JPH03174195A - Musical tone synthesizer and electronic musical instrument using the musical tone synthesizer - Google Patents

Abstract

PURPOSE:To allow the production of various tones based on the physical structure of a natural musical instrument by computing and calculating waveform data by a technique of vibration analyses. CONSTITUTION:This device has a parameter setting means 1 which sets the parameter data to approximate the musical instrument to be subjected to synthe sis of its musical tones with the finite sets of field of the discrete elements joined at discrete nodes and an initial condition setting means 2 which applies the initial conditions corresponding to the initial displacement to the presumed musical instrument to the prescribed equation of mation with respect to the respective discrete elements. A waveform computing means 3 repeats and calculates the solution to the prescribed equation of motion based on the parame ter data and the initial conditions 4 by the technique of the vibration analyses and forms musical tone waveform data 4 changing with time. The production of the various tones based on the physical structure of the natural musical instrument is executed in this way.

Description

[Detailed Description of the Invention] [Industrial Field of Application] The present invention relates to a musical tone synthesizer and an electronic musical instrument using this musical tone synthesizer, and more specifically to a musical tone synthesizer that synthesizes musical tones using a so-called vibration analysis method. The present invention also relates to an electronic musical instrument using this musical tone synthesis device.

[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.First, for each harmonic component, a sample value is calculated for each scheduled time interval of a sine wave with the same frequency as that harmonic, and this value corresponds to the amplitude value of that harmonic component. This method performs addition and synthesis after multiplication by a constant (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.

[Problems to be Solved by the Invention] However, according to the above-mentioned conventional techniques (■ to ■), it is not possible to create diverse sounds based on the physical structure of natural musical instruments whose pitch, volume, and timbre change over time. There was this inconvenience.

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 Problem] In order to achieve this objective distantly, the musical tone synthesis device according to the present invention constructs a musical instrument for which musical tones are to be synthesized by a finite collection of discrete elements connected by discrete nodes. Approximate parameters and initial conditions corresponding to the initial displacement given to this assumed instrument are set, while a predetermined equation of motion is given for each of the 11 elements of this assumed instrument, and solutions to this equation of motion are repeatedly calculated. By performing vibration analysis, time-varying musical sound waveform data is generated.

Further, in the electronic musical instrument according to the present invention, musical sound waveform data is generated by such a musical sound synthesis device prior to actual sound generation based on this musical sound waveform data, and the generated musical sound waveform data is stored in an appropriate storage means. Temporarily store it in
When a sound generation is instructed, the sound is generated based on this musical sound waveform data. Furthermore, the musical sound waveform data may be generated in real time almost in parallel with the actual sound production.

[Operation] According to the musical tone synthesizer having the above configuration, the musical instrument whose musical tone is to be synthesized is expressed by parameters approximated by predetermined discrete elements, and an initial condition corresponding to an initial displacement is given to the musical instrument. Then, under these conditions, a solution to a predetermined equation of motion is repeatedly calculated by a so-called vibration analysis method. As a result, musical waveform data that changes over time is generated.

Note that if you use data indicating the shape or material of the instrument corresponding to the pitch, or scaled data by multiplying these data by a predetermined coefficient corresponding to the pitch, as the parameter data, the generated musical waveform data will be The pitch 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 code] 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 an appearance as shown in Figure 3, and is a vocal drum instrument 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 indicate nodes of a rectangular plate-like cross section. It is assumed that nodes P7 and P8 are fixed. T1 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.

(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: However, u (x, y) is the displacement in the X direction, v (x, y
) represents the displacement in the y direction.

Strain: (2) Stress (average stress model): However, Young's modulus is E1 Poisson's ratio is ν, and dl=E
/(1-ν2) d2=υE/(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).

((5)=(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 its vertex number 1i
,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.

11=Q, 0+αIIX+α12y v = a 2(, + a 21X +a 22y
...---(6) For convenience, 3 vertices (i-th vertex, j
The displacements of the vertices (the th vertex, the kth vertices) are all written in the - column.

(u)-(u+, Vl, uj, Vj, ul
(, Vk)T... (7) For the kth displacement u, v in equation (6) to take the value of (7) above at each vertex i, j, k, alQ+(X++xl +Q+zyi =ut(Z r
o+ (Z IIX J+α123'J=IJJ(!1
g+αth Xk +α+23'=lJk'...°(a)
Q20+α21Xl +Q2zyl =V+α20+(
X21XJ +Q223/J =VJ(X20+α21
Since Xk + α22yk: must be vk, ... (9) However, = (XJ - Xi ) (yb - yt
) − (X+c −X+ ) (yj −yt
)...(10) (X+, yl) (XJ, y'') (X
k , 3′k ) are the coordinates of the i-th, j-th, and i-th points, respectively.

When formula (9) is summarized in matrix form,...
・(11) The above is the method for triangular elements, but by using this method, the displacement of the vertex of the triangle (Ll)−(u+,
The relationship ε between "Vl+ uj+ Vj, uk+ vt+)" and the strain (ε)=(ε., y, γxy)T in the element is obtained as follows. That is, equation (2) and equation (1
'l), ......(12) If the coefficient matrix on the right side of the above equation (12) is expressed as (B), (ε)=CB)(u) ......(1
3).

The above calculation focuses on one triangular element whose vertices are i, j, so to represent this, each matrix symbol in equation (13) has the subscript llk
If we add (e )+jb= (B tj
k) (u) IJk (14).

To summarize the above relationships, the triangular element component of stress (Q
)zh is obtained from equations (4) and (14) as (o)=(D)(ε)zk=(D)(BtJh)(uLJk---(x
s).

On the other hand, the triangular element component U IJk of strain energy is the inner product of strain and stress and is integrated, so = - × (triangular element area) × (u) Ijl (BIjk) T (D) (BIJk) (u
)zk = (ulzk”(KtJk)(u)tjk...
(16) However, (KIJk) = h x (triangle element area) x (B IJk
) T (D ) (B +, +b) (17) Next, the external force (f
)i''m is (f)+j1= (f+, g+, f, +, gj, f+c
, gk)...(18) However, the external force applied to the point is as follows: The X-direction component is the external force in the X-direction, f is the displacement in the X-direction, g is the external force in the y-direction, and V is the displacement in the y-direction. Then, the work done by the external force is =Σ (f.

U snow ten gl ■ take) =u+ft + Vigi +ujf''+ VjgJ+
ukfk+ vkgk= (u)1. +k” (f
L, +k''・(19).

Since the total energy of a triangular element is the sum of strain energy and work energy, n = U, j
k-W, Jk = (u)+, +1(K+Jit) (u
)+,+(u)tjk" (fLjk...
(20) If we partially differentiate this equation (20) with respect to ul and set it as fO, then “k14VJ”klSLlk”k16Vk”k21
Vl”k31uJ”k41VJ+51uk”ka+V
b) −f + = O...(21), but (K
+, +k) is a symmetric matrix according to the defining formula (17), so kll=kl.

Therefore, k++ut"k+zV+"k+3uj"k+4v, 1+
to +suh+ to +avk@f +...(22) Other external force components gt l fJ + gJ r fk・g
m can be calculated in the same way. When summarized in a matrix, (K+Jm) (u31'Jk= (f)lJk
”...(24) From the above, the stiffness matrix (K+, +i+
) has been found. Note that (K, k) obtained here represents only some i, j components in the stiffness matrix considering all elements. That is, as shown in FIG. 4, only a part (the shaded part) of the stiffness matrix considering all the elements was obtained. Therefore, to obtain the stiffness matrix K, first create a matrix K with a size equal to all the elements, and set all the elements to 0. Then, find the stiffness matrix (Kljk) as described above for certain i, j, k, and calculate K
I'm going to add it to. 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. A matrix like this is created. 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 calculated by multiplying this damping matrix C by the velocity (6) of the displacement vector to obtain the damping force=(C)(+:t
) is a matrix that provides a damping force in the form of 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.

In the sample model shown in FIG. 2, there are eight nodes P1 to P8. If the X coordinate of the node Pn is expressed by unq and the y coordinate by vn, the initial displacement u (0) is as follows: u (0) = (Ll+ +Vl +u2 +■2
+u3 +v3 +u4 +v4L'l+shi! +u6+
v8+u7+v7+ua+v6) It can be written as T. The equilibrium state ub is all O, ub-(o, o, o, o, o, o
, o, o.

o, o, o, o, o, o, o, o)". Now, for simplicity, suppose only the nodes Pi and P2 are pulled by 5 mm in the X direction, then the initial displacement u(
0) is u(0)''(0,5,0,5,0,0,0,0゜o,o
, o, o, o, o, o, o)". This is the value input as the initial displacement. Pull even harder, and only the nodes PI and P2 will be moved by 5 in the X direction.
If only InI11 is pulled, the initial displacement u (0
) is u(0)=(0,10,0,10,0,5,0,5゜0
．． 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.

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

(5) Next, mass matrix M prepared as above
1 stiffness matrix and 1 damping matrix C1 external force F (
t), and initial conditions u (0), (s(0), u
A waveform generation calculation for creating an equation of motion from (0) and obtaining a waveform sample value as a solution will be explained.

First, the equation of motion is generally as follows.

MQ(t)+CG(t)+Ku(t)-f(t)-0・
...(30) Note that u (t) in equation (30),
u (t), u (t) is X for all nodes
This is a vector in which data related to the direction and data related to the X direction are arranged. Further, f (t) is also a vector in which an external force in the X direction and an external force in the X direction that act on all nodes at regular intervals are arranged. 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, we can calculate Δ from the current data u (t), (s (t)ti (t)) at time t. Next sample point data u(t+Δt)Q(t+Δt), ti(t+Δt) at elapsed time t+Δt
Calculate. 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 (3
1) Here, the acceleration at each point of each element changes linearly,
Assume that it can be determined at certain times. That is, if the acceleration is α at one time and becomes β at the next time, the acceleration linearly changes from α to β between those times. From this assumption of linear acceleration, u(is 1Δt)−u(t)+ΔtI:I(
t)◆(Δt'/3) IQ (t) + <Δt2/
[1) IQ(t◆Δt)・・・・・・(32) cI(tIA t)−Q(t)” (Δt/2)
Q(t) + Q(t+Δ1)) (33) Substituting equation (32) into the following equation (34) where t is replaced with t+Δt in equation (31), MQ(t+Δt) +K (u (t) + ΔtQ (t) + (Δt”/3) umbrella a (t) + (Δt2/6)◆
Q(t+Δt)) −.

(35) becomes. Therefore, (M+(Δt2/13)+K) * Q(t◆ Δt
)−−K(u(t)◆Δtu (t) + (Δt'/
3) Same (t)) −・(3B) Therefore, Q(t+Δt)・−(M+(Δt2/6) +K) −′Umbrella K(u(
t)+Δ tQ (t)+ (Δ t2/3)IQ (
t)) (37) The above is the current data u(t) at time t.

Time t when Δ has passed from u (t), ti (t)
The next sample point ti(t+Δt) at +Δt is determined.

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

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

In the same 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 shape and material of the assumed instrument, and the stiffness is determined using Young's modulus E and Poisson's ratio υ. matrix and calculate the mass matrix M. And step S
2, calculate INV = (M+(Δt'/6)+K)-'.

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

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

Next, in step S4, ti(t
+Δt). Furthermore, in step S5, the above formula (
Q(t+Δt) is calculated based on the equation (33), and u(t+Δt) is calculated based on the above equation (32) in step S6.

Then, in step S7, the displacement at an appropriate point is extracted and used as a sample value of the waveform data. In this example, u(t+Δt)
The point closest to the fixed point in , that is, the node P5 in Figure 2
The displacement in the y 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 it may be possible to select it later.

In the second and subsequent iterations, the obtained u (t+Δt)
, Ll (tIAt), u (t+Δt) as the next u (
t), (x (t), (i (t)),
Calculations from step S4 onwards are performed. 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 using the musical tone synthesis device of the embodiment. 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 selects data in the waveform bank 14 based on voice data such as voice numbers outputted from the voice selection section 19, touch data outputted from the touch detection section 17, and pressed key codes outputted from the key pressed detection section 16. This is a reading unit that selects and reads out waveform data. 21 manually 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; This is an envelope generating section that receives a key-on signal from 16 and generates an envelope. 22 is waveform bank 1
Envelope generator 2 applies the waveform data read from 4
23 is a D/A converter that converts the digital tone signal output from the integrator 22 into an analog signal; 24 is a D/A converter 23;
This is a sound system that generates musical tones based on musical tone signals output from.

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 FIGS. 6 and 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 a key on the keyboard 15, data such as the pressed key/key code, touch data, and voice number are transmitted to the key press detection section 16 and the touch detection section. 17 and one voice selection section 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 sent to an envelope generator 21 in an integrator 22.
The waveform data is integrated with the envelope data outputted from the waveform data to give an envelope, and a musical tone is generated based on this waveform data via the D/A converter 23 and the sound system 24.

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. Parameter selection and scaling section 4 from waveform calculation section 51
5, the timing information of the arithmetic unit is passed.

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 Component data is stored.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 assumed size of the musical instrument is made larger or the material is made heavier, the pitch will be lowered, and vice versa, the pitch will be raised. 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 a suitable attenuation ring. Further, a drum pad 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 S18 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 waveforms calculated using Sump's 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)+u (t)Δt)u
(t+At)=Ij(t)+ti (t) Δtu(tensΔt) =u (t) +L1 (t)Δt■ Other examples of linear acceleration method ΔG=■(t+Δt)−U (t) Δα=α (t+Δt) −〇 (t) Δ U=U (t+Δt) (1) +ΔF) However, Δ F=F (t+Δt) (1) ■ Example of Newmark β method +F(t+Δt) ) +(Δt)2 β (0(t+Δt) −Q (t)
) Note that β is a parameter to obtain a stable solution,
Select from the range 0≦β≦1/2.

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

+F(t+θΔ1) ) (,. , = (E) -1)G(t)+(1(tl
? A t) b ■ Example of two-volt method Approximating a cubic equation using current data u (t), past data u (t-Δt) and u (t-2Δt), and external force f (t+Δt), Data u(t
+Δt) is obtained.

Further, in the above-described embodiment, a two-dimensional finite element method is used, but the present invention is not limited to this, and a three-dimensional or one-dimensional (for example, one in which the material is different for each part) finite element method may be used.

[Effects of the Invention] As explained above, according to the present invention, waveform data is calculated using a vibration analysis method based on the physical structure of a natural musical instrument. Provided are a musical tone synthesizer and an electronic musical instrument that can create various sounds based on physical structures and have natural transient response.

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 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 using a musical sound synthesis device according to an embodiment of the present invention. 7 is a memory map of the waveform bank of the electronic musical instrument shown in FIG. 6, and FIG. 8 is a diagram of the electronic musical instrument that calculates waveform data in real time using a musical tone synthesizer according to an embodiment of the present invention. 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 into account external force parameters; 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 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 unit, 17; Touch detection unit, 18; Voice selection operator, 19; Voice selection unit, 20, Memory reading unit, 21; Envelope generation unit, 22; Integration unit, 23 , D/A converter, 24; sound system.

Claims (9)

[Claims] (1) 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, and a predetermined equation of motion for each of the above-mentioned discrete elements. The apparatus further comprises: an initial condition setting means for providing an initial condition corresponding to an assumed initial displacement given to the musical instrument; and an arithmetic means for calculating a solution to the equation of motion based on the parameter data and the initial conditions; A musical tone synthesis device characterized in that musical sound waveform data that changes over time is generated by repeatedly calculating solutions to equations. (2) The musical tone synthesis device according to claim 1 is used to generate musical sound waveform data prior to actual sound generation, and the generated musical sound waveform data is temporarily stored in a storage means before sounding. electronic musical instrument. (3) An electronic musical instrument characterized in that the musical tone synthesis device according to claim 1 is used to generate musical sound waveform data in real time almost in parallel with actual sound production. (4) The musical tone synthesis device or electronic musical instrument according to any one of claims 1 to 3, wherein the parameter data includes data indicating a shape of the musical instrument corresponding to a pitch. (5) The musical tone synthesis device or electronic musical instrument according to claim 4, wherein the data indicating the shape of the musical instrument is scaled by multiplying by a predetermined coefficient corresponding to pitch. (6) The musical tone synthesis device or electronic musical instrument according to any one of claims 1 to 5, wherein the parameter data includes data indicating a material of the musical instrument corresponding to a pitch. (7) The musical tone synthesis device or electronic musical instrument according to claim 6, wherein the data indicating the material of the musical instrument is scaled by multiplying by a predetermined coefficient corresponding to the pitch. (8) The musical tone synthesis device or electronic musical instrument according to any one of claims 1 to 7, wherein the initial conditions include conditions of displacement, velocity, and/or acceleration corresponding to a touch of a performance operator of the electronic musical instrument. (9) The musical tone according to any one of claims 1 to 8, wherein the calculation means calculates a solution to the equation of motion using external force data including aftertouch data or breath data of the electronic musical instrument, as well as the parameter data and initial conditions. Synthesizer or electronic musical instrument.