that uses a predetermined regression device to output new sample values from a plurality of past sample values (sample values at fixed time intervals of musical tone signals).
It is disclosed in Japanese Patent No.-27518.

Parameter data approximated by a finite set of several elements is set, and the parameter data is manipulated by a calculation means to generate musical sound waveform data that changes over time.

[Problems to be Solved by the Invention] However, according to the prior art described in ■ to ■ above, it is difficult to create a variety of sounds based on the physical structure of natural musical instruments whose pitch, volume, and timbre change over time. There was an inconvenience that there was no one.

In view of the above-mentioned problems with the conventional method, the present invention provides a musical tone synthesizer and a musical tone synthesizer capable of creating a variety of sounds based on the physical structure of natural musical instruments, which could not be obtained using conventional methods. The purpose is to provide electronic musical instruments that use

[Means for Solving the Problems] In order to achieve this object, the musical tone synthesis device according to the present invention is based on the finite element method. Operation] According to the musical tone synthesis device having the above configuration, the musical instrument whose musical tone is to be synthesized is expressed by parameters approximated by predetermined discrete elements based on the finite element method, and the parameter data representing the musical instrument is By manipulating it, musical sound waveform data that changes over time is generated.

Note that if the parameter data is data indicating the shape or material of the instrument corresponding to the pitch, or data that is scaled by multiplying these data by a predetermined coefficient corresponding to the pitch, the pitch of the generated musical waveform data may be used. can be controlled as desired.

The initial conditions to be provided include displacement, velocity, and/or acceleration conditions corresponding to the touch of the performance operator of the electronic musical instrument. The calculation means calculates a solution to the equation of motion using external force data including aftertouch data or breath data (data representing the degree of blowing when assuming a wind instrument) of the electronic musical instrument, as well as parameter data and initial conditions. By doing so, musical sound waveform data can be generated in a state closer to the actual sounding state of the musical instrument.

[Example] Hereinafter, the present invention will be explained in detail using the drawings.

FIG. 1 shows a schematic configuration of a musical tone synthesis device according to an embodiment of the present invention. In the figure, 1 is a parameter setting means, 2 is an initial condition setting means, 3 is a waveform calculation means, and 4 is musical waveform data outputted from the waveform calculation means 3.

FIG. 2 is a schematic diagram showing a model of a musical instrument for which musical tones are to be synthesized, and FIG. 3 is an external view of this instrument. Here, as a simple example, we will explain an example that imitates the sump, a folk instrument of Zaire. The sump has the appearance shown in Figure 3 and is a plucked instrument that is widely distributed in Africa. As shown in the figure, the sump consists of a box-shaped (or plate-shaped) resonator 8 on which tongue-like thin pieces 9 are arranged. This tongue-like thin piece 9 is played with a finger to produce sound.

In this example, a model as shown in FIG. 2 was created imitating the sump, and its shape, density, elasticity, and other material parameters were set. In the figure, P1 to P8 do not indicate nodes of a rectangular plate-like cross section. It is assumed that nodes P7 and P8 are fixed. (1) to T6 indicate discrete elements (triangular elements) constituting this rectangular plate.

Using this model as an example, synthesize musical tones using the following steps.

(1) Each triangular element T1 to T from the given parameters
Create a stiffness matrix K of 6.

(2) Each triangular element T1 to T from the given parameters
Create a mass matrix M of 6.

(3) Each triangular element T1 to T from the given parameters
6 attenuation matrix C is created.

(4) Set initial conditions (position, speed, acceleration, etc.) for each triangular element.

(5) Based on each matrix created in (1) to (3) above, the initial conditions set in (4), and parameters such as external force data that takes into account the performance technique as necessary. synthesize musical waveform data.

v(x y) represents displacement in the X direction.

Strain: (2) Stress (average stress model): (1) First, the creation of a stiffness matrix of triangular elements will be explained.

In this example, a so-called two-dimensional finite element method was used. First, displacement, strain, and stress are set as follows for each point P1 to P8 of the model in FIG. 2.

Displacement・where u (x, y) is the displacement in the X direction, Young's modulus is E1, Poisson's ratio is ν, and dl-E/(1-ν2
) d2=νE/(1−ν2) G=E/(2(1+ν)).

Here, each term in the stress equation (3) is replaced with one symbol, and the equation (3) is expressed as the following equation (4).

(d)=(D)(ε) ・・・・・・(4
) Using the above symbols, the strain energy U can be expressed as. However, h is the plate thickness of the model in Figure 2, D
An integral over an object means an integral over the entire object.

Next, using the so-called triangular element method as an approximation method, we calculate the displacement (u) of the vertex of the triangular element and the strain (ε) within the element.
Get a relationship with.

First, focus on one triangular element, and calculate the vertex number i
,j,. The displacement within this triangular element of interest is approximated by a linear equation. This is to consider the strain (ε) to be constant within the element.

U:α10+αIIX+α12y ■=α2゜+α21X+α22y ・・・・・・(6
) For convenience, the displacements of the three vertices (the first vertex, the fifth vertex, and the kth vertex) are all written in the - column.

(u) - (01, V+, u, +, VJ ub, Vk)" ...... (7) The displacements u and v in equation (6) are each vertex i, and the value in (7) above is To take, αlo+αIIIXI +α+2y+=u+α10+αI
IXJ +α123'J=uJ(! to+ (! EyeX k+α+2yk=LIkα20+α21Xl +α
22yl=VIα20+α21XJ+α22yj=V,
+(X20+ (!2+Xk+ C122yk='Vk
Therefore, j, k odor...(8)...(9) However, = (XJ Xi) (yk 3'+
) − (xk Xi ) (yi '/l
)...(lO) (X+, yI) (XJ, 3'J) (Xh,
3'k) are the coordinates of the i-th, 1-th, and 2-th points, respectively.

When formula (9) is summarized in matrix form,...
・(11) The above is the method for triangular elements. By using this method, the displacement (U)−(tl+,V
The relationship between 1, uJ+ vJ, uk+Vk)T and the strain within the element (ε)=(εx+6y+γxy)T is obtained as follows. That is, from equation (2) and equation (11), 1 ...... (12) If the coefficient matrix on the right side of equation (12) above is expressed as (B), (ε) = (B) ( u) ・・・・・・(
13).

The above calculation focuses on one triangular element whose vertices are t and j, so to represent this, each matrix symbol in equation (13) has IJk as a subscript.
If we add (6LJh= (B zk)
(u)tJk”...(14).

To summarize the above relationships, the triangular element component of stress (σ)
■, from equation (4) and equation (14), (σ)+,
+ = (D) (ε) +Jh2 = (D) (Bzk) (u) IJk ・”(15
).

On the other hand, since the triangular element component UIJk of strain energy is obtained by taking the inner product of strain and stress and integrating it, = - × (triangular element area) × (u) IJkT (Bljk) T (D) (BIjk)
(u)l, ni = (u)zk”(Kt, n+)(
uL+jk...(le) However, (K+ai+) =hx (triangular element area)X (
B z++)” (D) (B zk) (17) Next, the external force (f
)lJk is (f)+jkT= (f ++g +, f J+gJ+
f br, gk)...(18) However, the external force applied to point n is as follows: If the displacement is ■, then the work done by the external force is; Σ (f s us + gs Vs )=
u+ft 10V+g+ + ujf, 1 + vjg
, 1 + ukfk+ Vkgk= (u)zk
(f) zb (19).

Since the total energy of a triangular element is the sum of strain energy and work energy, n 2U +jk
W +jh = (u)+, +h"(K +Jk) (u
)+tk-(u)zb(f)zh”(20
) By partially differentiating this equation (20) with respect to ul; and setting it to 0, +
J41+J++5ui+"k+eVk"kHvt"k
3+u, 1+ to 4+Vj+kHuk"ks+Vh)
f I = O...121), but (KIJ,)
is a symmetric matrix according to the definition formula (17), so k
Mouth = 11.

Therefore, k11u1+k12vI+J3uj++4v"++
suk + avk - f + (22) Other external force component gl + fJ - gJ = fk・
gk can also be calculated in the same way. When summarized in a matrix, 5, that is, (K+Jk) (u)+''h= (f)llk''
- (24) From the above, the values of the elements of the stiffness matrix (KIJk) focusing on the triangular elements whose vertices are t, j, and k have been found. In addition, the (+'C
zk) represents only some components of t, j, in the stiffness matrix considering all elements. In other words, as shown in Figure 4, a part (shaded area) of the stiffness matrix considering all six elements.
I just asked for it. Therefore, the stiffness matrix K
To find , first create a matrix K with the size of all the elements, and set all the elements to O. And some i, j
, k as described above for the stiffness matrix (Kljk
) and add it to K. As a result, a stiffness matrix K that takes all elements into consideration is obtained.

The stiffness matrix K of this musical instrument model has been determined above.

In this example, the above equation (23) (or equation (24)
) is extended to all elements, and a waveform is generated by creating an equation of motion in which components such as inertia and damping are added to (f), and solving it.

(2) Next, creation of the mass matrix M will be explained.

For simplicity in this example, we assume that the mass of each triangular element is concentrated at one vertex, a so-called lumped mass matrix.
matrix) method was used. As a result, the entire mass is divided into multiple regions centered on each point, and the mass of each region is assigned as the mass of that point.

This sample model assumes that a uniform plate is divided uniformly, so (1/2) mu is arranged in the part corresponding to the edge of the plate in the diagonal component of the matrix, and mu is arranged in the other diagonal components. You can create a matrix like this. Although the mass matrix M was created using the Lambut mass matrix method here, the mass matrix M is not limited to this.
Methods such as stent mass) can also be used.

(3) Next, creation of the attenuation matrix C will be explained.

The damping matrix C is a matrix that multiplies this damping matrix C by the velocity (0) of the displacement vector to give a damping force in the form of damping force - (C) (u). By introducing this component, it becomes possible to generate damped vibrations.

The damping matrix C can be created, as an approximation, by multiplying the above-mentioned stiffness matrix K by a constant to obtain the damping matrix C, or by multiplying the mass matrix M by a constant to obtain the damping matrix C.

(4) Next, how to give initial values and parameters to the musical tone synthesizer of this embodiment will be explained.

One of the initial values given at the beginning is the initial displacement of the musical instrument model, and by changing this, it is possible to change the strength with which the assumed instrument is played.

The sump model in FIG. 2 has eight nodes P1 to P8. The X coordinate of node Pn is U. , if the X coordinate is expressed by vn, the initial displacement u(0) is
4. v4u5・v5・u6・v6・u7・v7・u8・
It can be written as Vδ)1. The equilibrium state Llb is all O, 9 ul, -(0,0,0,0,0,0,0,0°0.0,
0, 0, 0, 0, 0.0)". Now, for simplicity, if only the nodes Pi and P2 are pulled by 5+nm in the X direction, the initial displacement u
(0) is u(0)-(0,5,0,5,0,0,0,0゜0.0
,0,0,0,0,0.0) T. This is the value manually applied as the initial displacement. Pull harder,
If only nodes Pi and P2 are pulled by 5+n+n in the X direction, the initial displacement u(0) is u(0)-(0,10,0,10,0,5,0,50,
0,0,0,0,0,0,0)". In this way, the initial touch is input to the system as an initial condition.

Next, a case will be explained in which the parameters to the system are changed. In the sump example discussed here, the vibration system is constant over time. For example, if we shorten the length of the plate in the model shown in Figure 2, the period of vibration will become shorter and the pitch will become higher.

0 In this case, since the nodal coordinates change, the above-mentioned stiffness matrix K, mass matrix M, and damping matrix C change. Therefore, the pitch of the output in the waveform generation calculation described later changes, and the pitch (key) also changes.

(5) Next, mass matrix M prepared as above
, stiffness matrix K, damping matrix C1 external force F(
t), and initial conditions u(0), Q(0), ti(
0) to create an equation of motion and obtain a waveform sample value as a solution to the waveform generation calculation.

First, the equation of motion is generally as follows.

MO(t)+Cu(t)+Ku(t)−f(t)
-0...(30) Note that u (t) in equation (30)
, u (t), ti (t) are vectors in which data related to the X direction and data related to the X direction are arranged for all nodes. Further, f (t) is also a vector that aligns the external force in the X direction and the external force in the X direction that act on all nodes at regular intervals. Therefore, in reality, equation (30) can be said to be a collection of equations of motion for each node in the X direction and in the X direction.

In this equation of motion (30), assuming linear acceleration where the change in acceleration is uniform for each section, from the current data u (t), Q (t)ii (t) at time t,
The next sample point data u (at 10 At) 11 (at 10 At), ti (at at
). This repetition generates waveform data that changes over time.

In the sample example used here, the attenuation is of a simple type, so the attenuation is added later as an envelope, and the attenuation matrix C is not incorporated into the calculation. Also, when playing a sump, no external force is applied except when you first play it.

That is, the term f (t) in the equation of motion (30) is also zero, and only the external force that provides the first displacement (initial displacement) acts.

Therefore, the equation of motion (30) becomes as follows.

Mu (t) + Ku (t) = O - (31) Here, it is assumed that the acceleration at each point of each element changes linearly and can be determined at a certain time interval. In other words, if the acceleration is α at one time and becomes β at the next time, then
It is assumed that the acceleration changes linearly from α to β during that time. From this assumption of linear acceleration, u(
t+Δt) −u (t)+ΔtQ (t)+(Δ t
2/3) ”G (t)+ (Δ t2/6)*Qft
+Δt)・・・・・・(32) u(t+Δt)−u(t)÷(Δt/2)*(Q(t)
+ Q (t + Δ1)) (33) Substituting formula (32) into formula (34) below, using formula (31) and substituting t + Δt for t, % formula % (34) , Mu(t÷Δt) +K (u (t)+Δtu(t) +(Δt2/3)*a(t) +(Δt'/a)*a(
t÷Δt)) -0(35). Therefore, 3 (Me(Δt 2/6) +K) Q(t +
Δt)−−K(u(t)+ΔtQ(t)+
(Δt2/31 *Q (t) ) −(36) Therefore, 0(t+Δt) −−(Me(Δt2/6) +K) −′ψK(u(t
)÷ΔtQ((Δt2/3) import(t))・・・・・・
・ (37) With the above, the current data u (t) at time t
), u (t), tj(t+Δt) of the next sample point at time t+Δt after Δ has passed can be found.

Furthermore, by substituting this u(t+Δt) into the above two equations (32) and (33), we obtain u(t+Δt) and 6(t+Δt).
t) is obtained.

FIG. 5 is a flowchart representing the process of musical sound waveform synthesis in the sample model.

In the figure, first, in step S1, the nodal coordinates, strain ε, and stress 0 are specified based on the input physical parameters of the system, such as the assumed shape of the instrument and the material, and the Young's modulus E and Poisson's ratio υ are Calculate the stiffness matrix and the mass matrix M. Then, in step S2, INV = (Me(A t2/6
)+K)-'.

On the other hand, in step S3, initial conditions are set.

Here, the initial velocity et (0) is set to zero, and the initial displacement u (
0) is set to the distance pulled by the finger.

Next, in step S4, U(t+
Δt). Furthermore, in step S5, the above formula (3
3), and in step S6, u(t+Δt) is calculated based on the above equation (32).

Then, in step S7, the displacement at an appropriate point is extracted and used as a sample value of the waveform data. For example, u'(t+Δt
) that is closest to the fixed point, i.e. the node P in Figure 2.
5 in the X direction is extracted and used as a sample value of the waveform data. Note that the displacement of any node can be used as a sample value, and may be selected later.

In the second and subsequent iterations, the obtained u(t+Δt),
u(t+Δt), U(t+Δt) as the next u(t), α(
t) and ti (t) to perform calculations from step S4 onwards. In this way, calculations are repeated to obtain sample values of the waveform output. After that, an envelope is applied to the waveform output to generate a musical tone.

Note that Δt here is a simulation step (sequential calculation interval) and is not the reciprocal of the sampling rate.

Next, an example in which the above-described musical tone synthesis device is applied to an electronic musical instrument will be described.

FIG. 6 is a schematic block diagram of an electronic musical instrument to which the musical tone synthesis device of the embodiment is applied. In the figure, 11 is a parameter setting and initial condition setting section of the musical tone synthesis device;
12 is a waveform calculation unit using the finite element method; 13 is a write processing unit for writing the musical tone waveform synthesized in the waveform calculation unit 12 into memory; and 14 is a waveform bank memory for storing the synthesized musical waveform data.

Further, 15 is a keyboard, 16 is a key press detection unit that detects a key press on the keyboard 15, 17 is a touch detection unit that detects touch data when a key is pressed on the keyboard 15, and 18 is an operation for selecting a voice number, etc. Child 19 is a voice selection section. Reference numeral 20 indicates the data in the waveform bank 14 based on the voice data such as the voice number outputted from the voice selection section 19, the touch data outputted from the touch detection section 17, and the pressed key code outputted from the key pressed detection section 16. This is a reading unit that selects and reads out waveform data. 21 inputs data such as voice numbers from the voice selection section 19, touch data output from the touch detection section 17, and data such as pressed key codes outputted from the key press detection section 16, and roughly detects key presses. This is an envelope generating section that receives a key-on signal from the section 16 and generates an envelope. 22 is waveform bank 1
an integrator for applying an envelope from the envelope generation section 78 to the waveform data read from the section 21;
3 is a D/A converter that converts the digital musical tone signal outputted from the integrator 22 into an analog signal, and 24 is a sound system that generates musical tones based on the musical tone signal outputted from the D/A converter 23.

FIG. 7 shows a memory map of waveform bank 14 of FIG. In the waveform bank 14, as indicated by number 31, waveform data calculated by a vibration analysis method is edited and stored for each voice number. The waveform data corresponding to one voice number is composed of waveform data for each range, as indicated by number 32. Furthermore, the waveform data of one range is composed of waveform data when the touch of the keyboard is weak and waveform data when the touch is strong, as indicated by number 33. Each waveform data has an attack part and a loop part.

The electronic musical instrument of the embodiment shown in FIG. 6.7 is basically a waveform memory type electronic musical instrument, and the waveform data calculated as described above is stored in the waveform bank memory 14 before performance. . That is, prior to performance, first, the shape and initial displacement amount of the assumed musical instrument are set using the parameter and initial condition setting section 11. and,
The waveform calculation section 12 calculates waveform data using the finite element method, and the writing section 13 writes this waveform data into the waveform bank 14 . At this time, assuming several different types of musical instruments, the parameters are changed as appropriate, and the initial displacement amount is further changed to obtain various musical tone data and stored for each voice number. As above,
The waveform bank 14 stores waveform data as shown in FIG.

Next, when the performer selects a voice number using the voice selection operator 18 and presses the keyboard 15, data such as the pressed key code, touch data, and voice number are transmitted to the pressed key detection section 16 and the touch detection section 17. and voice selection section 1
9 to the reading section 20. The readout section 20 reads out predetermined waveform data from the waveform bank 14 based on these data and inputs it to the integrator 22 . This waveform data is integrated with the envelope data output from the envelope generator 21 in an integrator 22 to give an envelope, and a musical tone is generated based on this waveform data via a D/A converter 23 and a sound system 24. do.

Note that the waveform data stored in the waveform bank 14 may be interpolated between different waveforms for each range or touch.

FIG. 8 shows the configuration of an electronic musical instrument that synthesizes waveform data in real time and generates musical tones using the musical tone synthesis device according to the present invention. In the figure, 41 is an operator for setting parameters and initial conditions representing the model of the assumed musical instrument, 42 is a calculation unit that creates a predetermined matrix and initial values from data such as the set parameters, and 43 is a A control section writes matrix data etc. created by the calculation section 42 into a parameter bank memory 44, and 44 is a parameter bank memory that stores matrix and initial value data. 46 is the keyboard of an electronic musical instrument,
47 is a key press detection unit that detects a key press on the keyboard 46; 48 is a touch detection unit that detects touch data when a key is pressed on the keyboard 46; 49 is an operator for selecting a voice number; 50
is a voice selection control section.

Further, 45 selects the parameters stored in the parameter bank 44 based on the key code from the key press detection section 47, the touch data from the touch detection section 48, and the voice data from the voice selection control section 50, and further scales the parameters. This is a parameter selection and scaling section that performs. 51 is a waveform calculation unit that receives a key-on signal from the key press detection unit 47 and calculates waveform data using the finite element method;
52 is an envelope generator; 53 is an integrator that integrates the waveform data from the waveform calculation section 51 and the envelope data from the envelope generator 52 to produce a digital musical tone signal; and 54 converts the digital musical tone signal into an analog musical tone signal. A D/A converter and 55 are a sound system. Timing information of the arithmetic unit is passed from the waveform arithmetic unit 511 2 to the parameter selection and scaling unit 45 .

FIG. 9 shows a memory map of the parameter bank 44 of FIG. Parameter bank 44 as indicated by number 61
Parameter data for each voice number is arranged in order. Parameter data corresponding to one voice number is divided into several sound ranges as indicated by number 62. The parameters corresponding to one sound range are configured as shown in number 63. That is, first, the component data of the matrix (M+(Δt'/6) umbrella K)-1 and the component data of the matrix (M+(Δt2/6)◆Kl-'*k) which is multiplied by the parameter for scaling each component. Next, a conversion table for converting touch data into initial value data numbers (1 to S) and initial value data 1 to S are stored.

The electronic musical instrument of the embodiment shown in FIG. 8.9 is of a type that synthesizes waveform data in real time in parallel with the performance and outputs musical sounds. Since the calculation in the waveform calculation section 51 needs to be performed at high speed, S4. S5. The calculation in S6 is performed by a high-speed parallel arithmetic unit.

In the electronic musical instrument of this embodiment, first, prior to performance, parameters such as the shape and material of the assumed musical instrument are set using the parameter setting operator 41. Here you can make settings for multiple instruments. By selecting one voice number using the voice selection operator 49, it is possible to select an instrument (musical instrument having a predetermined shape, material, etc.) that should generate a musical tone corresponding to that voice number. The calculation unit 42 performs the calculations described above based on the set parameters, and as a result, data as shown in FIG. 9 is stored in the parameter bank 44.

Next, assume that the performer selects a voice number using the voice selection operator 49 and presses the keyboard 46.

At this time, data such as key press key codes, touch data, and voice numbers are sent to the key press detection section 47 and the touch detection section 4.
8 and the voice selection section 50 to the parameter selection and scaling section 45. The parameter selection and scaling section 45 selects predetermined parameter data in the parameter bank 44 based on these data, and performs scaling processing to generate a sound with a pitch matching the pressed key. The waveform calculation unit 51 uses these parameter data to calculate and output waveform data using a finite element method. This waveform data is transmitted to the integrator 5.
3, it is integrated with the envelope data output from the envelope generator 52 to give an envelope,
Musical tones are generated via the D/A converter 54 and sound system 55 based on this waveform data.

According to this embodiment, the parameters set in the parameter bank 45 are selected based on key codes (pitch data) and the like. On the other hand, if the intended size of the instrument is made smaller or made of heavier material, the pitch will be lower, and if you set the opposite, the pitch will be higher. Therefore, by setting appropriate parameters based on the pitch data, the pitch can be adjusted. Furthermore, in the same way regarding touch,
If the input touch data indicates a strong touch, adjustment can be made by setting a correspondingly larger initial displacement.

Note that the envelope waveform generator may be omitted by introducing an appropriate attenuation term. Also, a drum bat may be used instead of a keyboard to generate percussion sounds. Furthermore, aftertouch detection may be added to add the effect of an external force to the calculation.

FIG. 10 is a flowchart showing a procedure for musical tone synthesis in consideration of external force and attenuation parameters. The attenuation matrix C is calculated in step Sit, a new step 318 for applying an external force is added, and step S12. The processing procedure is the same as the flowchart of FIG. 4, except that the calculation formula in S14 is different.

Figure 11.12 shows an example of the generation of a total of 56 waveforms using the sump model. Since the parameters are different between FIG. 11 and FIG. 12, the waveform in FIG. 12 contains harmonic components.

In addition, in the above-mentioned embodiment, an example was shown in which waveform data is calculated by vibration analysis using a linear acceleration method, but the calculation unit is not limited to this, and the calculation unit may perform calculations based on each of the following vibration analysis methods. You can also do it. In this case, the calculation section of the above embodiment is set to perform calculations based on the following equation.

■ Example of Euler's methodti(t+Δt) =M−'xKx (u(t)+G(t)Δt)G(
t+Δt) =LI (t) +ti (t)Δtu(
t+Δt) =u (t) +LI (t)Δt■ Other examples of linear acceleration method Δti=ij (t+Δt)−〇(1) ΔO=G (tenΔt)−〇(1) Δt =Δt ( t)+□Δd Δu=u (tenΔt)−u(t) (Δt)2 + Δ0 +ΔF) However, ΔF=F (t+Δt) F (t) ■ Example of Newmark β method Δ t Mu (t +Δt) = (M+ −C
+ B A t2)
+ Q (t) + (Δt)2 β (0
(t+Δt) −0(t)) Note that β is a parameter for obtaining a stable solution, and is selected from the range of 0≦β≦1/2.

(2) Example of Wilson's θ method As θ, select θ that provides a stable value when θ>1.

u(ti Δt) = u(t) ten(Δt)2 ΔtC+ (t) + O(t) ■ Example of two-volt method Current data u(t) and past data u(t-Δt) and u(t- 2Δt) and external force f(t+Δt)
By approximating the following equation, data u(t+
Δt) is obtained.

(θΔt)2 K (u (t) ten θΔtII(t) +
Q (t) ) + F (t + θΔ1) ) ti (ti Δ1) = (θ−1) Q (t) +0 (t + θΔt)θ In addition, the two-dimensional finite element method was used in the above example, but However, a three-dimensional or one-dimensional finite element method (for example, one in which the material is different for each part) may be used.

Furthermore, as a method for solving vibration problems expressed in a matrix, there is a so-called modal analysis method, or this moat analysis method may be used.

[Effects of the Invention] As explained above, according to the present invention, various parameters expressing the musical instrument are set using the finite element method based on the physical structure of the natural musical instrument, so that it is possible to overcome the problems previously obtained. A natural musical tone synthesis device with transient response is provided, which can create a variety of sounds based on the physical structure of natural musical instruments, which was previously impossible. Furthermore, by using parameters that do not exist in reality, new tones can be synthesized.

[Brief explanation of the drawing]

FIG. 1 is a schematic configuration diagram of a musical tone synthesis device according to an embodiment of the present invention, FIG. 2 is a schematic diagram representing a model 0 of a musical instrument for which musical tones are to be synthesized, and FIG. 3 is an external view of this musical instrument. , Figure 4 shows the calculated K IJ in the stiffness matrix.
FIG. 5 is a flowchart showing the process of musical sound waveform synthesis in the sample model. FIG. 6 is a block diagram of an electronic musical instrument to which a musical sound synthesis device according to an embodiment of the present invention is applied. FIG. 7 is a memory map of the waveform bank of the electronic musical instrument shown in FIG. 9 is a block diagram of the musical instrument; FIG. 9 is a memory map of the parameter bank of the electronic musical instrument shown in FIG. 8; FIG. 10 is a flowchart showing the processing procedure of the embodiment that also takes external force parameters into consideration; FIGS. 11 and 12. is an example of synthesized musical waveform data. 1; Parameter setting means; 2; Initial condition setting means; 3; Waveform calculation means; 4; Musical sound waveform data; 11: Parameter and initial condition setting section; 12; Waveform calculation section; 13; Synthetic waveform writing section; 14: Waveform bank, 15: keyboard, 16; key press detection section, 17: touch detection section, 18; whistle selection operator, 19; voice selection section, 20; memory reading section, 21; envelope generation section, 22: integration section, 23 , D/A converter, 24; sound system. No. 951-

Claims (1)

[Claims] (1) Based on the finite element method, a parameter setting means for setting parameter data that approximates an instrument whose musical tone is to be synthesized by a finite collection of discrete elements connected by discrete nodes; By operating
What is claimed is: 1. A musical tone synthesis device comprising: arithmetic means for generating temporally changing musical waveform data.