JP2023062930A - Method for synthesizing musical sound signal, musical sound signal synthesis device, and program - Google Patents

Abstract

To synthesize a high-quality and real musical sound signal of a wind instrument, with a lower calculation cost.SOLUTION: A method for synthesizing a musical sound signal includes: an instrument movement calculation process (112) of calculating, according to performance information, first information showing a pressure exerted to a voice generation source by a mouth, second information showing a displacement of the voice generation source, third information showing a flow rate exerted to a liner coupled system made of air and a body by the voice generation source, and fourth information showing a pressure exerted to the voice generation source by the linear coupled system; and a musical sound signal calculation process (113) of calculating a sound pressure at an observation point on the basis of the third information. The linear coupled system is expressed by a general viscosity attenuation model. A complex eigenvalue and a complex unique mode as modal parameters of the general viscosity attenuation model are identified with a frequency response of the linear coupled system or the inverse Fourier transform of the frequency response as a reference. The fourth information is calculated by using the complex eigenvalue and the complex unique mode.SELECTED DRAWING: Figure 3

Description

The present disclosure relates to a musical sound signal synthesizing method, a musical sound signal synthesizing device, and a program.

2. Description of the Related Art There is known a method of artificially (virtually) synthesizing realistic musical tones by modeling and simulating the sounding mechanism of a natural musical instrument based on physical laws. Taking a wind instrument as an example, Non-Patent Document 1 describes a method of synthesizing a musical tone signal by simulating the interaction between a sound source (lips or reeds) and the air inside the tube.

MoReeSC: A Framework for the Simulation and Analysis of Sound Production in Reed and Brass Instruments, ACTA ACOUSTICA UNITED WITH ACOUSTICA, Vol.100 (2014) p126-138

However, the technique described in Non-Patent Document 1 cannot synthesize a realistic musical tone signal according to the detailed design specifications of the main body (the body of a wind instrument) and reeds, because the model is simple. I have a problem.

In a musical sound signal synthesizing method according to an aspect of the present disclosure, when a sound generating source interacts with air, and the air interacts with a main body, a computer generates an arbitrary sound in the air according to performance information. a musical sound signal synthesizing method for synthesizing a musical sound signal indicating a sound pressure at an observation point, wherein the computer generates first information indicating the pressure exerted by the oral cavity on the sound generating source according to the performance information; second information indicative of the displacement of the source; third information indicative of the flow rate exerted by the source on the linearly coupled system of the air and the body; and the pressure exerted by the linearly coupled system on the source. and a musical sound signal calculation process in which the computer calculates the sound pressure at the observation point based on the third information, wherein the linear coupled system comprises: Complex eigenvalues and complex eigenmodes, which are modal parameters of the general viscous damping system model and are represented by the general viscous damping system model, are identified with reference to the frequency response of the linear coupled system or the inverse Fourier transform of the frequency response, and Fourth information is calculated using the complex eigenvalues and the complex eigenmodes.

FIG. 4 is a diagram for explaining a physical model; FIG. 4 is a diagram showing the configuration of a computer that generates synthesized musical tones; 3 is a block diagram showing the functional configuration of a computer; FIG. 4 is a flowchart showing the operation of tone signal synthesizing processing; 4 is a flow chart showing modal parameter identification processing in tone signal synthesizing processing; FIG. 10 is a diagram showing that the reference FR and the FR by mode synthesis are almost the same; FIG. 10 is a diagram showing that the reference FR and the FR by mode synthesis are almost the same; FIG. 10 is a diagram showing that the reference FR and the FR by mode synthesis are almost the same; FIG. 10 is a diagram showing that the reference FR and the IR by mode synthesis are almost the same; FIG. 10 is a diagram showing that the reference FR and the IR by mode synthesis are almost the same; FIG. 10 is a diagram showing that the reference FR and the IR by mode synthesis are almost the same;

A musical tone signal synthesizing method according to an embodiment of the present disclosure will be described below with reference to the drawings.
In each drawing, the dimensions and scale of each part are appropriately different from the actual ones. Further, since the embodiments described below are preferred specific examples, they are subject to various technically preferable limitations. It is not limited to these forms unless otherwise stated.

First, the principle of the tone signal synthesizing method according to the actual embodiment will be explained.
If the wind instrument is a brass instrument (trumpet, trombone, horn, etc.), the musical tone of the brass instrument is produced by putting the player's lips on the mouthpiece attached to the entrance side of the instrument body, in the mouth of the player. It is generated by releasing the stored air and vibrating the lips.
Similarly, if the wind instrument is a woodwind instrument (such as a clarinet, saxophone, oboe, etc.), the musical sound of the woodwind instrument is produced by the player holding a mouthpiece attached to the inlet side of the instrument body with his/her mouth, It is generated by releasing the trapped air and vibrating the reed.
In order to imitate such a pronunciation mechanism, the following physical model is used in this embodiment.

FIG. 1 is a diagram for explaining each physical model that is a premise of the musical tone signal synthesizing method according to the embodiment, and the coupling between each of these physical models. A physical model is a model of the sounding mechanism of a wind instrument. In this embodiment, the physical model is roughly divided into a sounding source (lips or reeds) Lp, air Ar, and main body Bd. Coupling between physical models means that two physical models influence each other.

Of the physical models, the sound source Lp is a model that imitates the movement of the sound source (a player's lips in the case of a brass instrument, and a reed in the case of a woodwind instrument). The main body Bd is a model that imitates the movement of the tube of a wind instrument. The air Ar imitates the motion of the air existing around the source Lp and the body Bd.

In such a physical model, the oral cavity Oc applies a pressure (1) to the sound source Lp, thereby generating a vibration displacement (2) in the sound source Lp and simultaneously giving a flow rate (3) to the air. A pressure (4) is applied to the sound source Lp.
In this embodiment, the oral pressure (1) is indicated by the first information, the displacement (2) is indicated by the second information, the flow rate (3) is indicated by the third information, and the pressure (4) is indicated by It is indicated by the fourth information.

The microphone Mc is not a physical model of the wind instrument, but is shown to virtually show the observation position of the musical tone signal to be generated. In other words, in this embodiment, a musical tone signal of the sound pressure observed at the position where the microphone Mc is provided is synthesized (generated). The microphone Mc can be provided at any position in the air where the main body Bd exists.

Although the technology described in Non-Patent Document 1 has been described as a simple model, the simple here means the following three points. Specifically, a first point ignoring the spatial distribution of the source (lips or reeds), a second point where the source (lips or reeds) and air are joined at one point, and a complex The third point is that the interaction between the tubular body having a three-dimensional shape and the air is ignored.

Therefore, in the musical tone signal synthesizing method according to the present embodiment, firstly, the coupled system between the air Ar and the main body Bd is represented by a general viscous damping system model. Specifically, the response pressure at the interface between the source and the coupled system is expressed as "superposition of complex eigenmodes," more specifically, as "superposition of first-order IIR filters with complex filter coefficients." decided to
In this description, the coupled system between the air Ar and the main body Bd is particularly referred to as the "linear coupled system Lc", and the "nonlinear coupled system" consisting of the oral cavity Oc and the sound source Lp, and all of them We distinguish it from the "nonlinear coupled system" including

The theoretical basis for the fact that the linear coupled system Lc consisting of the body Bd and the air Ar, that is, the acoustic structure coupled system can be represented by the general viscous damping system model is that the structural displacement and the air velocity potential depend on time and space. The acoustic structure interaction equation by the finite element method in the case of "variables" can be formally expressed by a real symmetrical mass matrix, damping matrix, and stiffness matrix. The form of the equation of motion composed of these three real symmetric matrices is a model of a structure with general viscous damping (not proportional viscous damping). is mathematically the same as
The advantage of expressing the acoustic-structure interaction system with a general viscous damping system model is that the eigenmodes of this model have orthogonality in a broad sense. At this time, high-speed time-domain simulation using the mode synthesis method becomes possible.

また、一般粘性減衰系モデルにおける周波数応答（Frequency Response）は、次式（２）のように示される。
インパルス応答と周波数応答との間には、インパルス応答のフーリエ変換が周波数応答であり、周波数応答の逆フーリエ変換がインパルス応答であるという関係がある。

An impulse response in the general viscous damping system model is expressed as in the following equation (1).

Also, the frequency response in the general viscous damping system model is expressed as in the following equation (2).
There is a relationship between the impulse response and the frequency response that the Fourier transform of the impulse response is the frequency response and the inverse Fourier transform of the frequency response is the impulse response.

In equation (1) or (2), j is the imaginary unit, * is the complex conjugate, and r is the modal order. i is the index of the excitation point and l is the index of the response point.
λ _r is the complex eigenvalue and is denoted by λ _r =−σ _r +jω _dr .
σ _r is the modal damping rate and ω _dr is the damped natural angular frequency.

なお、式（３）において、
ｘ_ｒｉは、加振点ｉにおける複素固有モードの実部であり、
ｙ_ｒｉは、加振点ｉにおける複素固有モードの虚部である。 R _ril is a modal residue and is represented by the following equation (3).

In addition, in formula (3),
x _ri is the real part of the complex eigenmode at excitation point i,
y _ri is the imaginary part of the complex eigenmode at excitation point i.

An important point in expressing the linear coupled system Lc with a general viscous damping system model is how accurately the modal parameters of the general viscous damping system model can be determined.
For this reason, in the present embodiment, secondly, the frequency response of a linear coupled system calculated by a multi-point excitation multi-reference (MIMO: Multi-Input Multi-Output) method using, for example, a fast multipole boundary element method ” as a reference, we decided to identify the complex eigenvalues and complex eigenmodes, which are modal parameters, so as to fit the general viscous damping model.

FIG. 2 is a block diagram of the computer 10 that executes the musical tone signal synthesizing method according to this embodiment. The musical tone signal synthesizing method according to this embodiment is realized by cooperation between a computer and software.
The computer 10 includes a control device 11 , a storage device 12 , a performance information output device 13 and a sound emitting device 14 .

The control device 11 is composed of one or more processing circuits such as a CPU (Central Processing Unit), and controls each element of the computer 10 in an integrated manner. Note that the control device 11 may be configured by a circuit such as a DSP (Digital Signal Processor) or an ASIC (Application Specific Integrated Circuit) in addition to the CPU.

The storage device 12 is, for example, one or more memories configured with known recording media such as magnetic recording media or semiconductor recording media, and stores programs executed by the control device 11 and various data used by the control device 11. Remember. Note that the storage device 12 may be configured by combining multiple types of recording media. Alternatively, a portable recording medium detachable from the computer 10 or an external recording medium (for example, online storage) with which the computer 10 can communicate via a communication network may be used as the storage device 12 .

The performance information output device 13 outputs performance information necessary for generating musical tone signals. The necessary performance information includes, for example, information specifying the generation start to end of the musical tone signal, information indicating the pitch of the musical tone signal to be generated, information indicating the magnitude (volume) of the musical tone signal to be generated, and the like. The performance information output device 13 includes a keyboard device 130 for outputting such performance information.
The keyboard device 130 corresponds to a keyboard of an electronic piano or the like, and has a keyboard on which a plurality of keys (black keys 131b and white keys 131w) are arranged. Keys 131b and 131w in the keyboard device 130 also include a key position sensor 132a that outputs information representing the amount of depression of each key when each key is pressed, and a key speed sensor 132a that outputs information representing the key pressing speed. 132b is provided.

The keyboard device 130 periodically outputs the amount of key depression, key depression speed, and information indicating the depressed key (for example, the key number) to the control device 11 via the bus B in a digital format at sampling intervals. .
The pressure exerted by the oral cavity Oc on the sound source Lp is calculated in the control device 11 based on the information indicating the amount of key depression or the information indicating the key depression speed output from the keyboard device 130 . As for the key depression speed, the key speed sensor 132b can be dispensed with by differentiating the key depression amount. Further, with respect to the key depression speed, if the key depression amount is differentiated, the key speed sensor 132b can be dispensed with. The information output from the keyboard device 130 may include information indicating the acceleration of key depression.

Since musical tones are generated by key depression, the information specifying the start of generation of musical tone signals can be obtained from the key depression speed information and the key depression amount information. Since the end of the musical tone is caused by releasing the key, the information designating the end of the generation of the musical tone signal can be obtained from the information indicating the pressing amount at the time of releasing the key.
The information indicating the pitch of the musical sound signal to be generated is information indicating the pressed key, and the information indicating the magnitude of the musical sound signal to be generated is information indicating the pressure exerted by the oral cavity Oc on the sound source Lp. .

Based on the information output from the keyboard device 130 and the information obtained by performing calculations on the information in this way, it is possible to obtain performance information necessary for generating musical tone signals.

The sound emitting device 14 reproduces sound according to instructions from the control device 11 . For example, speakers or headphones are typical examples of the sound emitting device 14 .
A display device, an operation panel device, and the like are also provided as the computer 10, but they are omitted because they are not important in this case.

FIG. 3 is a block diagram illustrating the functional configuration of the control device 11. As shown in FIG. The control device 11 executes a program stored in the storage device 12 to control a plurality of elements (processing control section 110, preprocessing section 111, musical instrument motion calculation section 112, and musical sound signal calculation section) for synthesizing a musical tone signal. ).
Note that a part of the functions of the control device 11 may be borne by another device, for example, a server device connected via a network.

Next, the procedure up to synthesizing the musical tone signal in the computer 10 will be explained.
FIG. 4 is a flow chart illustrating the procedure of tone signal synthesizing processing.

The processing control unit 110 in the computer 10 causes the preprocessing unit 111 to execute the processing from step S11 to step S14 to determine the modal parameters of the general viscous damping system model representing the linear coupled system Lc. Note that the processing from step S11 to step S14 is referred to as preprocessing because it is executed before the musical tone signal is calculated according to the performance information.

First, the preprocessing unit 111 creates a three-dimensional finite element model of the main body Bd after considering the three-dimensional orthogonal anisotropy of the elastic modulus and the hysteresis damping coefficient of the material constituting the main body Bd. A mass matrix, damping matrix and stiffness matrix are calculated (step S11).
The preprocessing unit 111 uses the mass matrix and the stiffness matrix calculated in step S11 as inputs to perform the three-dimensional finite element model of the main body Bd when the three-dimensional finite element model exists in a vacuum, that is, when air does not exist. Real eigenvalues and real eigenmodes of the element model are calculated by eigenvalue analysis (step S12).
The preprocessing unit 111 receives as input the damping matrix calculated in step S11 and the real eigenmode calculated in step S12, and calculates the modal damping matrix when the three-dimensional finite element model of the main body Bd exists in a vacuum ( step S13).

Next, the preprocessing unit 111 models the linear coupled system Lc as a general viscous damping system model, inputs the real eigenvalues and real eigenmodes calculated in step S12, and the modal damping matrix calculated in step S13, Modal parameters (complex eigenvalues and complex eigenmodes) of the general viscous damping system model are identified as follows (step S14).

FIG. 5 is a flowchart illustrating in detail the procedure of step S14 in FIG.
The preprocessing unit 111 receives as inputs the real eigenvalues, real eigenmodes, and modal damping matrix of the body in vacuum calculated in the processes up to step S13, and calculates the frequency response of the linear coupled system Lc by, for example, a fast multiple boundary method (Fast Multipole Boundary Element Method) or the finite element method (step S141).
The frequency responses calculated in this analysis are of the following two types, and are denoted as frequency response (a) and frequency response (b) in the sense of distinguishing between the two types. Of the two types, the first frequency response (a) is the Fourier transform of the input, that is, the flow rate at the interface between the source Lp and the linear coupled system Lc, and the output, that is, the source Lp and the linear coupled system Lc. It is obtained by dividing the Fourier transform of "the pressure at the interface with the synthetic system Lc".

Here, let the total number of excitation points i be m and the total number of response points 1 be n. Assume that the set of response points l includes the set of excitation points i.
Of the two types of frequency responses, the second frequency response (b) is the Fourier transform of the input, that is, the "flow rate at the interface between the source Lp and the linearly coupled system Lc", and the output, that is, the "flow in the air It is obtained by dividing the Fourier transform of "sound pressure at an arbitrary observation point".

The preprocessing unit 111 calculates the complex eigenvalue λ _r (=−σ _r +jω _dr ) in the linear coupled system Lc by using the calculated inverse fast Fourier transform of the frequency response (a) as a reference, for example, ESPRIT ( (Estimation of Signal Parameters via Rotational Invariance Techniques) (step S142). In identifying the complex eigenvalue, for example, the self-impulse response at the point m is referred to. For identification of complex eigenvalues, the Prony method may be used, but the identification accuracy tends to be inferior to that of ESPRIT.

The preprocessing unit 111 uses the frequency response (a) as a reference to identify the complex eigenmode at the excitation point i of the linear coupled system Lc using the nonlinear optimization method (step S143). Examples of non-linear optimization methods are the quasi-Newton method (with line search method) using the BFGS algorithm (Broyden Fletcher Goldfarb Shanno algorithm), or the modified Gauss-Newton method with trust region method (also called Levenberg-Marquardt method). ). Specifically, the real part and imaginary part of the complex eigenmode at the excitation point i are represented by x _ri and y _ri in the first term on the right side of Equation (5) described later. In identifying the complex eigenmode at the excitation point i, the self and mutual frequency responses at, for example, m·(m+1)/2 points are referred to.

The preprocessing unit 111 uses the frequency response (a) as a reference to identify the complex eigenmode at the response point l other than the excitation point i in the linear coupled system Lc using the linear optimization method (step S144). Examples of linear optimization methods include the QR decomposition method or the singular value decomposition method. Specifically, the real part and imaginary part of the complex eigenmode at the response point l are represented by x _rl and y _rl in the first term on the right side of Equation (5) described later. In identifying the complex eigenmode at the response point l, for example, the mutual frequency response at the m·(nm) point is referred to.
Note that if the scale of the linear coupled system Lc is not so large, or if there are not so many points at which the eigenmodes are desired to be output, the calculation cost of the frequency response analysis in step S141 will not be so large. good. In this case, step S144 is skipped.

Modal parameters (complex eigenvalues and complex eigenmodes) of a general viscous damping system model representing a linear coupled system are identified through steps S141 to S144, and first-order IIR filter coefficients are obtained.

Identification will be described with reference to the following equations (4) and (5).

Identification means that the left side of equation (5) is expressed as a residual obtained by subtracting the second term of the right side, the “frequency response of the reference”, from the first term of the right side, the “frequency response resynthesized using the model”. Secondly, as shown in the right side of the equation (4), the value (real part, imaginary part) that minimizes the sum of squares of the residuals is obtained.

Once the modal parameters of the general viscous damping system model have been identified by the preprocessing unit 111, preparations for synthesizing tone signals according to performance information are complete. Therefore, when the performance information is output from the performance information output device 13, the processing control section 110 causes the musical instrument movement calculation section 112 to execute the processing of step S15, and then causes the musical instrument movement calculation section 112 to perform the processing of step S15. The process of step S16 is executed.

Based on the performance information output from the performance information output device 13, the musical instrument motion calculator 112 provides first information indicating oral pressure (1), second information indicating displacement (2), and flow rate (3). The third information and the fourth information indicating the pressure (4) are calculated (step S15).
It should be noted that there are "physical parameters" and "performance information" as inputs for musical instrument movement calculation in step S15. Among these, the "physical parameters" include "modal parameters (complex eigenvalues, complex eigenmodes) of the linear coupled system Lc". "Physical parameters" include "physical parameters of lips (or reeds)" and the like, but they are omitted in FIG.
The 'performance information' may be real-time data obtained from 'keyboard sensing', or may be recorded MIDI data. Note that the MIDI data is data of performance information conforming to the MIDI (Musical Instrument Digital Interface) standard.
Further, in calculating the first information indicating the intraoral pressure (1), the second information indicating the displacement (2), the third information indicating the flow rate (3), and the fourth information indicating the pressure (4), The technique described in Patent Literature 1 can be used in consideration of the law of conservation of energy in fluid dynamics, that is, Bernoulli's theorem. Specifically, the musical instrument motion calculation unit 112 sequentially and numerically solves simultaneous nonlinear algebraic equations on the discrete time axis in which the displacement of the sound source and the pressure on the mode coordinates in the linear coupled system are unknown. .

The musical tone signal calculator 113 calculates a musical tone signal by high-speed convolution of the third information indicating the flow rate (3) calculated in step S15 and the frequency response (b) (step S16).

In this embodiment, when the modal parameters of the general viscous damping system model are identified in step S14, the complex number filter coefficients of the first-order IIR necessary for calculating the fourth information indicating the pressure (4) are determined. By using this coefficient, step S15 can be calculated sequentially at low cost and with high accuracy. It can be calculated sequentially.
Therefore, in the present embodiment, it is possible to synthesize high-quality and realistic musical tone signals while keeping the calculation cost low.

Next, the extent to which the modal parameters identified in the general viscous damping system model in this embodiment approach the reference will be described.

6 to 8 are diagrams showing frequency responses (marked with circles) by mode synthesis with respect to frequency responses (solid lines) used as a reference at three different points (points 1 to 3). 6 to 8, the phase and amplitude versus frequency characteristics are shown in the left column, and the real and imaginary part versus frequency characteristics are shown in the right column, respectively.
As shown in FIGS. 6 to 8, the frequency response obtained by mode synthesis almost matches the reference frequency response, and it can be seen that the identification is established with high accuracy.

9 to 11 are diagrams showing the impulse responses (marked with circles) by mode synthesis with respect to the impulse responses (solid lines) as IFFT of the reference frequency responses at the above three points (points 1 to 3). .
As shown in FIGS. 9 to 11, the impulse response obtained by mode synthesis almost matches the reference impulse response, and it can be seen that the identification is established with high accuracy.

<Modification>
The embodiments illustrated above can be variously modified. Specific modification aspects that can be applied to the embodiments are exemplified below. Two or more aspects arbitrarily selected from the following examples may be combined as long as they do not contradict each other.

The function of the computer 10 for synthesizing musical tone signals is realized by cooperation between one or more processors constituting the control device 11 and programs stored in the storage device 12, as described above.
This program can be provided in a form stored in a recording medium readable by the computer 10 and installed in the computer. The recording medium is, for example, a non-transitory recording medium, and a good example is an optical recording medium (optical disc) such as a CD-ROM. Also included are recording media in the form of It should be noted that the non-transitory recording medium includes any recording medium other than transitory, propagating signals, and does not exclude volatile recording media. In addition, in a configuration in which a distribution device distributes a program via a communication network, the storage device 12 that stores the program in the distribution device corresponds to the above-described non-transitory recording medium.

In the computer 10 described above, musical tone signals are synthesized in real time according to the performance operation to the performance information output device 13, but the musical tone signals may be synthesized in non-real time. Specifically, as in the embodiment, a musical tone signal synthesized by a physical model is sampled and recorded by PCM (Pulse Code Modulation), and the recorded signal is played back according to performance information to reproduce the musical tone signal. It is good also as composition composition.
Conventional sampling recording requires a lot of work and man-hours, such as playing acoustic instruments and setting up microphones. Since the work of recording can be done by calculation on the computer 10, it is possible to greatly reduce the labor of the work.
Also, with conventional sampling, unnecessary noise (mechanical noise) is recorded along with the musical sound, so it is necessary to remove these noises in the post-processing. On the other hand, in a configuration in which musical tone signals synthesized by a physical model are sampled by PCM and recorded, it is possible to record musical tones that do not contain unnecessary noise.

The control device 11, which is the substantial main body for synthesizing musical tone signals, may be arranged in a cloud separately from the performance information output device 13 and the sound emitting device 14, which output performance information. Specifically, the specifications of the musical tone desired by the user are transmitted to a computer including the control device 11 located in the cloud, and the computer synthesizes the musical tone signal by simulation using an elaborate physical model that satisfies the above specifications, It may be configured to be provided to the user. When synthesizing a musical tone signal by simulation using a physical model, since the position of the microphone M (speaker) is arbitrary, it is possible to synthesize a musical tone signal that matches the playback device of the user receiving the service. For example, even with a special reproduction device such as a 16-channel speaker reproduction device, it is possible to synthesize musical tone signals in accordance with the special reproduction device.
In this way, according to the configuration in which the computer arranged in the cloud synthesizes the musical tone signal of the specification desired by the user, the musical tone signal customized according to the user's request is provided to the user. becomes possible.

Synthesis of musical sound signals by simulation using a physical model may be used to support the design of acoustic musical instruments. Specifically, by changing the design of the physical model and synthesizing the musical sound signal using the changed physical model, the musical sound of the pre-prototype musical instrument can be listened to through simulation. Therefore, for example, new musical instruments can be efficiently developed. Synthesizing a musical sound signal by simulation using a physical model in this way clarifies the causal relationship between the specifications (cause) of the acoustic musical instrument and the generated musical sound (result), thereby improving the design efficiency of the musical instrument. becomes possible.
Also, various error factors can be involved in manufacturing an acoustic instrument, such as variations in materials and manufacturing. On the other hand, a simulation using a physical model can eliminate the above error factors.

<Appendix>
From the above description, for example, the following preferred embodiments of the present invention are understood. In order to facilitate understanding of each aspect, hereinafter, reference numerals in the drawings are written together in parentheses for the sake of convenience, but this is not intended to limit the present invention to the illustrated aspects.

In the musical sound signal synthesizing method according to one aspect (aspect 1) of the present disclosure, the sound source (Lp) and the air (Ar) interact, and the air (Ar) and the main body (Bd) interact. a musical sound signal synthesizing method in which a computer (10) synthesizes a musical sound signal indicating a sound pressure at an arbitrary observation point (Mc) in air (Ar) according to performance information, the computer (10 ) according to the performance information, the first information indicating the pressure exerted by the oral cavity (Oc) on the sound source (Lp), the second information indicating the displacement of the sound source (Lp), and the sound source (Lp) being air Third information indicating the flow rate acting on the linear coupled system (Lc) consisting of (Ar) and the body (Bd), and fourth information indicating the pressure exerted by the linear coupled system (Lc) on the source (Lp) and a musical sound signal calculation process (step S16) in which the computer (10) calculates the sound pressure at the observation point (Mc) based on the third information, The linear coupled system (Lc) is represented by a general viscous damping system model, and the complex eigenvalues and complex eigenmodes, which are the modal parameters of the general viscous damping system model, are the frequency response or frequency response of the linear coupled system (Lc). is identified as a reference, and the fourth information is calculated using the complex eigenvalues and complex eigenmodes.
According to this aspect 1, since the mode synthesis method can be applied to the time domain simulation of the linear coupled system (Lc), it is possible to synthesize high-quality and realistic musical tone signals while keeping the calculation cost low.

In the specific example of aspect 1 (aspect 2), the displacement (2) should be replaced by the derivative of the displacement with respect to time. Also in mode 2, high-quality and realistic musical tone signals can be synthesized at a low calculation cost.

In a specific example of Aspect 1 or Aspect 2 (Aspect 3), the identification of modal parameters is performed by the computer (10) as preprocessing for calculation. According to mode 3, it is possible to keep the calculation cost low when executing the musical tone signal calculation process (step S16).

In any specific example of Aspects 1 to 3 (Aspect 4), the identification of the modal parameters includes a first step in which the computer (10) calculates the frequency response of the linear coupled system (Lc), and a computer (10) , a second step of identifying complex eigenvalues using the inverse Fourier transform of the frequency response as a reference, and a computer (10) using the frequency response as a reference to identify the complex eigenmode of the excitation point in the linear coupled system (Lc) and a third step of performing.
According to aspect 4, the identification of complex eigenvalues and the identification of complex eigenmodes are performed separately rather than simultaneously. Therefore, it can be easily applied to a coupled system of the main body and air by increasing the number of excitation points.

In the specific example of aspect 4 (aspect 5), after the third process, the computer (10) uses the frequency response as a reference to generate a complex eigenmode of a response point different from the excitation point in the linear coupled system (Lc) and a fourth step of identifying.
According to aspect 5, the identification of complex eigenvalues and the identification of complex eigenmodes are performed separately rather than simultaneously. Therefore, it can be easily applied to a coupled system of the main body and air by providing a large number of excitation points and response points.

Also, the musical tone signal synthesizing method according to aspect 1 can be grasped as the following program. That is, the program according to aspect 6 causes the computer (10) to A program for synthesizing a musical sound signal indicating the sound pressure at an arbitrary observation point (Mc) in the air in accordance with performance information, wherein a computer (10) instructs a computer (10) to produce sound from an oral cavity (Oc) in accordance with performance information. A first information indicating the pressure exerted on the source (Lp), a second information indicating the displacement of the source (Lp), and a linearly coupled system in which the source (Lp) consists of air (Ar) and body (Bd). a musical instrument motion calculator (112) for calculating third information indicating the flow rate exerted on (Lc) and fourth information indicating the pressure exerted by the linear coupled system (Lc) on the sound source (Lp); 3 functions as a musical sound signal calculator (113) for calculating the sound pressure at the observation point (Mc) based on the information, and the linear coupled system (Lc) is represented by a general viscous damping system model, and the general viscous damping The complex eigenvalues and complex eigenmodes, which are the modal parameters of the system model, are identified with reference to the frequency response of the linear coupled system (Lc) or the inverse Fourier transform of the frequency response, and the fourth information is the complex eigenvalues and complex eigenmodes. calculated using

It should be noted that the musical tone signal synthesizing method according to aspect 1 can be understood as a musical tone signal synthesizing apparatus as follows. That is, in the musical sound signal synthesizer according to aspect 7, the computer (10 ) is a musical sound signal synthesizing device for synthesizing a musical sound signal indicating the sound pressure at an arbitrary observation point (Mc) in the air according to performance information, and the oral cavity (Oc) produces a sound according to the performance information. A first information indicating the pressure exerted on the source (Lp), a second information indicating the displacement of the source (Lp), and a linearly coupled system in which the source (Lp) consists of air (Ar) and body (Bd). (Lc) and the fourth information indicating the pressure exerted by the linear coupled system (Lc) on the sound source (Lp); a computer ( 10) includes a musical sound signal calculator (113) for calculating the sound pressure at the observation point (Mc) based on the third information, and the linear coupled system (Lc) is represented by a general viscous damping system model. , the complex eigenvalues and complex eigenmodes, which are the modal parameters of the general viscous damping system model, are identified with reference to the frequency response of the linear coupled system (Lc) or the inverse Fourier transform of the frequency response, and the fourth information is the complex eigenvalues and complex eigenmodes.

DESCRIPTION OF SYMBOLS 10... Computer 11... Control device 12... Storage device 13... Performance information output device 14... Sound emission device 110... Processing control part 111... Pre-processing part 112... Musical instrument motion calculation part 113... Musical sound signal Calculation part, Oc... oral cavity, Lp... source of sound (lip or reed), Bd... main body, Ar... air, Lc... linear coupled system.

Claims (7)

When the source and the air interact, and the air and the body interact,
the computer
A musical sound signal synthesizing method for synthesizing a musical sound signal indicating a sound pressure at an arbitrary observation point in the air according to performance information,
According to the performance information, the computer
first information indicating the pressure exerted by the oral cavity on the sound source;
second information indicating the displacement of the sound source;
third information indicating the flow rate of the sound source to a linearly coupled system composed of the air and the body;
fourth information indicating the pressure exerted by the linear coupled system on the sound source;
a musical instrument motion calculation process for calculating
a musical sound signal calculation process in which the computer calculates the sound pressure at the observation point based on the third information;
including
The linear coupled system is represented by a general viscous damping system model,
The complex eigenvalues and complex eigenmodes, which are modal parameters of the general viscous damping system model, are identified with reference to the frequency response of the linear coupled system or the inverse Fourier transform of the frequency response,
The fourth information is calculated using the complex eigenvalue and the complex eigenmode.
2. The method of synthesizing a musical tone signal according to claim 1, wherein said displacement is replaced by a derivative with respect to time of said displacement.
The identification of the modal parameters includes:
3. The method of synthesizing a musical tone signal according to claim 1, wherein said computer executes preprocessing for calculation.
The identification of the modal parameters includes:
a first step in which the computer calculates a frequency response of the linear coupled system;
a second step in which the computer identifies the complex eigenvalues using the inverse Fourier transform of the frequency response as a reference;
a third step in which the computer identifies a complex eigenmode of the excitation point in the linearly coupled system using the frequency response as a reference;
4. The musical tone signal synthesizing method according to any one of claims 1 to 3, comprising:
After the third step,
a fourth step in which the computer identifies a complex eigenmode at a response point different from the excitation point in the linear coupled system, using the frequency response as a reference;
5. The musical tone signal synthesizing method according to claim 4, comprising:
When the source and the air interact, and the air and the body interact,
the computer
A program for synthesizing a musical sound signal indicating sound pressure at an arbitrary observation point in the air according to performance information,
According to the performance information, the computer
first information indicating the pressure exerted by the oral cavity on the sound source;
second information indicating the displacement of the sound source;
third information indicating the flow rate of the sound source to a linearly coupled system composed of the air and the body;
fourth information indicating the pressure exerted by the linear coupled system on the sound source;
a musical instrument motion calculation process for calculating
a musical sound signal calculation process in which the computer calculates the sound pressure at the observation point based on the third information;
including
The linear coupled system is represented by a general viscous damping system model,
The complex eigenvalues and complex eigenmodes, which are modal parameters of the general viscous damping system model, are identified with reference to the frequency response of the linear coupled system or the inverse Fourier transform of the frequency response,
The program, wherein the fourth information is calculated using the complex eigenvalue and the complex eigenmode.
When the source and the air interact, and the air and the body interact,
the computer
A musical sound signal synthesizing device for synthesizing a musical sound signal indicating sound pressure at an arbitrary observation point in the air according to performance information,
According to the performance information, the computer
first information indicating the pressure exerted by the oral cavity on the sound source;
second information indicating the displacement of the sound source;
third information indicating the flow rate of the sound source to a linearly coupled system composed of the air and the body;
fourth information indicating the pressure exerted by the linear coupled system on the sound source;
a musical instrument motion calculation process for calculating
a musical sound signal calculation process in which the computer calculates the sound pressure at the observation point based on the third information;
including
The linear coupled system is represented by a general viscous damping system model,
The complex eigenvalues and complex eigenmodes, which are modal parameters of the general viscous damping system model, are identified with reference to the frequency response of the linear coupled system or the inverse Fourier transform of the frequency response,
The fourth information is calculated using the complex eigenvalue and the complex eigenmode. A musical sound signal synthesizing device.

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