JP2824555B2 - Sound pressure estimation device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a sound pressure estimating device, and more particularly to a sound pressure estimating device capable of estimating a sound pressure for synthesizing a sound of a tubular musical instrument.

[0002]

2. Description of the Related Art Conventionally, there has been known a technique of synthesizing a musical tone by simulating a sound model of a natural musical instrument using a DSP (Digital Sound Processor) or the like.

FIG. 21 is a schematic block diagram of a conventional sound pressure estimating device (physical model sound source) required for tone synthesis.

Referring to FIG. 21, a sound pressure estimation device (physical model)
The Dell sound source 1 includes a nonlinear operation unit 3 and a linear operation unit 5
Including. The non-linear operation part 3 is a lead (lip) in a wind instrument.
Simulate the part. The linear operation unit 5 is used for wind instruments.
Simulate the resonant tube, which is a linear part. Non-linear performance
The arithmetic unit 3 generates a blowing pressure signal pre indicating the blowing pressure of the player,
Embouchur showing the lips tension of the performer
e) The signal emb is input. And a non-linear operation unit
3 indicates to the linear operation unit 5 that the pressure traveling wave signal p_oIs output.
The linear operation unit 5 receives the input pressure traveling wave signal p._oBased on
Pressure reflection signal p _iIs output to the nonlinear operation unit 3. did
Accordingly, the non-linear operation unit 3 outputs the embouchure signal emb and
And not only the blowing pressure signal pre but also the pressure reflected wave signal p_i
Based on the traveling wave signal p_oIs output.

An oscillating circuit is formed by the non-linear operation unit 3 and the linear operation unit 5, and a digital-to-analog converter (DAC in the drawing) 7 extracts a pressure wave signal or the like, converts it into an analog signal, and outputs it as a tone signal. .

In particular, the linear operation section 5 includes a delay circuit, a low-pass filter, and the like. The delay circuit simulates a propagation delay of the pressure wave in the resonance tube of the wind instrument. The low-pass filter simulates the propagation loss of the pressure wave in the resonance tube. Low-pass filters have been used to make approximations to bring the simulated sound closer to the actual instrument sound.

However, approximation using a low-pass filter has a limit in accuracy. On the other hand, Helmhol
Starting from the study of pioneering wind instrument pronunciation by tz,
Studies have been made to incorporate nonlinearities in woodwind and brass pronunciations that represent the clarinet. As a result, the pronunciation conditions and the like that should be understood as coordination with the musical instrument and the player can be examined in detail. However, the method of series expansion of the nonlinear term used in these studies is not enough to obtain a waveform at the time of actual sound generation in which stronger nonlinearity is involved. That is, it is necessary to solve the modeled equation system using a numerical calculation method.

A method using such a numerical calculation method is described in, for example, “Ab Initio Calculations of the Oscillations”.
of a Clarinet "Acustica 48 71-85 (1981).
Proposed by Schumacher. Schum
Acher applied the numerical calculation method to the clarinet and obtained a result that sufficiently approximated the sounding waveform seen in natural musical instruments. The method will be described.

A characteristic of a musical instrument is represented by an input impedance Z _in . The reflection function r (t) indicating the reflection of sound is defined by the inverse Fourier transform of r ^hat shown in Expression (1). As shown in Expression (2), the sound pressure p (t) and the volume velocity U (t) are efficiently numerically calculated by using the reflection function r (t). However, in the equation (2), _Zc is a characteristic impedance.

The reflection function r (t) used in equation (2)
Represents a sound pressure reflected wave observed when the pulse sound pressure traveling wave is incident on the musical instrument. The reflection function r (t) is
It is desired to be faithful to the resonance characteristics of natural musical instruments.

However, when the reflection function r (t) is digitally calculated using the musical instrument input impedance Z _in obtained from the actual natural musical instrument shape or from the measurement, the causality is often broken. Causality violation
At t <0, the reflection function r (t) has a finite value. In such a case, the causally broken reflection function r
(T) is not directly used in equation (2). This is because the integration interval of the equation (2) is from 0 to ∞. Therefore, Schumacher simulated by the formula (2), assuming that the causality was not violated. Similarly, “Physical Modeling of Wind In
Music J. 16 No. 4 57-73 (1992), the reflection function r (t) is also calculated from the instrument input impedance Z _{in of a} natural instrument, as proposed in DH Keefe. Without causality, ie, t
The simulation according to the equation (2) has been performed assuming a simplified schematic reflection function r (t) such that r (t) = 0 is satisfied when <0. As a result, when the causality of the reflection function is broken, a tone close to a musical tone emitted from a natural musical instrument cannot be obtained.

Therefore, the present invention solves the above-mentioned problems and provides a sound pressure estimating apparatus capable of accurately estimating a sound pressure for synthesizing a musical tone emitted from a natural musical instrument. is there.

[0013]

(Equation 2)

[0014]

According to one aspect of the present invention, a sound pressure estimating apparatus estimates a sound pressure in order to synthesize a sound of a tubular musical instrument having a change in internal cross-sectional shape near one end thereof. The sound pressure estimating device includes an estimating means for estimating a sound pressure caused by a change in an internal cross-sectional shape. The estimating means includes a flow rate change estimating means for estimating a flow rate change of a fluid to be flowed into one end, and a sound pressure estimating means for estimating a sound pressure according to a change in the internal cross-sectional shape based on the estimated flow rate change. Prepare. The sound pressure estimating means multiplies the estimated signal representing the change in the flow rate by a predetermined coefficient, sequentially delays the signal, and reflects the reflection function r of the formula (3) representing the reflection of sound.
A plurality of delay stages for multiplying a predetermined value of ^causal (t), a signal multiplied by a coefficient and an output of each delay stage are added to output as a signal representing an estimated sound pressure, and the coefficient is multiplied. And a loop means for adding the calculated signal to the signal representing the estimated sound pressure and outputting the signal to each delay stage.

According to another aspect of the present invention, a sound pressure estimating device is a sound pressure estimating device for estimating a sound pressure in order to synthesize a sound of a tubular musical instrument having a change in internal cross-sectional shape near one end thereof. And estimating means for estimating a sound pressure caused by a change in the internal cross-sectional shape. The estimating means is a traveling wave signal output means for obtaining and outputting a sound pressure traveling wave signal representing a traveling wave of sound pressure based on a change in the flow rate of the fluid to be flowed into one end, and A reflected wave signal output means for calculating and outputting a sound pressure reflected wave signal representing a reflected wave of sound pressure, and a first sound for obtaining sound pressure by adding outputs of the traveling wave signal output means and the reflected wave signal output means. Adding means. The reflected wave signal output means sequentially delays the traveling wave signal of the traveling wave signal output means and multiplies the predetermined value of the reflection function ^rcausal (t) of the expression (3) representing sound reflection. And second adding means for adding the outputs of the respective delay stages and outputting as a reflected wave signal.

According to yet another aspect of the present invention, a sound pressure estimating apparatus for estimating a sound pressure for synthesizing a sound of a tubular musical instrument having a change in internal cross-sectional shape near one end thereof. And a sound pressure p corresponding to a change in the flow rate U (t) of the fluid to be flown into one end and a change in the internal cross-sectional shape.
Since the reflection function r (t) representing the reflection of the sound guided by the relationship with (t) has a finite value at time t <0, the reflection function r (t) is changed to the reflection of the expression (3). Function r
Change the ^causal (t), comprising estimation means for estimating sound pressure p (t) in response to changes in the internal cross-sectional shape based on the equation (4) containing the instrument input impedance _{Z in} and the characteristic impedance _{Z c.}

Preferably, the reflection function r (t) is defined by the inverse Fourier transform of r ^hat in equation (1).

Preferably, the sound pressure estimating apparatus further comprises:
There is provided another end sound pressure estimating means for estimating the sound pressure at the other end of the musical instrument in accordance with the sound pressure estimated by the estimating means.

[0019]

[0020]

(Equation 3)

[0021]

[0022]

According to one aspect of the present invention, a sound pressure estimating apparatus estimates a change in the flow rate of a fluid to be flown into one end by a flow rate changing means of an estimating means, and estimates the change by a plurality of delay stages of the sound pressure estimating means. The signal representing the change in the flow rate is multiplied by a predetermined coefficient, the signal is sequentially delayed, and the reflection function r of the expression (3) representing the reflection of sound is given.
^The signal multiplied by a predetermined value of ^causal (t) and the signal multiplied by the coefficient by the loop means of the sound pressure estimating means and the output of each delay stage are added to output as a signal representing the estimated sound pressure. Is added to the signal representing the estimated sound pressure and output to each delay stage to estimate the sound pressure according to the change in the internal cross-sectional shape based on the change in the estimated flow rate.

The above-mentioned sound pressure estimating device obtains and outputs a sound pressure traveling wave signal representing a traveling wave of sound pressure based on a change in the flow rate of the fluid to be flowed into one end by the traveling wave signal output means of the estimating means. A plurality of delay stages of the wave signal output means sequentially delays the traveling wave signal of the traveling wave signal output means, and the reflection function r of the expression (3) representing sound reflection.
multiplied by a predetermined value of ^causal (t), the output of each delay stage is added by the second adding means of the reflected wave signal output means and output as a reflected wave signal, and the traveling wave signal output means is output by the first adding means. And the output of the reflected wave signal output means are added to determine the sound pressure.

According to another aspect of the present invention, the sound pressure estimating device is configured to determine a change in the flow rate U (t) of the fluid to be flown into one end of the tubular musical instrument and a change in the internal cross-sectional shape near the one end by the estimating means. The reflection function r (t) representing the reflection of sound guided by the relationship with the corresponding sound pressure p (t) is expressed as time t <0.
, The reflection function r (t) is changed to the reflection function r ^causal (t) in the expression (3),
Estimating the sound pressure p (t) in response to changes in the internal cross-sectional shape based on the equation (4) containing the instrument input impedance Z _in and the characteristic impedance Z _c.

The above-mentioned sound pressure estimating apparatus calculates the value of r in the equation (1).
reflection function defined by the inverse Fourier transform of the ^hat r (t)
Is used to estimate the sound pressure.

The sound pressure estimating device estimates the sound pressure at the other end of the musical instrument according to the sound pressure estimated by the estimating means by the other end sound pressure estimating means.

[0027]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Before describing an embodiment of the sound pressure estimating device, the principle required by the sound pressure estimating device will be described.

Brass instruments are examples of wind instruments in which the above-mentioned causality can be broken. Therefore, the principle will be described by taking, as an example, a mouthpiece and a vibrator which is a model of the lips of a player, which is a cause of breaking the causal rule.

FIG. 1 is a diagram showing a relationship between a mouthpiece and a lip which is an example of a vibrating body.

Referring to FIG. 1, lip 11 is in contact with mouthpiece 9. The lips 11 are partially open,
A fluid such as air flows into the mouthpiece 9 from the oral cavity 13. Therefore, the three variables describing the pronunciation of such brass instruments are the sound pressure p (t) in the mouthpiece 9
And an air flow rate (volume velocity) U (t) per unit time which flows from the oral cavity 13 toward the lip opening 15 of the lip 11 and flows into the mouthpiece 9, and a position coordinate x representing the displacement of the lip 11 (T) or the angle θ (t). In the following, a model in which these three variables satisfy three equations will be described. The first equation is based on the fluid dynamics that is satisfied by the airflow passing through the lip opening area of the lip 11 due to the pressure difference between the blowing pressure p ₀ obtained in the oral cavity 13 and the sound pressure p (t) in the mouthpiece 9. It is an equation. The second equation is an equation of motion of the lip 11 that is forcibly vibrated by the application of the surrounding pressure. The third equation is an integral equation representing the characteristic of the musical instrument that gives the sound pressure p (t) generated in the mouthpiece 9 by the volume velocity U (t).

Next, the first equation, that is, the equation of air flow, will be described. The air pressure at the lip opening 15 is represented by p _lip in FIG. The airflow is assumed to be a one-dimensional flow. Similar to the one-mass or two-mass model used for voice synthesis, the law of conservation of energy is applied to the airflow compression section between the oral cavity 13 and the lip opening 15, and the conservation of momentum is applied to the airflow expansion section between the lip opening 15 and the mouthpiece 9. Is applied. These conservation laws are expressed by equations (5) and (6). Here, ρ represents the average density of air, S _lip represents the lip opening area, d represents the lip thickness, and S _cup represents the area of the mouthpiece entrance.
In the airflow expansion section, the inertia term of the airflow is ignored.
Since the lip opening area S _lip is proportional to the displacement of the _lip , the (5)
Equation (6) is expressed by three variables p (t), U (t), x
(T) (or θ (t)).

Next, a lip model will be described for the second equation. In order to handle an elastic body such as the lip 11, it is necessary to consider a continuum in which the mass and restoring force are distributed in space. However, Martin,
The lip 11 applied to the mouthpiece 9 is vibrating as a unit, as shown by the lip vibration strobe photographing when the Hall plays the musical instrument. This indicates that, even if the lips 11 are treated as vibrators having one mass in modeling, at least as a first approximation, this is not wrong. Although the restoring force can be considered to be nonlinear with respect to the displacement, here, for simplicity, only the force that obeys Hooke's law is considered. Although there is a difference between the amplitudes of the movements of both lips 11, they are treated as the same amplitude for simplicity.

2 necessary for modeling the motion of the lip 11
The second is the direction of movement. It has long been believed that both lips move in the opening direction when the blowing pressure increases when a brass instrument is sounded. That is, it has been believed that only outward vibration is realized. However, due to the proposal of Mikichi and the subsequent simultaneous measurement of the sound pressure p (t) in the mouthpiece 9 and the lip vibration, both lips 11
Has been found to move in the closing direction. That is, it has been found that inward vibration also occurs. Therefore, in the following, a model of two lips will be taken because there is a possibility of both vibrations.

The first lip model is a model in which the motion of the harmonic oscillator representing the lip 11 is allowed only in a direction perpendicular to the direction of the air flow. This model is used when vocal cord vibrations are modeled. This first model is called a one-mass model. The fact that this one-mass model realizes inward vibration means that when the airflow flows through the opening 15,
It can be seen from the noulli effect that the air pressure p _lip decreases and both lips 11 move in the closing direction. Assuming that the mass of the lips is m, the elastic coefficient is k, and the width of the lip opening 15 is b, the equation of motion of the lips 11 is expressed by the following equation (7).
In the equation (7), r 'is an attenuation coefficient of the lip movement.
The damping coefficient r 'is related to the Q value of the lip resonance by equation (8). The first term on the right side of the equation (7) represents the damping force, the second term represents the external force, and the third term represents the restoring force. The spacing of the lips opening 15 at equilibrium as x _0, if the displacement x of the lips below the -x _0/2, i.e., when the lips 11 are in contact to close the third second (7) other restoring force due claim, restoring force that is proportional to x + x _0/2 is applied. The lip opening area S _lip is expressed as S _lip = max ｛b (x ₀ +2
x), 0}.

The second lip model is a lip 11 that rotates toward the inside of the cup with one point at the rim of the mouthpiece 9 as a fulcrum. In this case, since the lip 11 is driven mainly by the difference between the blowing pressure p ₀ and the pressure p in the mouthpiece 9, outward vibration is realized. This second lip model is called a hinge model. If the length from the rim to the tip of the lip 11 is l, and the angle formed by the lip 11 at equilibrium with the plane perpendicular to the airflow is θ ₀ , the equation of motion of the lip 11 is expressed by the following equation (8). The first term on the right side of the equation (8) is the damping force, the second term is the external force due to the pressure difference, and the third term is B
The ernoulli force and the fourth term represent the restoring force.
As in the case of the one-mass model represented by the equation (7), a restoring force proportional to θ-θ _cl is applied at the time of contact with both lips. However,
θ _cl is the angle when the lips are closed. For this hinge model, lips opening area _{S lip, S li p = max} {2bl
(Cos θ _cl −cos θ), 0 °. Also,
In the Hinge model, a volume velocity bl ² dθ / dt resulting from the movement of the lips 11 is added to the hydrodynamic volume velocity U. Table 1 shows the parameters required below. However, from the measurement results of Elliot and Bowsher, it is assumed that the mass m of the lip and the elastic coefficient k of the lip are inversely proportional and proportional to the natural frequency f _{lip of the lip} , respectively.

[0036]

(Equation 4)

[0037]

[Table 1]

Next, the input impedance and the reflection function of the musical instrument will be described. As described above, the characteristics of the musical instrument are represented by the input impedance Z _in . Reflection function r (t)
Is calculated by Schumacher as r in equation (1).
It was defined by the inverse Fourier transform of ^hat . With this reflection function r (t), equation (2) efficiently represented the relationship between the sound pressure p (t) and the volume velocity U (t). Therefore, equation (2) is used in the same manner as in the conventional example. However, the reflection function r (t) will be described in detail later, but will be redefined.

Next, an experiment for confirming this principle will be described. There are two methods for obtaining the input impedance Z _in . The first is a method of performing measurement using an existing musical instrument, and the second is a method of dividing a musical instrument tube into components having a simple shape and calculating the numerical value from a product of a transfer matrix for each element. is there. In this experiment,
Of the latter methods, R.I. A method using a Kose frustocone as an element was used. Therefore, viscous resistance due to friction between the wave traveling through the tube and the tube wall and heat loss lost along the tube wall are taken into account. Further, in order to obtain the radiation loss from the bell, the calculation is performed on the assumption that a spherical wave is radiated from the bell into free space.

Since the shape data of the modern trumpet could not be obtained for the data of the musical instrument shape, the data of the baroque trumpet (D tube) was calculated by shortening the cylindrical portion so that the entire length was about 145 cm. Used for The opening of this baroque trumpet has a length of about 30
It had a cm cone and a bell of about 5 cm, and the diameter at the open end was about 12 cm. Also, the mouthpiece data, which is slightly larger than the mouthpiece of a modern musical instrument but has almost the same shape, was used as it is.

FIG. 2A shows the frequency f (kHz).
| Z_in/ Z_cFIG. 2 is a graph showing the value of |
(B) shows Z with respect to frequency f (kHz)._inShows the phase of
It is the graph which did. Where Z_inIs the instrument input impedance
Dance, Z_in= P / U. Z_cIs special
Impedance, and as described above, Z_c= Ρc /
S _cupIs represented by

| Z _in / Z _c |, which is the vertical axis of FIG.
Is a dimensionless value, and the characteristic impedance Z _c
Shows how many times the input impedance Z _in is. Characteristic impedance Z _c, since illustrates the impedance in the case of infinitely long tubular instruments sectional shape of the mouthpiece inlet area _{S cup, | Z in / Z} c | by how peak caused by the shape of the mouthpiece Is obtained. From FIG. 2A, the peaks are almost aligned at equal intervals. The names of the peaks are named Pd, A ₃ , E ₄ , A ₄ , C ^# ₅ , and E _{5 in} ascending order of frequency. The non-uniformity of the peak interval is thought to be due to the fact that the shape of the trumpet opening used in the calculation was simplified compared to that of modern instruments. A maximum peak is observed around 650 Hz, which is the resonance frequency of the cup. This tendency is characteristic of brass instruments having a mouthpiece.

Arg [Z _in ] shown in FIG. 2 (b)
Represents the phase difference between p and U because Z _in = p / U. This instrument input impedance Z _in and the characteristic impedance Z _c, the equation (1), r ^hat is obtained. The reflection function r (t) is calculated by ^{performing an} inverse Fourier transform on this r ^hat . However, in the case of calculation for the brass instrument shape, the causality is broken because of the sharp reflection immediately after time t = 0 due to the cup (change in internal cross-sectional shape) and the finite cutting frequency (sampling frequency) accompanying the numerical calculation. As a result, the value of the reflection function r (t) at t <0, which should be originally zero, becomes finite, and it becomes impossible to obtain the sound pressure P (t) from the relationship shown in Expression (2). That is, the acoustic characteristics shown in FIGS. 2A and 2B cannot be obtained. Therefore, the reflection function r (t)
The re-defined as the (3) reflection function shown in the expression ^{r ca} usal (t). The basis for such a redefinition is that, for the even function component of the reflection function r (t) whose causality is broken, t
This is because it is considered that the influence of the finite cutting frequency is small since = 0 and continuous.

[0044]

(Equation 5)

FIG. 3 is a graph of the reflection function r ^causal (t) versus time.

Referring to FIG. 3, the reflection function r ^causal (t)
Then, reflection from the opening of the musical instrument is observed from time 7 to 9 msec. After that, reflections reciprocating between the instrument opening and the mouthpiece throat are seen. Further, the peak near time zero and the subsequent reflection having a negative value are reflections by the cup and the throat constituting the mouthpiece, respectively. This peak near zero was one of the causes of breaking the causality as described above.

Next, the reflection function r defined by the equation (3)
^A sound pressure estimation device based on ^causal (t) will be described.

FIG. 4 is a schematic block diagram of a sound pressure estimation device according to one embodiment of the present invention. Referring to FIG. 4, sound pressure estimating device 17 includes a control unit 19, an estimating unit 21, and a filter 23. The estimating unit 21 includes a nonlinear operation unit 25,
And a linear operation unit 27. The non-linear operation unit 25 and the linear operation unit 27 are controlled by the control unit 19. Accordingly, the control unit 19 sends parameters such as the blowing pressure p ₀ , the reed (lip) lip natural frequency f _lip , the reed (lip) Q value, and the reed (lip) opening length x ₀ at equilibrium to the nonlinear calculation unit 25. Output. Further, the control unit 19 ^causes the linear operation unit 27 to ^output discrete sample values r ₁ , r ₂ ,..., R of the reflection function r ^causal (t).
Give _n as a parameter.

The nonlinear operation unit 25 controlled in this way
Simulates the vibration of the reed (lips) and the airflow passing through the reed opening for wind instruments. The linear operation unit 27 simulates the acoustic characteristics of the musical instrument resonance tube. When the sound pressure p in the mouthpiece, which is the output of the linear calculation unit 27, is input, the non-linear calculation unit 25 calculates the lead opening area, and further passes through the opening and flows into the mouthpiece U. Is output to the linear operation unit 27. The linear operation unit 27 outputs the sound pressure p of the mouthpiece resulting from the musical instrument resonance tube to the non-linear operation unit 25 according to the input volume flow U. Nonlinear operation unit 25 and linear operation unit 2
An oscillation system is configured by the loop connection between the loops 7.

The sound pressure p in the mouthpiece, which is the output of the linear operation unit 27, is input to the filter 23. The filter 23 calculates the sound pressure at the end of the musical instrument, and calculates the sound pressure signal P
Output as _out .

FIG. 5 is a circuit diagram of the linear operation unit 27 of FIG. The linear operation unit 27 includes a multiplier 29, an adder 31,
33 includes a delay circuit D ₁ to D _n, a multiplier r ₁ ~r _n.

The volume flow U output from the non-linear operation unit 25 is
Is input to the multiplier 29, and the multiplier 29
Impedance Z_cMultiply by And the multiplier 29
Are input to the adders 31 and 33. This signal Z_c
U gives the pressure traveling wave p_oAnd the pressure reflected wave p_iThe sum of the spots
Is simulated. The output signal of the multiplier 21 is
Not only the signal but also the output signal of the adder 33 described later.
A signal representing the sound pressure p is input. Therefore,
The adder 31 calculates Z_cPressure traveling wave p from U and p_o2
Output double. Its output is the delay that comprises the delay stages.
Extension circuit D₁~ D _nIs input to

Delay circuit D₁~ D_nConnected to the serial
Have been. Delay circuit D₁~ D_nIn each, one sun
The signal is delayed by the pulling time. As a result, the delay times
Road D ₁~ D_nMultiplier r to which each of the outputs of₁
~ R_nFrom 1 sampling time to n sampling times
A signal having a delay between them is input. Multiplier r₁~ R_nso
Is the reflection function r defined in equation (3)^causal(T)
The discrete sample values are each multiplied. And the multiplier
r₁~ R_nIs input to the adder 33. Adder 3
Multiplier r before being input to 3₁~ R_nEach signal of
The sound propagates into the instrument resonance tube during the
Pressure reflection wave p_iIs simulating twice
You. The adder 33 includes a multiplier r₁~ R_nAdd the outputs of
The pressure traveling wave p in the mouthpiece_oAnd the pressure reflected wave p_i
Is output to the adder 31 to form a loop circuit.
And outputs the sound pressure p to the non-linear operation unit 25.
You.

As a result, the linear operation unit 27 realizes Expression (4) including the reflection function r ^causal (t) defined by Expression (3).

FIG. 6 is a schematic block diagram of a sound pressure estimation device according to another embodiment of the present invention. Referring to FIG. 6, sound pressure estimating device 35 includes a control unit 19 and a filter 23 similarly to sound pressure estimating device 17 shown in FIG.
Including. The estimation unit 37 includes a non-linear operation unit 39, a linear operation unit 41, and an adder 43.

As described above, the control unit 19 controls the non-linear operation unit 39 and the linear operation unit 41. Therefore,
The control unit 19 outputs parameters such as the blowing pressure p _o , the reed (lip) lip natural frequency f _lip , the reed (lip) Q value, and the reed (lip) opening length x _o at equilibrium to the non-linear operation unit 39. I do. Further, the control unit 19 calculates the discrete sample values r ₀ , r ₁ , r ₂ , and r 3 of the reflection function r ^causal (t) defined by the expression (3).
.., R _n are output as parameters.

In the case of a wind instrument, the non-linear operation unit 39 simulates the vibration of the reed (lip) and the airflow passing through the reed opening. However, unlike the non-linear operation unit 25 shown in FIG. The signal _po is output to the linear operation unit 41. The linear operation unit 41 simulates the acoustic characteristics of the musical instrument resonance tube, but outputs the sound pressure reflected wave signal _pi to the non-linear operation unit 39 unlike the linear operation unit 27 shown in FIG. In response to the input of the sound pressure reflected wave signal p _i , the non-linear operation unit 39 adds the signal p _i and the held sound pressure traveling wave signal p _o to generate the sound pressure p in the mouthpiece. Is calculated.
The lead opening area is calculated from the signal representing the sound pressure p, and the volume flow U passing through the opening and flowing into the mouthpiece is simulated. On the other hand, to the input sound pressure reflected signal p _i is multiplied by the reciprocal of the characteristic impedance Z _c, the signal and the volume flow results U has been added is output as the sound pressure traveling wave signal p _o.

[0058] Further, the linear operation unit 41, in response to the sound pressure traveling wave signal p _o is input, and outputs the resulting sound pressure reflected wave signal p _i instrument resonance. As a result, a loop connection is formed by the non-linear operation unit 39 and the linear operation unit 41, and an oscillation system that satisfies Equation (4) is formed.

The adder 43 supplies the sound pressure traveling wave signal p
_o and the sound pressure reflected wave signal p _i are input. Adder 43
As a result, the sound pressure p in the mouthpiece is applied to the filter 23.
Is output. Since the sound pressure P is obtained by the non-linear operation unit 39, the sound pressure P may be input from the non-linear operation unit 39 to the filter 23 without using the adder 43.

As described above, the filter 23 calculates the sound pressure signal at the musical instrument end from the signal representing the sound pressure p in the mouthpiece, and outputs it as a sound pressure signal p _out .

FIG. 7 is a circuit diagram of the linear operation unit 41 of FIG. Linear operation unit 41 includes a delay circuit D ₁ to D _n, a multiplier r ₀ ~r _n, and an adder 45.

[0062] The sound pressure traveling wave signal p _o input by the non-linear calculation unit 39, while being sequentially inputted to the delay circuit D ₁ to D _n, is input to the multiplier r _0. Delay circuits D ₁ to
D _n each delay the signal by one sampling time. Then, each of the delay circuits D ₁ to D _n, and outputs a signal having a multiplier r ₁ ~r _n from one sampling time to the n sampling time delay. Therefore, signals are input to the multipliers r _{0 to} r _n , each having a delay of 0 sampling time to n sampling times. The multipliers r _{0 to} r _n are provided by the reflection function r defined by the equation (3).
discrete sample values r _i (i = 0,..., n) of ^causal (t)
Is multiplied by the respective outputs of the delay circuits D _{1 to} D _n . Each multiplier r ₀ ~r _n outputs a signal representing the result of the multiplication to the adder 45. Each signal input to the adder 45 is a signal indicating that the pressure reflected wave propagating in the musical instrument resonance tube during each delay time and returning to the mouthpiece is simulated. The adder 45 adds each of the input signals, thereby propagating the pressure reflected wave signal p propagating in the instrument resonance tube from the 0 sampling time to the n sampling time delay and returning to the mouthpiece.
_i is output to the non-linear operation unit 39.

[0063] In this manner, the multiplier r ₀ ~r in each of _n, the (3) reflected function defined by the equation r
^The simulation is performed by multiplying the discrete sample values of ^causal (t).

Next, in describing the principle of the sound pressure estimation device shown in FIGS. 4 and 6, the effect of sound pressure estimation due to the redefined reflection function r ^causal (t) will be described.

FIG. 8 is a graph showing acoustic characteristics obtained from the shape of a wind instrument. FIG. 8A shows the frequency f (k
8) is a graph showing the value of | _Zin / _Zc | with respect to the frequency f (kHz).
9 is a graph showing rg [Z _in ] (deg).

FIG. 9 is a graph showing a reflection function from t = 0 to t = 50 msec of the reflection function obtained from the acoustic characteristics shown in FIG. 8, and FIG.
FIG. 9B is a graph showing (t), and FIG.
FIG. 6 is a graph showing a reflection function r ^trun (t) when the value of t <0 in the reflection function r (t) in FIG.
FIG. 9C shows the reflection function r defined by the expression (3).
It is the graph which showed ^causal (t).

FIG. 10 shows that the reflection function t = 0 shown in FIG.
FIG. 10A is a graph showing a state in the vicinity, and FIG.
FIG. 10B is a graph corresponding to FIG. 9A, and FIG.
FIG. 10C is a graph corresponding to FIG. 9B, and FIG.
It is a graph corresponding to FIG.9 (c).

FIG. 11 is a graph showing acoustic characteristics when the reflection function r ^trun (t) is used, where Z _in = (1+
FIG. 11 is a graph showing acoustic characteristics when r ^{hat (trun)} ) / (1-r ^{hat (trun)} ) is used (where r ^{hat (trun)} is the Fourier transform of r ^trun (t)). (A)
FIG. 11B is a graph corresponding to FIG.
Is a graph corresponding to FIG.

FIG. 12 is a graph showing acoustic characteristics when the reflection function r ^causal (t) is used, where Z _in = (1
FIG. 12 (a) is a graph showing acoustic characteristics when (+ ^{rhat (causal)} ) / (1- ^{rhat (causal)} ) is used ^{(where rhat (causal)} is the Fourier transform of ^rcausal ).
Is a graph corresponding to FIG. 8A, and FIG.
Is a graph corresponding to FIG.

FIG. 13 is a graph showing acoustic characteristics when the reflection function r ^causal (t) is used, and shows a case where only the linear operation unit is simulated using the operation expression of the expression (4). FIG. 13A is a graph showing acoustic characteristics, and FIG.
FIG. 13B is a graph corresponding to FIG.
Is a graph corresponding to FIG.

The reflection function r (t) obtained from the acoustic characteristics shown in FIG. 8 has a finite value at t <0, as shown in FIG. That is, at t <0, the reflection function r
(T) is not constant at zero. Therefore, in order to perform the calculation according to the expression (4), the reflection function when t <0 and forcibly set to a constant value at 0 as shown in FIG. 10B is used in the conventional method. It seems necessary. In the present invention, as shown in FIG. 10C, the value of the reflection function r (t) at t <0 is folded and added to t> 0. Such reflection functions r (t), r ^trun (t), r
^causal (t) is clearly different in FIG.
As shown in FIG. 9, there is not much difference between t = 0 and t = 50 msec.

However, the reflection function shown in FIG.
Number r^trunThe acoustic characteristics when (t) is used are shown in FIG.
Completely different from acoustic characteristics. This is shown in FIG.
As shown, the value of the reflection function was forcibly set to 0 at t <0.
It is. The acoustic characteristic shown in FIG.
^trunFourier transform r of (t)^{hat (trun)}To Z_in= (1
+ R ^{hat (trun)}) / (1-r^{hat (trun)}) Calculated using
The acoustic characteristics were

On the other hand, when the reflection function r ^causal (t) as shown in FIG. 12 is used, the acoustic characteristics accurately match the acoustic characteristics shown in FIG. Figure acoustic characteristics shown in 12, Z _in = (1 + r from the Fourier transform r ^{hat (causal)} of the reflection function r ^causal shown in FIG. 10 (c) (t)
^{hat (causal)} ) / (1-r ^{hat (causal)} ). Therefore, when comparing the method using r ^trun (t) and the method using r ^causal (t), it is apparent that the acoustic characteristics are more accurately reproduced when the reflection function r ^causal (t) is used. . The acoustic characteristic shown in FIG. 13 was an acoustic characteristic simulated by using the calculation function defined by the expression (4) instead of the Fourier transform using the reflection function r ^causal (t). The acoustic characteristics shown in FIG. 13 also accurately match the acoustic characteristics shown in FIG. Therefore, the reflection function r ^causal (t)
It can be seen how effective the sound pressure estimating device shown in FIG. 4 or FIG.

As described above, when the reflection function r ^causal (t) is used, the acoustic characteristics are accurately reproduced. Especially,
The acoustic characteristics can be accurately reproduced not only in the numerical calculation but also by simulating the linear operation unit using the operation expression represented by Expression (4).

Next, the principle described with reference to FIGS.
As a continuation, not only the mouthpiece but also the lip-like vibration
The experimental results that take the body into consideration will now be described. That is,
The time domain simulation will be described. No. (4)
The equation shown in the equation is differentiated by the forward Euler method.
A simulation was performed using the data obtained. sound
Fig. 2 shows the blowing pressure when the sound is moderate (mf).
Pd to E shown in (a) _FiveTo the impedance peak of
20, 20, 25, 30, 35, 40 kdyn
/ Cm^TwoAnd The Q value of the lips is A_Four
I chose 8.0 for the peak, but everything else
5.0. The natural frequency of the lips is from 60 to 800 Hz
The sounding frequency was determined by changing the frequency by 20 Hz.
X representing the equilibrium position of the lips₀Or θ₀For a long time
Avoid touching, and the displacement of the lips gives the maximum amplitude
Was adjusted to

FIG. 14 is a diagram in which the sound frequency is plotted against the natural frequency of the lips. As shown in FIG.
Pronunciation is observed in both the inge model and the one-mass lip model. As expected from the theory, the one-mass model is sounded at a frequency lower than each peak position. Conversely, in the hinge model, sound is generated at a high frequency. The natural frequency of the lips is the same or slightly higher than each peak position in the one-mass model. On the contrary,
In the hinge model, the natural frequency of the lips is considerably low when a sound in the high range is produced. The sound generation condition is determined by the balance between the absolute value and the phase of the impedance Z _in and the mobility G of the musical instrument. The reason why the natural frequency of the lips is low in the hinge model is that the phase condition is satisfied only in that case.

FIG. 15 is a graph showing the difference in pronunciation between the one-mass model and the hinge model.
Is the sound pressure p (kdyn / c
m ² ), FIG. 15B is a graph showing the volume velocity U (cm ³ / sec) with respect to time of the one-mass model, and FIG. 15C is a graph showing the volume velocity of the one-mass model. It is the graph which showed displacement x (mm) of the lip with respect to time. FIG. 15D is a graph showing the sound pressure p (kdyn / cm ² ) with respect to time in the hinge model. FIG. 15E is a graph showing the volume velocity U (cm ³ / sec) with respect to time in the hinge model. ).
FIG. 15F is a graph showing the displacement of the lips θ (deg.) With respect to the time of the hinge model.

As shown in FIGS. 15A to 15C, _in the case of the one-mass model, argZ _in = argp-argU
= 81.0, argG = argx-argp = -34.
It becomes 2. That is, between the sound pressure p and the volume velocity U,
The phase difference is 81.0, and the phase difference between the sound pressure p and the lip displacement x is -34.2. In the case of the hinge model, argZ _in = −52.0, argG = argθ
−argp = 16.2. That is, the sound pressure p
And the volume velocity U have a phase difference of −52.0, and the sound pressure p and the lip displacement θ have a phase difference of 16.2. From these signs, the inward oscillation, hin,
It is considered that outward oscillation is performed in the e model.
Also, the phase condition argZ _in + ar derived from the linear theory
gG = 0 is not satisfied by this pronunciation.

FIG. 16 is a graph showing a tone generation waveform from the impedance peak Pd shown in FIG. 2A to C ^# ₅ . Figure 16 (a) ~ (e) is a graph corresponding to 1 mass model, 16 (a) is a graph corresponding to the impedance peak Pd, FIG. 16 (b), the impedance peak A ₃ FIG. 16 is a corresponding graph.
16C is a graph corresponding to the impedance peak E _o , FIG. 16D is a graph corresponding to the impedance peak A ₄ , and FIG. 16E is a graph corresponding to the impedance peak C ^# _5. It is. FIG. 16 (f)
~ (J) is a graph corresponding to the hinge model, FIG. 16 (f) is a graph corresponding to the impedance peak Pd, FIG 16 (g) is a graph corresponding to the impedance peak A _3, FIG. 16H is a graph corresponding to the impedance peak E ₄ , and FIG.
6 (i) is a graph corresponding to the impedance peak A _4, FIG. 16 (j), the impedance peak C ^#
₅ is a graph corresponding to FIG.

FIGS. 16 (a) to 16 (e) and FIG.
As shown in (f) to FIG. 16 (j), the harmonic components are reduced as the range changes from the low range to the high range. However, the high range of the hinge model is an exception.
This is presumably due to the fact that the natural frequency of the lips is lower than the peak position in this case, causing an oscillation system different from the bass range.

By the way, the waveform shown in FIG.
First name D_TwoIs equivalent to The waveform of FIG._ThreeTo
Equivalent to. The waveform of FIG.^b _FourEquivalent to
You. The waveform of FIG.^b _FourIs equivalent to Figure
The waveform of 16 (e) is sound name B _FiveIs equivalent to FIG.
The waveform of (f) is the note name B^b _TwoIs equivalent to FIG. 16 (g)
Waveform of note name B^b _ThreeIs equivalent to The waveform of FIG.
Is the note name F_FourIs equivalent to The waveform in FIG.
A_FourIs equivalent to The waveform of FIG.^# _FiveTo
Equivalent to.

Note names D ₂ , F ₃ , E ^b ₄ , A ^b ₄ , B
₅ is the impedance peak name Pd, shown in FIG.
Should match A ₃ , E ₄ , A ₄ , C ^# ₅ , E ₅ , but 1
In the mass model, the sound drops and deviates from the semitone by about one and a half, so that they do not have the same note name. Similarly, note name B ^{b
_{2, B b 3, F 4}} , A 4, C # 5 the impedance peak name _{Pd, A 3, E 4,} A 4, C # 5, but should be consistent with E _5, when the hinge model, increases the sound Since the pitch is shifted by one and a half tone from a semitone, the pitch names do not match. In other words, the impedance peak name and the synthesized sound name do not match even though the sound is generated in each resonance mode.

FIG. 17 is a diagram showing the amplitude for each overtone shown in FIG. In particular, FIG.
It is the figure which plotted the amplitude with respect to each overtone in the 1 mass model shown to (a)-(e), and FIG.17 (b) shows each of the hinges model shown to FIG.16 (f)-(j). It is the figure which plotted the amplitude with respect to an overtone.

In FIG. 17 (a), .largecircle.
Shows the amplitude of the sound name F ₃ shown in (b). × indicates FIG.
6C shows the amplitude for the pitch name E ^b ₄ shown in FIG. + Indicates the amplitude at the pitch name A ^b ₄ shown in FIG. * Indicates the note name B ₅ shown in FIG.
Shows the amplitude at.

In FIG. 17 (b), .largecircle.
The amplitude at the pitch name B ^b ₃ shown in (g) is shown. ×
Shows the pitch name F ₄ shown in FIG. 16 (h). +
Shows the amplitude of the sound names A ₄ shown in FIG. 16 (i). * Indicates the amplitude of note name C ^# ₅ shown in FIG.

As can be seen from FIGS. 17A and 17B,
As a whole, there is a tendency for the logarithmic amplitude to decrease steadily with respect to the harmonic order derived by Elliot and Bowsher. However, particularly in the high range of the hinge model in FIG. 17B (note name C ^# ₅ indicated by *), the tendency to decrease constantly is not seen.

Next, what is the sound pressure waveform depending on the sound intensity?
Peak A to see how it changes_ThreeAt blowing pressure p₀
Is 5 (pp), 20 (mf), 60 (ff) kdyn /
cm ^TwoTo perform simulation by changing
Will be described.

[0088] Figure 18 is a diagram showing a sound pressure waveform by a different blowing pressure peak A _3. FIG. 18A shows the blowing pressure p ₀ = 5 (pp) kdyn / cm in the one-mass model.
Is a diagram showing the ^2. FIG. 18B shows the blowing pressure p ₀ = 20 (mf) kdyn / cm in the one-mass model.
Is a diagram showing the ^2. FIG. 18C shows the blowing pressure p ₀ = 60 (ff) kdyn / cm in the one-mass model.
Is a diagram showing the ^2. FIG.
Wind pressure p ₀ = 5 (pp) kdyn / c in e model
FIG. 7 is a diagram illustrating m ² . FIG.
blowing pressure p ₀ = 20 (mf) kdyn in the ge model
/ Cm ^2. FIG. FIG. 18F shows h
blowing pressure p ₀ = 60 (ff) kd in the inge model
FIG. 4 is a diagram showing yn / cm ² .

FIG. 19 is a diagram showing the amplitude corresponding to each harmonic order at the time of sound generation corresponding to FIG. FIG. 19 (a)
FIG. 19 is a diagram showing a case of a one-mass model corresponding to FIGS. FIG. 19 (b) shows the state shown in FIG.
It is a figure showing the hinge model corresponding to (f).

In FIG. 19 (a), x indicates that in FIG.
The blowing pressure p shown in (a)₀= 5 (pp) kdyn / cm^Two
FIG. ○ is shown in FIG.
Blowing pressure p ₀= 20 (mf) kdyn / cm^TwoAbout
FIG. + Indicates the blowing pressure p shown in FIG.₀
= 60 (ff) kdyn / cm^TwoFIG.
You. Also in FIG. 18 (b), × indicates the opposite to FIG. 18 (d).
18 corresponds to FIG. 18E, and + corresponds to FIG.
This corresponds to (f).

Referring to FIGS. 18 and 19, peak A
_3, even with different blowing pressure p _0, it tends to logarithmic amplitude will fall linearly with the harmonic orders can be seen. However, it is not clear from the graph shown in FIG. 19 whether the linearly decreasing slope of the logarithmic amplitude becomes gentler as the sound level increases.

Referring again to FIG. 14, the sounding frequency significantly changes with the change in the natural frequency of the lips in the sounding for the same peak. In particular, with respect to sound at peak A _3, 1
The change occurs four times in the mass model and twice in the hinge model.

[0093] Figure 20 is a diagram showing the pronunciation sound pressure waveforms at the time of changing the natural frequency of the lip by the impedance peak A _3. FIGS. 20A to 20C are diagrams for the one-mass model, and FIGS. 20D to 20F are diagrams for the hinge model. FIG. 20A is a diagram in which E ^b ₃ is named as the note name closest to the sound generation frequency.
FIG. 20B shows F ₃ as the note name closest to the sounding frequency.
FIG. FIG. 20C is a diagram in which A ^b ₃ is named as the note name closest to the sound generation frequency.
FIG. 20D shows A ₃ as the note name closest to the sounding frequency.
FIG. FIG. 20E is a diagram in which B ^b _{3 is} named as the note name closest to the sound generation frequency. Figure 20 (f) are diagrams named B ₃ as nearest pitch name pronunciation frequency.

The same impedance A_ThreeSo
However, in the one-mass model, it is shown in FIGS.
U, E^b _Three, F_Three, A^b _ThreeAnd the impedance
Arc A_ThreeThe note name is off. Similarly, hingemo
At Dell, as shown in FIGS.
Dance Peak A_ThreeEven, note name A_Three, B^b _Three, B _Three
Like impedance peak A_ThreeNote name is shifted from
You. Such variability in pitch is the instrument's impedance.
Probably due to non-uniformity of dance peak positions
It is. In general, due to the nonlinearity of the system,
Coupling occurs. Peak positions are perfectly evenly spaced
Instrument, if the fundamental frequency is near the peak position,
Overtones also coincide with other peak positions. Because of that
A stable and stable oscillation system is completed. In contrast
For instruments with non-uniform peak positions, the fundamental frequency
Even if the peak position is shifted, another peak position
If the frequency matches, sound can be generated. Therefore, the figure
As shown in FIG.

Table 2 shows which overtone actually matches the impedance peak.

[0096]

[Table 2]

As can be seen from Table 2, the one-mass model E ^b
In _3, 4th, 3rd and 5th order in F _3, A ^b ₃ is first order (fundamental) harmonic contributes to the oscillation regime. Also, hin
ge Model A ₃ In order third-4, Fourth to B ^b _3, B
_In No. ₃ , the fourth and fifth harmonics contribute to the oscillation system.

In a system having time-feedback feedback such as a musical instrument, different sounds can be obtained depending on the past history (hysteresis) even if the sound is generated under exactly the same parameters. In fact, this hysteresis has been observed in experiments of artificial sounding of clarinets. In the simulation shown in this embodiment, two or more different sounding parameters are not obtained. However, certain parameters (p ₀
= 5 kdyn / cm ² , x ₀ = 0.01 cm, Q = 5.
In 0), it was found that there were cases where the pronunciation was made depending on the past history and cases where the pronunciation was not made. Also, the strange pronunciation is 2
One simultaneously Could example the peak A ₄ and C ^# ₅ was obtained.

The above is summarized. First, it became clear from the graphs shown in FIGS. 8 to 13 that the reflection function r ^causal (t) required for the present invention was effective in sound pressure estimation.

Further, it was shown that the pronunciation was realized in both models using two lip models. It was shown that the sound obtained by the simulation changes from a sound including harmonics to a sound close to a pure sound as the pitch of the sound increases, similarly to the sound of a natural instrument. In addition, a change in sound quality similar to that seen in a natural musical instrument sound could be exhibited with respect to the strength of the sound. Furthermore, through the nonlinearity of the system, a sound was generated by the oscillation system with the cooperative action of multiple instrument impedance peaks.

The effect of sound pressure estimation by using the reflection function r ^causal (t) needs to be limited to only a shape such as a mouthpiece of a brass instrument whose cross-sectional shape decreases as it goes inside the wind instrument. There is no. That is, the cross-sectional shape of one end of the musical instrument may be widened. For example, even if the cross-sectional shape of the instrument is a conical tube, the reflection function r
^causal (t) is effective. This is because reflection occurs where impedance changes. That is, the change in the sectional area S causes the characteristic impedance Z of the tube to change.
_{This is because c} = ρc / S changes and reflection occurs.

Therefore, the musical instrument is not limited to a brass instrument, but may be a woodwind instrument as long as it has a portion where the internal cross-sectional shape changes, such as a mouthpiece.

As a definition of the reflection function r ^causal (t), the section from t = −∞ to t = 0 does not necessarily need to be folded back to the section from t = 0 to t = + ∞. That is, the reflection function r near t = 0 and at t <0
The section up to the section where the value of (t) has a finite value may be folded.

[0104]

As described above, according to the present invention, the sound pressure for synthesizing the sound of a musical instrument having an internal cross-sectional shape near one end of the musical instrument can be estimated as accurately as possible.

[Brief description of the drawings]

FIG. 1 is a diagram showing a state of a mouthpiece, a lip, and an oral cavity.

FIG. 2 is a graph showing the input impedance of a musical instrument.

FIG. 3 is a graph showing a reflection function.

FIG. 4 is a schematic block diagram showing a sound pressure estimation device according to one embodiment of the present invention.

FIG. 5 is a circuit diagram of a linear operation unit of FIG. 4;

FIG. 6 is a schematic block diagram showing a sound pressure estimation device according to another embodiment of the present invention.

FIG. 7 is a circuit diagram of the linear operation unit of FIG. 6;

FIG. 8 is a graph showing acoustic characteristics of a musical instrument obtained from the shape of the musical instrument.

FIG. 9 is a graph showing a reflection function from t = 0 to 50 (msec).

FIG. 10 is a graph showing a reflection function near t = 0.

FIG. 11 is a reflection function r where the reflection function r (t) is t = 0.
⁷ is a graph showing acoustic characteristics when ^trun (t) is used, and is a graph showing acoustic characteristics when inverse Fourier transform and Fourier transform are used.

FIG. 12 is a graph showing acoustic characteristics when a reflection function r ^causal (t) is used, and is a graph showing acoustic characteristics when an inverse Fourier transform and a Fourier transform are used.

FIG. 13 is a graph showing acoustic characteristics when a reflection function r ^trun (t) is used, and showing acoustic characteristics when an inverse Fourier transform and Expression (4) are used.

FIG. 14 is a graph showing the relationship between the natural frequency of the lips and the pronunciation frequency.

FIG. 15 is a graph showing waveforms of sound pressure p, volume velocity U, and lip displacement x (or θ) at the mouthpiece.

FIG. 16 is a graph showing sound pressure waveforms at different impedance peaks (from Pd to C ^# ₅ ) in FIG. 2 (a).

FIG. 17 is a graph showing the amplitude with respect to each harmonic order when sound is generated at different impedance peaks (Pd to C ^# ₅ ) in FIG. 2A.

FIG. 18 shows a blowing pressure p ₀ of 5 (pp), 20 (mf), 6
It is the graph which showed the sounding sound pressure waveform in different levels by 0 (ff) kdyn / cm < ² >.

FIG. 19: blowing pressure p ₀ is 5 (pp), 20 (mf), 6
It is the graph which showed the amplitude with respect to each overtone order at the time of tone generation at 0 (ff) kdyn / cm < ² > different levels.

FIG. 20 shows the same impedance peak (A
₃ is a graph showing a sound pressure waveform when the natural frequency of the lips is changed in ₃ ).

FIG. 21 is a schematic block diagram of a conventional sound pressure estimation device (physical model sound source).

[Explanation of symbols]

 17, 35 Sound pressure estimation device 21, 37 Estimation unit 23 Filter 25, 39 Non-linear operation unit 27, 41 Linear operation unit

Continuation of the front page (58) Field surveyed (Int.Cl. ⁶ , DB name) G10H 7/08 G10H 7/00

Claims (5)

(57) [Claims] 1. A sound pressure estimating apparatus for estimating a sound pressure for synthesizing a sound of a tubular musical instrument having a change in internal cross-sectional shape near one end thereof, wherein the sound pressure generated by the change in internal cross-sectional shape is determined. A flow rate change estimating means for estimating a flow rate change of a fluid to be flowed into the one end, and a flow rate change estimating means for estimating a change in the internal cross-sectional shape based on the estimated flow rate change. Sound pressure estimating means for estimating sound pressure, wherein the sound pressure estimating means multiplies a signal representing the estimated flow rate change by a predetermined coefficient, sequentially delays the signal, and represents a sound reflection. A plurality of delay stages for multiplying a predetermined value of the reflection function ^rcausal (t) of the expression (1); a signal multiplied by the coefficient and an output of each of the delay stages to add the estimated sound pressure Output as a signal And a loop means for adding a signal multiplied by the coefficient to the signal representing the estimated sound pressure and outputting the signal to each of the delay stages. 2. A sound pressure estimating apparatus for estimating a sound pressure for synthesizing a sound of a tubular musical instrument having a change in internal cross-sectional shape near one end thereof, wherein the sound pressure generated by the change in internal cross-sectional shape is determined. Estimating means for estimating, the estimating means, a traveling wave signal output means for obtaining and outputting a sound pressure traveling wave signal representing a traveling wave of sound pressure based on a change in the flow rate of the fluid to be flowed into the one end, A reflected wave signal output unit that obtains and outputs a sound pressure reflected wave signal representing a reflected wave of sound pressure based on the output sound pressure traveling wave signal; and the traveling wave signal output unit and the reflected wave signal output unit. A first adding means for adding the output to obtain a sound pressure, wherein the reflected wave signal output means sequentially delays the traveling wave signal of the traveling wave signal output means and represents sound reflection (1). Equation reflection function r
^A sound pressure estimating device comprising: a plurality of delay stages for multiplying a predetermined value of ^causal (t); and a second adding unit for adding outputs of the respective delay stages and outputting a reflected wave signal. 3. A sound pressure estimating device for estimating a sound pressure for synthesizing a sound of a tubular musical instrument having a change in internal cross-sectional shape near one end thereof, wherein a change in a flow rate of a fluid to be flowed into the one end is provided. The reflection function r (t) representing the reflection of sound guided by the relationship between U (t) and the sound pressure p (t) corresponding to the change in the internal cross-sectional shape has a finite value at time t <0. Accordingly, the reflection function r (t) is changed to the reflection function r of the equation (1).
Change the ^causal (t), instrument input impedance _{Z in} and the characteristic impedance _Z a containing _c (2) the sound pressure p in response to changes in the internal cross-sectional shape based on the formula
A sound pressure estimating device comprising: estimating means for estimating (t). 4. The sound pressure estimating device according to claim 3, wherein the reflection function r (t) is defined by an inverse Fourier transform of r ^{hat in} the equation (3). 5. The sound pressure estimating device according to claim 3, further comprising another end sound pressure estimating means for estimating a sound pressure at the other end of the musical instrument according to the sound pressure estimated by the estimating means. (Equation 1)