JP5182484B2 - Music synthesizer and program - Google Patents

Description

  The present invention relates to a technique for synthesizing musical sounds of wind instruments.

2. Description of the Related Art Conventionally, a physical model type musical sound synthesizer (physical model sound source) that synthesizes musical sounds by simulating the principle of musical instrument pronunciation has been proposed. For example, a technology that simulates the behavior of the clarinet after modeling the reed as a rigid air valve that moves freely as a whole (Non-Patent Document 1), or a long-plate-like vibrating body with one end fixed ( A technique (Non-Patent Document 2) that simulates the behavior of a clarinet after modeling a lead with a cantilever beam) has been proposed. Non-Patent Document 3 discloses a technique for reflecting the action of the performer's lips at the time of playing in the behavior of the lead.
RTSchumacher, "Ab Initio Calculations of the Oscillations of a Clarinet", ACUSTICA, 1981, Volume 48 No.2, p.75-p.85 SDSommerfeldt, WJStrong, "Simulation of a player-clarinet system", Acoustical Society of America, 1988, 83 (5), p.1908- p.1918 Isao Miyaji and Yoshimitsu Takasawa, “Lead vibration analysis in clarinet”, Acoustical Society of Japan Acoustical Society, MA00-17, p.3- p.10

  By the way, the elastic value (for example, bending rigidity and spring constant) of the lead of an actual wind instrument varies nonlinearly according to the strength of the external force acting on the lead from the lips and the position in the longitudinal direction of the lead. Further, the elastic value of the performer's lips varies nonlinearly according to the strength of the external force acting on the performer's teeth and leads and the position on the lips. However, none of Non-Patent Document 1 to Non-Patent Document 3 simulates a non-linear change in the elastic value of the lead or lips. Therefore, the behavior of the lead is not faithfully reproduced, and it is difficult to synthesize a musical tone that is sufficiently close to that of an actual wind instrument. In view of the above circumstances, an object of the present invention is to synthesize a faithful musical sound that reflects a non-linear change in the elasticity value of a wind instrument lead or a player's lips.

In order to solve the above problems, a musical tone synthesizing apparatus according to the present invention, the elasticity of the position of the lead so as to vary non-linearly with the position of the longitudinal direction of the wind instrument of the lead (e.g., a position x in Fig. 6) Based on a plurality of variables in accordance with the first specifying means (for example, the specifying part 22B in FIG. 6 and the specifying part 22C in FIG. 11) for specifying (for example, the spring constant and bending rigidity) and the elastic value specified by the first specifying means. Musical tone synthesizing means for synthesizing the musical tone of the wind instrument (for example, the synthesizing unit 14 in FIG. 1). In the above configuration, since the elasticity value of the lead used for synthesizing the musical tone is specified so as to change nonlinearly according to the position in the longitudinal direction of the lead, it is compared with the configuration in which the elasticity value of the lead is fixed. Thus, it is possible to faithfully reproduce the actual sound of a wind instrument.

  In a specific aspect of the present invention, the relationship between the first input value and the elastic value specified by the first specifying means is set based on the actually measured value. According to the above aspect, since the relationship between the first input value and the elastic value is set based on the actually measured value, it is possible to bring the musical sound synthesized by the musical tone synthesizing means closer to the actual musical tone of a wind instrument.

  The musical tone synthesizer according to a preferred aspect of the present invention is a selection unit that selects one of a plurality of types of relationships set for the first input value and the elastic value specified by the first specifying unit (for example, the selection shown in FIG. 13). The first specifying means specifies the elasticity value of the lead corresponding to the first input value in the relationship selected by the selection means. According to the above aspect, since the relationship between the first input value and the elastic value is selected from among a plurality of candidates and used for specifying the elastic value by the first specifying means, the first input value and the elastic value are used. It is possible to synthesize a variety of musical sounds as compared with a configuration in which the relationship with values is fixed.

  The musical tone synthesizer according to a preferred aspect of the present invention is a control means (for example, FIG. 14) that variably controls the relationship between the first input value and the elastic value specified by the first specifying means in accordance with an instruction from the user. A control unit 24). According to the above aspect, since the relationship between the first input value and the elasticity value is variably controlled in accordance with an instruction from the user, it is compared with the configuration in which the relationship between the first input value and the elasticity value is fixed. Thus, it is possible to synthesize various musical sounds while reflecting the user's intention.

Tone synthesis apparatus according to a preferred embodiment of the present invention, each position of the lips so as to vary non-linearly with longitudinal position of the lead in the player's lips in contact with the lead (e.g., a position x in Fig. 6) The second specifying means (for example, the specifying unit 22A in FIG. 6) for specifying the elastic value (for example, the spring constant) of the musical tone synthesizing means includes the lead elastic value specified by the first specifying means and the second specifying means. A musical tone is synthesized based on a plurality of variables according to the specified elasticity value of the lips. According to the above aspect, since the elasticity value of the lips is variably set so as to change nonlinearly according to the position of the lips in the longitudinal direction of the lead , compared to the configuration in which the elasticity value of the lips is fixed, It is possible to faithfully reproduce the actual sound of a wind instrument.

  Note that each aspect described above with respect to the first specifying means is similarly applied to the second specifying means. For example, in a preferred aspect of the present invention, the relationship between the second input value and the elastic value specified by the second specifying means is set based on the actually measured value. Further, in the musical sound synthesizer including a selection unit that selects any of a plurality of types of relationships set for the second input value and the elastic value specified by the second specification unit, the second specification unit includes: The elasticity value of the lead corresponding to the second input value in the selected relationship is specified. Furthermore, a configuration including a control unit that variably controls the relationship between the second input value and the elastic value specified by the second specifying unit according to an instruction from the user is also preferable.

  In a preferred aspect of the present invention, the tone synthesis means is a means for synthesizing the tone of a wind instrument that is pronounced in response to the vibration of the lead that contacts the lips during playing, and the behavior of the lead at the time of equilibrium when an external force acts on the lips. Lip displacement and lead displacement at equilibrium by solving a first equation of motion (eg, equation A1 in FIG. 4) and a second equation of motion (eg, equation A2 in FIG. 4) representing lip behavior at equilibrium. The first calculation means for calculating the lip and the calculation result by the first calculation means are used as the initial values of the lip displacement and the lead displacement to solve the equation of motion of the lip-lead vibration (for example, the equation B in FIG. 4). Thus, a musical tone is synthesized based on the displacement calculated by the second calculation means. In the above configuration, the displacement of the lead is calculated based on the equation of motion of the coupled vibration between the lips and the lead. Compared with the configuration in which the displacement of the lead is calculated based on the equation of motion that does not reflect the behavior of the lips. Thus, the behavior of the lead is accurately simulated. Therefore, it is possible to faithfully reproduce the actual tone of a wind instrument.

The musical tone synthesizer according to the present invention is realized by hardware (electronic circuit) such as a DSP (Digital Signal Processor) dedicated to each processing, and a general-purpose arithmetic processing device such as a CPU (Central Processing Unit) and a program It is also realized through collaboration with. Program according to the present invention includes a first identification processing for identifying the elasticity of the position of the lead so as to vary non-linearly with longitudinal position of the wind instrument of the lead, the elasticity value identified in the first specific treatment A computer is caused to execute a musical tone synthesis process for synthesizing musical tones of a wind instrument based on a plurality of variables. With the above program, the same operations and effects as the musical tone synthesizer according to the present invention are exhibited. The program of the present invention is provided to the user in a form stored in a computer-readable recording medium and installed in the computer, or is provided in a form distributed via a communication network and installed in the computer. The

  A musical tone synthesizer according to another aspect of the present invention is a device for synthesizing a musical tone of a wind instrument that generates sound in response to vibration of a lead, and the displacement of the lead at the time of equilibrium when an external force is applied to the elastic value of the lead. First calculating means for specifying the non-linear change, and second calculating means for calculating the lead displacement by solving the equation of motion of the lead using the displacement specified by the first calculating means as an initial value of the lead displacement, And a musical tone is synthesized based on the displacement calculated by the second calculation means. According to the above aspect, since the state in which the lead displacement changes nonlinearly with respect to the elastic value when the lead is operated outside the range of the proportional limit, the musical tone of the actual wind instrument can be faithfully reproduced. Is possible. A program for realizing a musical tone synthesizer according to the above aspect is a program for synthesizing a musical tone of a wind instrument that is pronounced in response to vibration of a lead. A first calculation process that identifies the values so as to change nonlinearly, and a second calculation that calculates the lead displacement by solving the equation of motion of the lead using the displacement specified by the first calculation process as an initial value of the displacement of the lead. Causes the computer to execute arithmetic processing.

  A musical tone synthesizer according to another aspect of the present invention is a device that synthesizes the musical sound of a wind instrument that is pronounced in response to the vibration of a lead that comes into contact with the lips during blowing, and the displacement of the lips at the time of equilibrium when an external force is applied. First motion means for specifying non-linear change with respect to the elasticity value of the lips, and solving the equation of motion of the coupled vibration between the lips and the reed with the displacement specified by the first calculation means as the initial value of the lip displacement Thus, a second calculation means for calculating the displacement of the lead is provided, and a musical tone is synthesized based on the displacement calculated by the second calculation means. According to the above aspect, when the lips move outside the range of the proportional limit, it is simulated that the displacement of the lips changes nonlinearly with respect to the elastic value, so that the actual musical tone of a wind instrument can be faithfully reproduced. Is possible. A program for realizing a musical tone synthesizer according to the above aspect is a program for synthesizing a musical tone of a wind instrument that is pronounced in response to the vibration of a lead that comes into contact with the lips at the time of blowing, and is a program for synthesizing a lip at the time of equilibrium when an external force is applied. The first calculation process for specifying the displacement so as to change nonlinearly with respect to the elasticity value of the lips, and the movement of the combined vibration between the lips and the reed with the displacement specified by the first calculation process as the initial value of the lip displacement The computer is caused to execute a second calculation process for calculating the displacement of the lead by solving the equation.

<A: First Embodiment>
FIG. 1 is a block diagram showing the configuration of a musical tone synthesis apparatus according to the first embodiment of the present invention. The musical tone synthesizer 100 of this embodiment synthesizes musical sounds by simulating (simulating) the sound generation principle of a single-lead wind instrument such as a saxophone or a clarinet. As shown in FIG. 1, the musical sound synthesizing device 100 is realized by a computer system including an arithmetic processing device 10, a storage device 42, an input device 44, and a sound emitting device 46.

  An arithmetic processing unit (for example, CPU (Central Processing Unit)) 10 generates musical tone data representing a time waveform (temporal fluctuation of sound pressure) of a musical tone of a wind instrument by executing a program stored in the storage device 42. And output. The storage device 42 stores a program executed by the arithmetic processing device 10 and data used by the arithmetic processing device 10. A known storage medium such as a magnetic storage device or a semiconductor storage device is arbitrarily adopted as the storage device 42.

  The input device 44 includes a plurality of operators that are operated by the user. The user can instruct the arithmetic processing device 10 from the input device 44 with various parameters used for the synthesis of musical sounds. An input device such as a keyboard or a mouse or a musical instrument type input device (for example, a MIDI (Musical Instrument Digital Interface) controller) for inputting information related to the performance of a wind instrument is employed as the input device 44.

  The sound emitting device 46 emits a sound wave corresponding to the musical sound data output from the arithmetic processing device 10. In practice, a D / A converter for converting the musical sound data into an analog musical sound signal and an amplifier for amplifying the musical sound signal and outputting it to the sound output device 46 are installed. In FIG. Further, the illustration of the amplifier is omitted.

  The arithmetic processing device 10 in FIG. 1 functions as the setting unit 12 and the combining unit 14. A configuration in which each function of the arithmetic processing unit 10 is realized in a distributed manner by a plurality of integrated circuits is also employed. Also, some of the functions of the arithmetic processing unit 10 may be realized by an electronic circuit (DSP) dedicated to the synthesis of musical sounds.

  The setting unit 12 sets parameters necessary for the synthesis of musical sounds. The synthesizer 14 generates musical sound data based on the parameters set by the setting unit 12. The synthesis unit 14 includes a lead simulation unit 31 and a tube simulation unit 33. The lead simulating unit 31 simulates the coupled vibration between the player's lips and the lead. The tubular body simulation unit 33 responds to the action of the tubular part from the mouthpiece to the bell of the wind instrument (that is, the part other than the lead, hereinafter referred to as the “tube part”) and the sound emitted from the bell and each tone hole. Simulates imparting transfer characteristics.

  FIG. 2 is a conceptual diagram showing the vicinity of the lead of the wind instrument simulated by the lead simulation unit 31. The lead MR is a long plate-like vibrating body whose one end is fixed to the mouthpiece MP. As shown in FIG. 2, the X axis, the Y axis, and the Z axis are assumed with the center in the width direction at the tip of the lead MR as the origin. The Z axis extends in the width direction of the lead MR. The X-axis is orthogonal to the Z-axis in the upper surface of the lead MR (the surface facing the mouthpiece MP) when no external force is applied. The Y axis is orthogonal to the X axis and the Z axis (extends in the vertical direction with respect to the lead MR).

  FIG. 3 is a schematic view of the player's lips ML in contact with the lead MR when the wind instrument is played from the Z direction. As shown in FIG. 3, the reed simulating unit 31 simulates a state in which the performer presses the lips ML against the reed MR with the teeth MT when the wind instrument is played. The lip ML contacts a section of the lead MR from the position xlip1 (leading end side of the lead MR) in the X direction to the position xlip2 (base side of the lead MR). Further, the performer's teeth MT are in contact with the section from the position xteeth1 (the leading end side of the lead MR) to the position xteeth2 (the root side of the lead MR) in the X direction on the lower surface of the lip ML, and the pressing force flip (x) Work equally.

  FIG. 4 is a block diagram illustrating functions of the lead simulation unit 31. On the left side of FIG. 4, parameters set by the setting unit 12 and stored in the storage device 42 are listed. The meaning of each parameter will be described below.

First, parameters (Stiff (x), breed (x), A (x), μreed (x), ρreed) related to the lead MR will be described. Stiff (x) is the bending stiffness [N · m ² ] of the lead MR at the position x in the X direction. That is, the bending stiffness Stiff (x) corresponds to a product of the Young's modulus Ereed [Pa] of the lead MR and the cross-sectional secondary moment I (x) [m ⁴ ] of the lead MR at the position x. As shown in FIG. 2, breed (x) is the lateral width (dimension in the Z direction) [m] of the lead MR at the position x, and A (x) is the cross-sectional area (position x of the lead MR at the position x). The area in the YZ plane that passes through) [m ² ]. In this embodiment, the shape of the cross section of the lead MR changes according to the position x in the X direction. Accordingly, the cross-sectional secondary moment I (x), the lateral width breed (x) of the lead MR, and the cross-sectional area A (x) used for calculating the bending stiffness Stiff (x) are functions of the position x. Further, μreed (x) in FIG. 4 is a distribution [(kg / sec) / m] of the internal resistance of the lead MR, and ρreed is a density [kg / m ³ ] of the lead MR.

Next, parameters (klip (x), dlip (x), μlip (x), mlip (x)) related to the lips ML will be described. klip (x) is a spring constant distribution [N / m ² ] in the X direction of the lips ML (for example, a spring constant per unit length in the X direction). dlip (x) is the dimension (thickness) [m] in the Y direction of the lip ML at the position x when no external force is applied. μlip (x) is a distribution [(kg / sec) / m] of the internal resistance of the lip ML at the position x. mlip (x) is a mass distribution [kg / m] (for example, mass per unit length in the X direction) of the lips ML in the X direction. The spring constant distribution klip (x), the thickness dlip (x), the internal resistance distribution μlip (x), and the mass distribution mlip (x) vary according to the position x.

P in FIG. 4 is the pressure [Pa] in the performer's mouth, and ρair is the air density [kg / m ³ ] at room temperature (for example, 25 ° C.). As shown in FIG. 2, H (x) is a position in the Y direction (hereinafter referred to as “facing position”) of the surface of the mouthpiece MP that faces the lead MR. When the displacement y (x, t) in the Y direction of the lead MR reaches the facing position H (x), the upper surface of the lead MR comes into contact with the mouthpiece MP, and the facing position H (x) is the limit value of the displacement of the lead MR. (Lower limit value). Zc is a characteristic impedance against air flow at the start point (the root of the lead MR) of the portion of the mouthpiece MP that can be regarded as a tubular body.

  As shown in FIG. 4, the lead simulation unit 31 includes a first calculation unit 311, a second calculation unit 312, a third calculation unit 313, and a fourth calculation unit 314. The first calculation unit 311 performs the displacement y0 (xf) of the lead MR and the displacement yb of the bottom surface of the lip ML when the pressing force flip (xf) is statically applied to the position xf in the X direction of the lip ML and balanced. Calculate (xf). The second calculation unit 312 uses the displacement y0 (xf) and the displacement yb (xf) calculated by the first calculation unit 311 as the initial values of the displacement of the bottom surfaces of the lead MR and the lip ML (numerical values at t = 0) and the lip ML. By solving the equation of motion of the coupled vibration with the lead MR, the displacement y (x, t) in the Y direction at the time t at each position x of the lead MR in the X direction is calculated. The third calculation unit 313 and the fourth calculation unit 314 calculate the pressure POUT of the sound wave output from the lead MR to the tube body (the mouthpiece MP side) based on the displacement y (x, t) of the lead MR. Details of processing by the lead simulation unit 31 will be described below.

As shown in FIG. 3, a state is assumed in which a pressing force flip (xf) is applied from the tooth MT to the position xf (xteeth1 ≦ xf ≦ xteeth2) of the performer's lip ML. Assuming that the lead MR is deformed by the distance d1 in the Y direction and the lip ML is deformed by the distance d2 in the Y direction by the action of the pressing force flip (xf), the elastic force R1 acting on the lips ML from the lead MR and the lips ML The elastic force R2 acting on the lead MR is expressed by the following equations including the bending rigidity Stiff (xf) of the lead MR and the spring constant klip (xf) of the lip ML. In practice, the upper surface of the lip ML is in contact with the lower surface of the lead MR, but in FIG. 3, it is simplified so that the upper surface of the lip ML is positioned on the upper surface of the lead MR.

From the balance of forces at the contact point (position xf) between the lead MR and the lip ML,
R1-R2 = 0
From the balance of forces at the contact point (position xf) between the lip ML and the tooth MT,
flip (xf) = R2
Is established. Also, from the relationship between deformation and displacement of the lead MR,
d1 = y0 (xf)
From the relationship between deformation and displacement of the lip ML,
d2 = {yb (xf) -dlip (xf)}-y0 (xf)
Is established.

The following equations of motion A1 and equation of motion A2 are derived from the above equations.

  4 substitutes the bending stiffness Stiff (xf), the pressing force flip (xf), the spring constant klip (xf), and the thickness dlip (xf) set by the setting unit 12 to obtain the equation of motion. The displacement yb (xf) of the bottom surface of the lip ML and the displacement y0 (xf) of the lead MR are calculated by solving simultaneous equations of A1 and the equation of motion A2. More specifically, the first calculation unit 311 calculates the displacement y0 (xf) of the lead MR from the equation of motion A1 using a difference equation formula, Gaussian elimination method, etc., and calculates the displacement y0 (xf) of the equation of motion. By substituting for A2, the displacement yb (xf) of the lip ML is calculated. A method for solving the equation of motion A1 will be described later.

The dynamic characteristic when the lip ML and the reed MR are vibrated in combination by playing the wind instrument by the performer is expressed by the following equation of motion B.

  The second calculation unit 312 sets the displacement y0 (xf) calculated by the first calculation unit 311 to the initial value of the displacement y (x, t) of the lead MR in the equation of motion B, and the first calculation unit 311 calculates The displacement y (x, t) of the lead MR is calculated by substituting the displacement yb (xf) into the displacement yb (x) of the lip ML in the equation of motion B and solving the equation of motion B. The right side of the equation of motion B corresponds to the external force fex (x) acting on the position x of the lead MR in the X direction. First, the second calculation unit 312 first sets each parameter (breed (x), P, klip (x), dlip (x)) set by the setting unit 12 and the pressure p (t calculated by the fourth calculation unit 314. ) Is substituted into the right side of the equation of motion B, and the displacement y0 (xf) and the displacement yb (xf) calculated by the first calculation unit 311 are used as the displacement y (x, t) and the displacement yb on the right side of the equation of motion B. The external force fex (x) is calculated by substituting as the initial value of (x). The pressure p (t) means the pressure in the space between the lead MR and the mouthpiece MP in the vicinity of the tip of the lead MR (hereinafter referred to as “directly above the lead”). The calculation of the pressure p (t) by the fourth calculation unit 314 will be described later.

  Second, the second calculation unit 312 uses the equation of motion (mlip (x), A (x), μlip (x), μreed (x), Stiff (x), ρreed) set by the setting unit 12 as an equation of motion. The displacement y (x, t) of the lead MR is calculated by substituting for the left side of B and setting the previously calculated external force fex (x) on the right side of the equation of motion B. A specific method for solving the equation of motion B is illustrated below.

The second term on the left side of the equation of motion B is transformed as follows.

Therefore, the equation of motion B is transformed into the following equation B1.

また、図５に示すように、相互に等しい間隔Δｘをあけて分布するようにＸ方向における位置ｘを離散化する。すなわち、位置ｘを整数ｎと所定値Δｘとの乗算値として離散化（ｘ＝ｎ・Δｘ）したうえで、位置微分を以下の差分に置換する。

なお、以上におけるｙ(n,i)は、ｙ(n・Δx，i・Δt)を略記した記号である。 Next, the time t is discretized as a product of the integer i and a predetermined value Δt (t = i · Δt), and the time derivative is replaced with the following difference.

Further, as shown in FIG. 5, the position x in the X direction is discretized so as to be distributed with an equal interval Δx. That is, the position x is discretized as a product of an integer n and a predetermined value Δx (x = n · Δx), and the position differential is replaced with the following difference.

In the above, y (n, i) is a symbol that abbreviates y (n · Δx, i · Δt).

ただし、式Ｂ2においては各項が以下のように置換されている。

また、式Ｂ2の各文字に付加された記号(n，i)は(n・Δx，i・Δt)の略記である。 Therefore, the equation B1 is expressed as a difference equation as the following equation B2.

However, in the formula B2, each term is substituted as follows.

The symbol (n, i) added to each character of the formula B2 is an abbreviation for (n · Δx, i · Δt).

Next, an equation in which the second item to the fourth item on the left side in Expression B2 are multiplied by 1/2, and i in Expression B2 are replaced with (i + 1), and then the second item to the fourth item on the left side. By adding the equation multiplied by 1/2, an equation B3 that approximates the equation B2 is derived.

ただし、式Ｂ4においては各項が以下のように置換されている。

When the terms of equation B3 are arranged and transformed for each type of variable y, the following equation B4 is derived.

However, in the formula B4, each term is substituted as follows.

さらに、式Ｂ4_1と式Ｂ4_2を加算することで以下の式Ｂ4_3が導出され、式Ｂ4_3の３倍から式Ｂ4_2を減算することで以下の式Ｂ4_4が導出される。
０・ｙ(0,i)＋ｙ(1,i)−２ｙ(2,i)＋ｙ(3,i)＝０ ……Ｂ4_3
ｙ(0,i)＋０・ｙ(1,i)−３ｙ(2,i)＋２ｙ(3,i)＝０ ……Ｂ4_4 As shown in FIG. 5, if the lead MR is fixed to the mouthpiece MP at the position N, y (N, i) and y (N + 1, i) become zero at an arbitrary time point i. . Further, as shown in FIG. 5, at the tip of the lead MR where no external force acts (n = 0), acceleration (∂ ² y (0, i) / ∂x ² ) and shear force (力³ y (0, i ) / ∂x ³ ) becomes zero, so the following equations B4_1 and B4_2 are established.

Further, the following expression B4_3 is derived by adding the expressions B4_1 and B4_2, and the following expression B4_4 is derived by subtracting the expression B4_2 from three times the expression B4_3.
0 · y (0, i) + y (1, i) -2y (2, i) + y (3, i) = 0 …… B4_3
y (0, i) + 0 · y (1, i) -3y (2, i) + 2y (3, i) = 0 …… B4_4

ｎ＝３〜Ｎ−１を同様に式Ｂ4に代入して導出される式と前述の式Ｂ4_3および式Ｂ4_4とから以下の式Ｂ5が導出される。

式Ｂ5の解法としてはGaussの消去法が好適である。 Further, substituting 2 for n in the expression B4 yields the following expression B4_5.

Similarly, the following formula B5 is derived from the formula derived by substituting n = 3 to N-1 into formula B4 and the formula B4_3 and formula B4_4 described above.

The Gaussian elimination method is suitable as the solution of equation B5.

  The second calculation unit 312 solves the equation B5 using the results (y0 (xf), yb (xf)) calculated by the first calculation unit 311 as the initial values of the displacement y (x, y) and the displacement yb (x). To calculate the displacement y (x, t) of the lead MR. More specifically, first, the second calculation unit 312 calculates the variables y (0, i) to y (N-1, i) corresponding to the current displacement among the right side of the formula B5 and the right side of the formula B5. Among them, y0 (0) to y0 (N-1) calculated by the first calculation unit 311 for both variables y (2, i-1) to y (N-1, i-1) corresponding to past displacements, and Substituting y0 (2) to y0 (N-1) and substituting yb (xf) calculated by the first arithmetic unit 311 into yb (2) to yb (N-1) of Expression B5, solves Expression B5 Thus, the variables y (0, i + 1) to y (N-1, i + 1) corresponding to the future displacement on the left side of the equation B5 are calculated. Second, in order to advance the time by Δt, the second calculation unit 312 sets variables y (2, i) to y (N−1, i) corresponding to the current displacement in the past on the right side of the formula B5. Substitute variables y (2, i-1) to y (N-1, i-1) corresponding to displacements, and variables y (0, i + 1) to y corresponding to future displacements calculated immediately before Substituting (N-1, i + 1) into variables y (0, i) to y (N-1, i) corresponding to the current displacement in the right side of the formula B5, solving the formula B5, the formula B5 The variables y (0, i + 1) to y (N-1, i + 1) corresponding to the future displacement are calculated from the left side of. As described above, the displacement y (0, i) to y (N-1, i) at the time point i and the displacement y (2, i-1) to y (N-1, i) at the time point (i-1). -1) is substituted and equation B5 is solved to calculate the displacement y (0, i + 1) to y (N-1, i + 1) at time (i + 1) Thus, the second calculator 312 calculates the change over time of the displacement y (x, t) at each position x of the lead MR.

  Further, every time the pressing force flip (x) set by the setting unit 12 changes, the first computing unit 311 uses the changed pressing force flip (x) as the pressing force flip (xf in the equations of motion A1 and A2. ) To calculate new y0 (xf) and yb (xf). Each time the first calculation unit 311 calculates the displacement yb (xf), the second calculation unit 312 calculates a new displacement yb (xf) that substitutes a numerical value to be substituted for yb (2) to yb (N-1) in the formula B5. Update to According to the above configuration, it is possible to synthesize a musical sound that faithfully reproduces a performance method that arbitrarily changes the pressing force flip (x). On the other hand, even if the first calculation unit 311 calculates a new displacement y0 (xf) when the pressing force flip (x) changes, the second calculation unit 312 calculates the displacement y (0, i) to y ( For N−1, i), the displacement y 0 (xf) calculated by the first calculation unit 311 is not reflected. According to the above configuration, since a discontinuous change in the displacement y (x, t) is avoided, it is possible to generate a natural musical sound in terms of hearing.

  As shown in FIG. 4, the second calculation unit 312 includes a range limiting unit 32 that limits the displacement y (x, t) of the lead MR within a predetermined range. The range limiting unit 32 uses the displacement y (x, t) of the lead MR calculated from the formula B5 as the displacement yb (xf) of the lip ML calculated by the first calculation unit 311 (the tooth MT of the lip ML contacts). The range from the bottom surface position) to the facing position H (x) set by the setting unit 12 is limited. That is, the range limiting unit 32 determines the displacement y (x, t) when the displacement y (x, t) exceeds the displacement yb (xf) (exceeds the displacement yb (xf) with the Y-axis being positive downward). The displacement yb (xf) is changed, and when the displacement y (x, t) exceeds (below) the facing position H (x), the displacement y (x, t) is changed to the facing position H (x). According to the above configuration, it is possible to avoid an absurd situation where the lead MR is located below the bottom surface of the lip ML or above the mouthpiece MP. In the above, the limit value (upper limit value) of the displacement y (x, t) is the displacement yb (x) of the bottom surface of the lip ML. However, since the lip ML actually has a thickness, Displacement by a predetermined value corresponding to the thickness (a fixed value corresponding to the minimum value of the lip ML thickness or a variable value corresponding to the minimum value of the lip ML thickness depending on the pressing force flip (x)) A position close to the facing position H (x) from yb (x) may be set as a limit value (upper limit value) of the displacement y (x, t).

式Ａ1_1の各項を変数ｙの種類毎に整理して変形すると以下の式Ａ1_2が導出される。

ただし、式Ａ1_2においては各項が以下のように置換されている。

The calculation of the displacement y0 (x) by the first calculation unit 311 (solution of the equation of motion A1) is the same method as the displacement y (x, t) by the second calculation unit 312 as outlined below. Used. First, the equation A1 is converted into a differential equation like the following equation A1_1 by the same method as the transformation from the equation of motion B1 to the equation B2.

When the terms of the expression A1_1 are rearranged for each type of the variable y and transformed, the following expression A1_2 is derived.

However, in the formula A1_2, each term is replaced as follows.

第１演算部３１１は、Gaussの消去法などの解法を利用して式Ａ1_3を解くことで変位ｙ0(x)（式Ａ1_3におけるｙ(0)〜ｙ(N-1)）を算定する。以上が運動方程式Ａ1の解法の具体例である。 Expression A1_2 is transformed into the following expression A1_3 by the same method as the modification of Expression B4 to Expression B5.

The first computing unit 311 calculates the displacement y0 (x) (y (0) to y (N-1) in the formula A1_3) by solving the formula A1_3 using a solution such as Gaussian elimination. The above is a specific example of the method of solving the equation of motion A1.

  The third calculation unit 313 in FIG. 4 includes the parameters (H (x), ρair, breed (x), Zc) set by the setting unit 12 and the displacement y (x, t) calculated by the second calculation unit 312. Based on the above, the volume flow velocity f (t) immediately above the lead is calculated. In the third calculation unit 313 of this embodiment, the volume flow velocity U (t) generated due to the pressure difference between the upper surface and the lower surface of the lead MR, and each part of the lead MR is displaced (y (x, t)). Is calculated as the volume flow velocity f (t) immediately above the lead (f (t) = U (t) −u (t)).

第３演算部３１３は、設定部１２が設定したリードＭRの横幅ｂreed(x)と第２演算部３１２が算定した変位ｙ(x,t)の時間微分（すなわちリードＭRの速度）とを式Ｃ1に代入してSimpson法などの数値積分を実行することで体積流速ｕ(t)を算定する。 The volume flow velocity u (t) is expressed by the following equation C1. Note that leff in the formula C1 is the distance from the tip of the lead MR to the fulcrum (effective length of the lead MR).

The third calculation unit 313 calculates the lateral width breed (x) of the lead MR set by the setting unit 12 and the time derivative of the displacement y (x, t) calculated by the second calculation unit 312 (that is, the speed of the lead MR). The volume flow velocity u (t) is calculated by substituting for C1 and executing numerical integration such as the Simpson method.

  The volume flow velocity U (t) is calculated by the following procedure. First, the third calculation unit 313 calculates an interval ξ (t) [m] between the mouthpiece MP and the lead MR at the tip of the lead MR. The interval ξ (t) is determined by the displacement y (0, t) at the tip (x = 0) of the lead MR out of the displacement y (x, t) of the lead MR calculated by the second calculation unit 312 ( It is calculated as a difference value (ξ (t) = y (0, t) −H (0)) from the facing position H (0) at x = 0).

式Ｃ2のＲ(t)は、リードＭRの先端における横幅ｂreed(0)と間隔ξ(t)との相対比（Ｒ(t)＝ｂreed(0)／ξ(t)）である。第３演算部３１３は、設定部１２が設定したリードＭRの横幅ｂreed(0)および空気の密度ρairと相対比Ｒ(t)とを式Ｃ2に代入することで有効質量Ｍ(t)を算定する。 Next, the third calculation unit 313 calculates the effective mass M (t) [kg] of air passing through the gap between the mouthpiece MP and the lead MR at the tip of the lead MR. The effective mass M (t) is expressed by the following formula C2.

R (t) in Expression C2 is a relative ratio (R (t) = breed (0) / ξ (t)) between the lateral width breed (0) and the interval ξ (t) at the tip of the lead MR. The third calculation unit 313 calculates the effective mass M (t) by substituting the lateral width breed (0) of the lead MR and the air density ρair and the relative ratio R (t) set by the setting unit 12 into the formula C2. To do.

式Ｃ3のＡは、所定の係数（例えばＡ＝0.0797）である。式Ｃ3を利用した体積流速Ｕ(t)の算定には例えば以下の方法が採用される。 The following formula C3 holds for the effective mass M (t) and the volume flow velocity U (t) (see Non-Patent Document 1, for example). The third calculator 313 calculates the volume flow velocity U (t) by solving the formula C3.

A in the formula C3 is a predetermined coefficient (for example, A = 0.0797). For example, the following method is used for calculating the volume flow velocity U (t) using the formula C3.

The expression C3 is transformed into the following expression C4 using the expressions D1 and D2 described later.

第３演算部３１３は、図４に示すように、以上の手順で算定した体積流速Ｕ(t)と体積流速ｕ(t)との差分値を体積流速ｆ(t)として算定する。 When the differentiation in the equation C4 is discretized by the backward difference, the following equation C5 is derived. The third calculation unit 313 calculates the volume flow velocity U (t) from the formula C5 by using a numerical solution of a nonlinear equation (for example, Newton Raphson method).

As shown in FIG. 4, the third calculation unit 313 calculates a difference value between the volume flow velocity U (t) and the volume flow velocity u (t) calculated by the above procedure as the volume flow velocity f (t).

  4 calculates the output wave pressure POUT (t) and the sound pressure p (t) immediately above the lead. The outgoing wave pressure POUT (t) is the pressure of a sound wave (hereinafter referred to as “outgoing wave”) that travels from the lead MR into the tubular body. A part of the sound wave that has traveled in the tube part (hereinafter referred to as “reflected wave”) is reflected by the open end (bell) of the wind instrument and travels in the reverse direction to reach the mouthpiece MP. Therefore, the outgoing wave pressure POUT (t) is the pressure generated by the volume flow velocity f (t) and the reflected wave pressure (hereinafter referred to as “reflected wave pressure”) PIN (t) propagating from the tube to the lead MR side. It corresponds to addition. The reflected wave pressure PIN (t) is calculated by the tube simulation unit 33.

Since the pressure caused by the volume flow velocity f (t) is a product of the volume flow velocity f (t) and the characteristic impedance Zc, the outgoing wave pressure POUT (t) is expressed by the following equation D1.
POUT (t) = Zc · f (t) + PIN (t) ...... D1
The fourth calculation unit 314 calculates the characteristic impedance Zc set by the setting unit 12, the volume flow velocity f (t) calculated by the third calculation unit 313, and the reflected wave pressure PIN (t) calculated by the tube simulation unit 33. The outgoing wave pressure POUT (t) is calculated by substituting for D1.

Further, since the outgoing wave pressure POUT (t) and the reflected wave pressure PIN (t) act immediately above the lead, the pressure p (t) immediately above the lead is expressed by the following formula D2.
p (t) = POUT (t) + PIN (t) ...... D2
The fourth calculation unit 314 substitutes the reflected wave pressure POUT (t) calculated based on the equation D1 and the reflected wave pressure PIN (t) calculated by the tube simulation unit 33 into the equation D2, thereby converting the pressure p (t ) Is calculated. The pressure p (t) calculated by the fourth calculation unit 314 is calculated by calculating the external force fex (x) by the second calculation unit 312 (formula B) or by calculating the volume flow velocity U (t) by the third calculation unit 313 (formula C3).

  The tube simulation unit 33 synthesizes musical tone data (time series of data) indicating the musical tone of the wind instrument based on the outgoing wave pressure POUT (t). For example, Japanese Patent Laid-Open No. 5-61474 and Japanese Patent Laid-Open No. Hei 6 (1994) disclose a processing (simulation of the behavior of sound waves inside the tube portion) in which the tube simulation unit 33 generates musical tone data corresponding to the outgoing wave pressure POUT (t). Known techniques such as the invention disclosed in Japanese Patent No. -67675 are arbitrarily adopted.

  Next, the setting unit 12 in FIG. 1 will be described. As shown in FIG. 1, the setting unit 12 includes an elastic value specifying unit 20 and a parameter converting unit 26. The elastic value specifying unit 20 specifies various parameters (elastic values) regarding the elastic characteristics of the lead and lips. The parameter conversion unit 26 converts a large number of parameters supplied from the elastic value specifying unit 20 and the input device 44 into parameters necessary for synthesizing musical sounds.

  FIG. 6 is a block diagram illustrating a functional configuration of the elasticity value specifying unit 20. As illustrated in FIG. 6, the elastic value specifying unit 20 includes a specifying unit 22A and a specifying unit 22B. The specifying unit 22A specifies a spring constant klip_sample of a sample imitating a player's lips (hereinafter referred to as “lip sample”). The lip sample is a test piece whose elastic characteristics and shape (shape and size) are close to (ideally match) an actual human lip. The spring constant klip_sample of the lip sample depends on the strength FA of the external force (pressing force) acting on the lip sample and the position x on the lip sample (klip_sample (FA, x)). The strength FA is input to the specifying unit 22A. The intensity FA is instructed by the user appropriately operating the input device 44. Further, a plurality of positions x set in advance as positions on the lip sample are instructed to the specifying unit 22A. The specifying unit 22A specifies a spring constant klip_sample corresponding to the strength FA for each position x. Note that the position x may be specified in accordance with the user's operation on the input device 44, similarly to the intensity FA.

  The relationship between the spring constant klip_sample of the lip sample, the strength FA and the position x is determined according to the result of actual measurement. FIG. 7 is a conceptual diagram for explaining a method of actually measuring the spring constant klip_sample. As shown in FIG. 7, the surface of the lip sample 82 placed on the work table 80 is pressed by the pressurizing body 84. Similar to the pressing of the lips ML by the performer's teeth MT, the pressing body 84 presses only a part of the surface of the lip sample 82. The operation of measuring the deformation amount at a plurality of positions x of the lip sample 82 and calculating the spring constant klip_sample at each position is repeated for a plurality of cases where the strength FA of the pressing force is changed. Through the above test, the relationship between the strength FA of the external force and the spring constant klip_sample is measured at each of the plurality of positions x.

  FIG. 8 is a graph showing the results of the above test. In FIG. 8, a spring constant klip_sample (vertical axis) and an external force intensity FA (horizontal axis) at one position x on the lip sample 82 are shown. As shown in FIG. 8, the spring constant klip_sample at a specific position x of the lip sample 82 changes nonlinearly according to the strength FA of the external force. On the other hand, assuming that the strength FA of the external force is fixed, the spring constant klip_sample changes nonlinearly according to the position x.

  Based on the results of the above test, a function FNC_A (klip_sample = FNC_A (FA, x)) that approximates the measured relationship between the spring constant klip_sample, the strength FA, and the position x is created. The specifying unit 22A in FIG. 6 holds the function FNC_A. Then, the specifying unit 22A calculates the spring constant klip_sample by substituting the strength FA and the position x into the function FNC_A. Therefore, the spring constant klip_sample specified by the specifying unit 22A changes nonlinearly according to the strength FA and the position x as understood from FIG.

  The identifying unit 22B in FIG. 6 identifies the spring constant kreed_sample of a sample simulating a lead (hereinafter referred to as “lead sample”). The lead sample is a test piece whose elastic characteristics and form (shape and size) are close to (ideally match) the lead of an actual wind instrument. The spring constant kreed_sample of the lead sample depends on the strength FB of the external force acting on the lead sample and the position x in the lead sample (kreed_sample (FB, x)). The strength FB is input to the specifying unit 22B. The intensity FB is instructed by the user appropriately operating the input device 44. Further, a plurality of positions x (x = n · Δx) discretized in the X direction as shown in FIG. 5 are instructed to the specifying unit 22B. The specifying unit 22B specifies a spring constant kreed_sample corresponding to the strength FB for each position x. It should be noted that the position x in the lead sample may be specified in accordance with the user's operation on the input device 44, similarly to the intensity FB.

  The relationship between the spring constant kreed_sample of the lead sample, the strength FB, and the position x is determined according to the result of actual measurement. The spring constant kreed_sample is measured by, for example, pressing the surface of the lead sample 83 whose end is fixed to the work table 81 with a pressurizing body 85, as shown in FIG. That is, the operation of measuring the deformation amount of the lead sample 83 at a plurality of positions x and calculating the spring constant kreed_sample at each position is repeated for a plurality of cases where the strength FB of the pressing force is changed. By the above test, the relationship between the external force intensity FB and the spring constant kreed_sample is actually measured for each of a plurality of positions x (x = 1 · Δx, 2 · Δx, 3 · Δx,...). Similar to the lip sample 82, the spring constant kreed_sample of the lead sample 83 changes nonlinearly according to the strength FB and the position x.

  When the above test is completed, a function FNC_B (kreed_sample = FNC_B (FB, x)) that approximates the measured relationship between the spring constant kreed_sample, the strength FB, and the position x is created. The specifying unit 22B in FIG. 6 holds the function FNC_B and calculates the spring constant kreed_sample by substituting the strength FB and the position x into the function FNC_B. The spring constant kreed_sample specified by the specifying unit 22B changes nonlinearly according to the strength FB and the position x.

  Next, FIG. 10 is a block diagram showing a specific configuration of the parameter conversion unit 26. Various parameters listed on the left side of FIG. 10 are input to the parameter conversion unit 26. Parameters input to the parameter conversion unit 26 are physical property values (cair, ρair) relating to air, physical property values relating to the lip ML (ρlip, Elip, tanδlip), physical property values relating to the lip sample (mlip_sample, klip_sample), and lead MR. The physical property value (tan δreed), the physical property value (mreed_sample, kreed_sample), the breath pressure P0, and the pitch fn. As described above, the elasticity value specifying unit 20 specifies the spring constant klip_sample of the lip sample and the spring constant kreed_sample of the lead sample. On the other hand, parameters other than the spring constants (klip_sample, kreed_sample) are instructed to the arithmetic processing unit 10 by the user appropriately operating the input device 44, for example. The specific contents of each parameter are as follows.

cair is the speed of sound in air [m / sec], and ρair is the density of air [kg / m ³ ]. The breath pressure P0 is the pressure of air in the user's mouth during blowing. The pitch fn is a numerical value indicating the pitch of the musical sound to be synthesized by the arithmetic processing unit 10. It is possible to synthesize a musical performance sound by appropriately changing the pitch fn.

The physical property values related to the lip ML include the density ρlip [kg / m ³ ] of the lip ML, the Young's modulus Elip [Pa] of the lip ML, and the loss coefficient tanδlip of the lip ML. The physical property value related to the lip sample includes the mass mlip_sample [kg] of the lip sample in addition to the spring constant klip_sample specified by the specifying unit 22A. The physical property value relating to the lead MR includes the loss coefficient tanδreed of the lead MR. The physical property value of the lead sample includes the mass mreed_sample [kg] of the lead sample in addition to the spring constant kreed_sample specified by the specifying unit 22B.

The characteristic impedance Zc of the wind instrument mouthpiece MP is expressed by the following equation (a1). Note that Sin in the following expression is an area at the start point of a portion of the mouthpiece MP that can be regarded as a tubular body.
Zc = (ρair · cair) / Sin
= (Ρair · cair) / {π · (φin / 2) ² } (a1)
As shown in FIG. 10, the parameter converter 26 calculates the characteristic impedance Zc by performing the calculation of the equation (a1) for the sound velocity cair, the density ρair, and the diameter φin. Φin is the inner diameter [m] of the mouthpiece MP at the root of the lead MR (portion fixed to the mouthpiece MP).

The spring constant distribution klip (x) [N / m ² ] of the lips ML is expressed by the following equation (a2).
klip (x) = {(Elip · blip (x) · llip (x)) / dlip (x)} / llip (x)
= Elip ・ blip (x) / dlip (x) (a2)
As shown in FIG. 10, the parameter conversion unit 26 performs the calculation of the equation (a2) on the physical property values (Elip, blip (x), dlip (x)) of the lip ML, thereby distributing the spring constant of the lip ML. klip (x) [N / m ² ] is calculated. In the expression (a2), the lateral width blip (x) and the thickness dlip (x) of the lip ML at the position x in the X direction are specified from the pitch fn (details will be described later).

パラメータ変換部２６は、図１０に示すように、唇ＭLの物性値（tanδlip）と唇サンプルの物性値（mlip_sample，ｋlip_sample）とについて式(a3)の演算を実行することで唇ＭLの内部抵抗の分布μlip(x)を算定する。バネ定数ｋlip_sampleを算定した複数の位置ｘの各々について内部抵抗の分布μlip(x)が算定される。 The distribution μlip (x) of the internal resistance of the lip ML is expressed by the following equation (a3).

As shown in FIG. 10, the parameter conversion unit 26 performs the calculation of the equation (a3) on the physical property value (tan δlip) of the lip ML and the physical property value (mlip_sample, klip_sample) of the lip ML, thereby performing the internal resistance of the lip ML. The distribution μlip (x) of is calculated. The internal resistance distribution μlip (x) is calculated for each of the plurality of positions x for which the spring constant klip_sample is calculated.

パラメータ変換部２６は、図１０に示すように、リードＭRの物性値（tanδreed）とリードサンプルの物性値（ｍreed_sample，ｋreed_sample）とについて式(a4)の演算を実行することでリードＭRの内部抵抗の分布μreed(x)を算定する。バネ定数ｋreed_sampleを算定した複数の位置ｘの各々（ｘ＝１・Δｘ，２・Δｘ，３・Δｘ，……）について内部抵抗の分布μreed(x)が算定される。 On the other hand, the internal resistance distribution μreed (x) of the lead MR is expressed by the following equation (a4).

As shown in FIG. 10, the parameter conversion unit 26 performs the calculation of the equation (a4) on the physical property value (tan δreed) of the lead MR and the physical property values (mreed_sample, kreed_sample) of the lead MR, thereby performing the internal resistance of the lead MR. The distribution μreed (x) of is calculated. The internal resistance distribution μreed (x) is calculated for each of the plurality of positions x where the spring constant kreed_sample is calculated (x = 1 · Δx, 2 · Δx, 3 · Δx,...).

  Also, as shown in FIG. 10, the parameter conversion unit 26 includes a plurality of parameters (blip (x), dlip (x), xteeth1, xteeth2, xlip1, xlip2, xlip2, Flip () on the embouchure (the state of the lip ML during playing). x)), a coefficient pmul for correcting the breath pressure P0, and a plurality of parameters r relating to the fingering of the wind instrument are specified based on the pitch fn by key scale processing (symbol “KSC” in FIG. 10). The key scale process is a process of specifying a numerical value corresponding to the actually designated pitch fn for each parameter from a table in which each numerical value that can be taken by the pitch fn is associated with each numerical value of the parameter. The plurality of parameters r is a coefficient r indicating the state of the tone hole or bell of the wind instrument, and is used for the simulation inside the tube section by the tube simulation section 33.

  A plurality of parameters relating to the embouchure are the width of the lip ML (dimension in the Z direction) blip (x) [m] and the thickness of the lip ML when no external force is applied (dimension in the Y direction) dlip (x) [m]. And a force Flip (x) [N] that the performer's tooth MT presses the lip ML, and parameters (xlip1, xlip2, xteeth1, xteeth2) regarding the position of the performer's lip ML and the tooth MT with respect to the lead MR. .

  The parameter conversion unit 26 specifies the width blip (x) and the thickness dlip (x) corresponding to the pitch fn by key scale processing, and sets the multiplication value of the width blip (x) and the thickness dlip (x). The mass distribution mlip (x) [kg / m] of the lip ML is calculated by multiplying the density lip of the lip ML. The width blip (x) and the thickness dlip (x) are also applied to the calculation of the spring constant distribution klip (x) of the lips ML described above.

  As shown in FIG. 5, in order to discretize each position x in the X direction, the parameter converter 26 divides the numerical value obtained by dividing the position (xlip1, xlip2) of the lip ML by the interval Δx (nlip1, nlip2), and a value obtained by dividing the position of the tooth MT (xteeth1, xteeth2) by the interval Δx is calculated as a post-discrete position (nteeth1, nteeth2). Further, the parameter converter 26 calculates the difference value between the position xteeth1 and the position xteeth2 as the length lteeth of the tooth MT in the X direction, and calculates the difference value between the position xlip1 and the position xlip2 as the length llip of the lip ML in the X direction. Calculated as The parameter converting unit 26 divides the pressing force Flip (x) by the length lteeth of the tooth MT, so that the pressing force flip (x) [N / m] acting on the unit length of the lip ML from the tooth MT. Is calculated (flip (x) = Flip (x) / lteeth).

  The parameter conversion unit 26 specifies the coefficient pmul corresponding to the pitch fn by key scale processing, and calculates the pressure P in the player's mouth by multiplying the breath pressure P0 and the coefficient pmul. The coefficient pmul is a coefficient that changes according to the pitch fn. The range of the player's breath pressure for sounding a wind instrument is actually different depending on the pitch of the musical sound (for example, the breath pressure range when playing a high tone is different from that when playing a low tone. Tend to be wide). In this embodiment, since the coefficient pmul multiplied by the breath pressure P0 is a variable value corresponding to the pitch fn, even if the breath pressure P0 is selected regardless of the pitch fn, the above-mentioned value of the wind instrument is not exceeded. There is an advantage that the characteristics are faithfully simulated.

  As described above, in this embodiment, the displacement y (x, t) of the lead MR is calculated on the basis of the equation of motion B expressing the coupled vibration of the lead MR and the lip ML. The behavior of the lead MR is faithfully simulated in comparison with the techniques of Non-Patent Document 1 that models the lead MR as a rigid air valve that moves in a straight line and Non-Patent Document 2 that models the lead MR with a long plate-like vibrating body. Is done. Therefore, it is possible to synthesize musical sounds having characteristics close to those of actual wind instruments with high accuracy. In addition, the displacement yb (x) of the lip ML in the equation of motion B is obtained from the equation A1 and the equation of motion A1 from the changed pressing force flip (x) every time the pressing force flip (x) acting on the lead MR from the lip ML changes. Since the result calculated based on the equation of motion A2 is updated, it is possible to faithfully reproduce a performance technique for changing the pressing force flip (x). On the other hand, even if the pressing force flip (x) is changed, the displacement y (x, t) of the lead MR in the equation of motion B is maintained, so that it is caused by the discontinuous change of the displacement y (x, t). The uncomfortable feeling of the musical tone is effectively suppressed.

  Furthermore, in this embodiment, the spring constant klip_sample is calculated so as to change nonlinearly according to the external force intensity FA on the lip sample and the position x on the lip sample, and the external force intensity FB on the lead sample and the position on the lead sample. Since the spring constant kreed_sample is calculated so as to change nonlinearly according to x, the lip ML characteristic (internal resistance distribution μlip (x)) and the lead MR characteristic (internal resistance distribution μreed (x)) are positioned. The phenomenon of changing according to x and the strength of external force (FA, FB) is faithfully reproduced. Therefore, it is possible to synthesize a natural musical tone that is close to the actual musical tone of a wind instrument as compared with the case where the elasticity values (klip_sample, kreed_sample) of the lips and leads are fixed. In particular, in this embodiment, since the relationship between the spring constant klip_sample and the intensity FA and the position x and the relationship between the spring constant kreed_sample, the intensity FB and the position x are set based on the actually measured values, the characteristics of the synthesized sound are actually It is possible to approximate the sound of a wind instrument.

<B: Second Embodiment>
Next, a second embodiment of the present invention will be described. The bending stiffness Stiff (x) of the lead MR in the first embodiment corresponds to a product of the Young's modulus Ereed and the cross-sectional secondary moment I (x). In this embodiment, the bending stiffness Stiff (x) is specified based on the actual measurement result for the lead sample. In addition, about the element in which an effect | action and a function are equivalent to 1st Embodiment in each following form, the same code | symbol as the above is attached | subjected and each detailed description is abbreviate | omitted suitably.

  FIG. 11 is a block diagram illustrating a configuration of the elasticity value specifying unit 20 in the present embodiment. As shown in FIG. 11, the elasticity value specifying unit 20 includes a specifying unit 22C in addition to the specifying unit 22A and the specifying unit 22B of the first embodiment. The specifying unit 22C specifies the bending stiffness Stiff (x) used for the calculation in the lead simulating unit 31. As shown in FIG. 5, a plurality of positions x (x = n · Δx) discretized in the X direction are instructed to the specifying unit 22C. The specifying unit 22C specifies the bending stiffness Stiff (x) at each of the plurality of positions x (x = 1 · Δx, 2 · Δx, 3 · Δx,...), And outputs it to the lead simulating unit 31.

  In the present embodiment, each of the plurality of positions x indicated to the specifying unit 22C and the bending stiffness Stiff (x) specified by the specifying unit 22C based on the actual measurement value of the bending rigidity Stiff (x) for the lead sample. Is set. That is, as shown in FIG. 9, the state (deformation) of the lead sample 83 when a predetermined external force FB is applied from the pressure member 85 is observed, and the bending stiffness Stiff (x) at each position x is determined from the observation result. Calculate. FIG. 12 is a graph showing the results of actual measurement of the position x of the lead sample 83 and the bending stiffness Stiff (x). As shown in FIG. 12, the bending stiffness Stiff (x) changes nonlinearly with respect to the position x due to the change in the cross section of the lead sample 83 according to the position x.

  Based on the results of the above test (FIG. 12), a function FNC_C (Stiff (x) = FNC_C (x)) that approximates the results actually measured for the bending stiffness Stiff (x) and the position x is created. The specifying unit 22C in FIG. 11 holds the function FNC_C, and calculates the bending stiffness Stiff (x) by substituting the input position x into the function FNC_C. Therefore, the bending stiffness Stiff (x) calculated by the specifying unit 22C changes nonlinearly with respect to the position x as shown in FIG. As described above, in this embodiment, since the bending stiffness Stiff (x) at each position x is calculated based on the actual measurement value, there is an advantage that a natural musical sound that faithfully reflects the actual behavior of the lead can be synthesized. is there.

<C: Third Embodiment>
FIG. 13 is a block diagram showing a configuration of the elastic value specifying unit 20 according to the third embodiment of the present invention. As shown in FIG. 13, the elasticity value specifying unit 20 includes a specifying unit 22 and a selecting unit 23. The specifying unit 22 corresponds to any of the specifying unit 22A, the specifying unit 22B of the first embodiment, and the specifying unit 22C of the second embodiment, and an elastic value e () corresponding to the input value v (FA, FB, x). klip_sample, kreed_sample, Stiff (x)) are specified and output.

  The specifying unit 22 holds M functions FNC (1) to FNC (M) that define different relationships between the input value v and the elastic value e. For example, when the present embodiment is applied with the specific portion 22A in FIG. 6 as the specific portion 22, the relationship between the spring constant klip_sample, the strength FA, and the position x is set for each of M lip samples having different elastic characteristics and shapes. M functions FNC_A (1) to FNC_A (M) that are actually measured and approximate the results of each measurement are created. Similarly, when the specific part 22B in FIG. 6 is used as the specific part 22, the result of actual measurement for each of the M lead samples having different elastic characteristics and forms (relationship between the spring constant kreed_sample, the strength FB, and the position x) M functions FNC_B (1) to FNC_B (M) are created so as to approximate. Further, when the specifying unit 22C in FIG. 11 is used as the specifying unit 22, the M functions FNC_C (1) to FNC_C (M) are approximated to the measured values of the bending stiffness Stiff (x) in each of the M lead samples. ) Is created.

  The selection unit 23 selects any one of the M functions FNC (1) to FNC (M) held by the specifying unit 22. More specifically, the selection unit 23 selects any one of the functions FNC (1) to FNC (M) according to the operation of the input device 44 by the user. For example, when the user designates any one of M leads having different manufacturers and models from the input device 44, the selection unit 23 selects the M functions FNC (1) to FNC (M). A function FNC corresponding to the specified lead (a function set from the actual measurement value of the lead sample whose characteristics are close to the lead specified by the user) is selected. The specifying unit 22 calculates the elasticity value e by substituting the input value v into the function FNC selected by the selection unit 23.

  As described above, in this embodiment, the elastic characteristics of the lead MR and the lip ML are changed by variably selecting the relationship between the input value v and the elastic value e from M candidates. It is possible to generate various synthesized sounds corresponding to leads and lips.

<D: Fourth Embodiment>
FIG. 14 is a block diagram showing a configuration of the elastic value specifying unit 20 according to the fourth embodiment of the present invention. As shown in FIG. 14, the elastic value specifying unit 20 of this embodiment includes a specifying unit 22 and a control unit 24. Similar to the third embodiment, the specifying unit 22 corresponds to any of the specifying unit 22A, the specifying unit 22B, and the specifying unit 22C of the second embodiment, and the input value v (FA, FB, x ) Corresponding to the elasticity value e (klip_sample, kreed_sample, Stiff (x)).

  The control unit 24 variably controls (ie, edits) the relationship between the input value v and the elastic value e. For example, the control unit 24 changes the contents of the function FNC (FNC_A, FNC_B, FNC_C) held by the specifying unit 22 according to an operation (instruction from the user) on the input device 44. Further details are as follows.

  A display device 48 is connected to the arithmetic processing device 10 of this embodiment. The control unit 24 displays an image indicating the relationship between the input value v and the elasticity value e on the display device 48 based on the function FNC held by the specifying unit 22. For example, the control unit 24 causes the display device 48 to display a graph as illustrated in FIG. 8 or FIG.

  The user edits the graph (curve) displayed on the display device 48 by appropriately operating the input device 44. For example, when the user moves a point (an arbitrary point or a predetermined representative point) on the graph by operating the input device 44 such as a mouse or a touch pen, the graph displayed on the display device 48 displays the point after the movement. It is changed to a graph with a passing shape. The control unit 24 updates the function FNC held by the specifying unit 22 to a new function FNC corresponding to the graph changed by the user. The new function FNC is created, for example, by appropriately changing each coefficient of the arithmetic expression representing the relationship between the input value v and the elastic value e according to an instruction from the user. The specifying unit 22 uses the function FNC updated by the control unit 24 to specify the elastic value e from the input value v.

  Further, the user can create a new function FNC by operating the input device 44. For example, when the user designates a plurality of points on the screen of the display device 48, the control unit 24 creates a function FNC that passes through the plurality of points. The specifying unit 22 specifies the elastic value e from the input value v based on the new function FNC created by the control unit 24.

  As described above, in this embodiment, since the relationship between the input value v and the elastic value e is changed according to an instruction from the user, there is an advantage that the user can appropriately adjust the characteristics of the synthesized sound. In addition, since a function FNC is newly created according to an instruction from the user, there is an advantage that a variety of synthesized sounds can be generated without a lead sample or a lip sample.

  Note that the configuration for allowing the user to edit the relationship between the input value v and the elasticity value e is arbitrary. For example, a plurality of coefficients defining the function FNC are displayed on the display device 48 and changed by the user, or both the plurality of coefficients of the function FNC and the graph of the function FNC are displayed on the display device 48. When the coefficient is changed, a configuration in which the display on the display device 48 is updated to the graph of the function FNC after the change is also adopted.

<E: Modification>
Various modifications as exemplified below can be added to the above embodiments. Two or more aspects may be arbitrarily selected from the following examples and combined.

(1) Modification 1
In each of the above embodiments, the elastic value e is calculated from the input value v by calculation using the function FNC. However, the method for specifying the elastic value e from the input value v is appropriately changed. For example, a configuration in which a table that associates the input value v with the elastic value e is set in the specifying unit 22 is also suitable. The specifying unit 22 searches the table for an elastic value e corresponding to the input value v and outputs it. In the third embodiment, the selection unit 23 selects one of M tables having different correspondences between the input value v and the elasticity value e. That is, the selection unit 23 may be any means that selects any one of a plurality of types of relationships (function FNC and table) set for the input value v and the elasticity value e. In the fourth embodiment, the control unit 24 changes the contents of the table (elastic value e corresponding to each input value v) in accordance with an instruction from the user. That is, the control unit 24 may be any means that variably controls (edits) the relationship between the input value v and the elastic value e.

(2) Modification 2
The content of the elastic value e is changed as appropriate. For example, a configuration in which the spring constant klip_sample is a variable that depends only on one of the position x and the strength FA, and a configuration in which the spring constant kreed_sample is a variable that depends only on one of the position x and the strength FB are also employed. A configuration in which the bending stiffness Stiff (x) in the second embodiment is a variable depending on the external force acting on the lead is also suitable. As described above, the elasticity value e in the present embodiment is sufficient to be a numerical value indicating the elasticity characteristic of the lead (or lead sample) or the player's lips (or lip sample). It is appropriately changed according to the contents of the calculation (configuration of the physical model).

(3) Modification 3
In each of the above embodiments, the strength FA and the strength FB instructed to the elastic value specifying unit 20 are input from the input device 44, but the method for setting the strength FA and the strength FB is arbitrary. For example, a configuration in which the pressing force flp (x) generated by the parameter conversion unit 26 is instructed to the elastic value specifying unit 20 as the strength FA, or an external force fex (x) calculated by the lead simulation unit 31 is used as the strength FB to specify the elastic value. A configuration instructing the unit 20 or a configuration in which the elastic value specifying unit 20 includes only one of the specifying unit 22A, the specifying unit 22B, and the specifying unit 22C is also employed. In each of the above embodiments, the function FNC (or table) is set based on the actual measurement results for the lip sample and the lead sample, but the actual player's lips and the actual wind instrument lead are targeted. The function FNC (or table) may be set based on the actual measurement result.

(4) Modification 4
Assuming the case where the lead MR is displaced outside the range of the proportional limit as in the above embodiments (that is, when the elastic value e is a variable value), the displacement y0 (xf) of the lead MR calculated from the equation A1. Changes nonlinearly with respect to the elastic value e (for example, bending stiffness Stiff (x)). Therefore, the first calculation unit 311 of FIG. 4 calculates the displacement y0 (xf) from the bending stiffness Stiff (x) so that the bending stiffness Stiff (x) set by the setting unit 12 changes nonlinearly. Is also adopted. More specifically, the first calculation unit 311 defines the relationship between the bending stiffness Stiff (x) and the displacement y0 (xf) so that the displacement y0 (xf) changes nonlinearly with respect to the bending stiffness Stiff (x). The function or table to be held is held for each numerical value of the pressing force flip (x). Then, the first calculation unit 311 selects the relationship corresponding to the pressing force flip (x) set by the setting unit 12, and then has the relationship with respect to the bending stiffness Stiff (x) set by the setting unit 12. And the corresponding displacement y0 (xf) is specified. The displacement y0 (xf) specified by the first calculation unit 311 is used by the second calculation unit 312 as an initial value of the displacement y (x, t) of the lead MR in the equation of motion B, as in the first embodiment. The

  Similarly, when the performer's lip ML is displaced outside the range of the proportional limit (that is, when the elastic value e is a variable value), the displacement yb (xf) of the lip ML calculated from the equation A2 is the elastic value. e (for example, a spring constant distribution klip (x)) changes nonlinearly. Accordingly, the first calculation unit 311 of FIG. 4 changes the displacement yb (xf) from the spring constant distribution klip (x) so as to change nonlinearly with respect to the spring constant distribution klip (x) set by the setting unit 12. A configuration for calculating the value is also adopted. For example, the first calculation unit 311 determines the relationship between the spring constant distribution klip (x) and the displacement yb (xf) so that the displacement yb (xf) changes nonlinearly with respect to the spring constant distribution klip (x). A function or table to be defined is held for each combination of numerical values of the pressing force flip (x) and the lip ML thickness dlip (x). Then, the first calculation unit 311 selects the relationship corresponding to the pressing force flip (x) and the thickness dlip (x) set by the setting unit 12 and then distributes the spring constant distribution klip ( The corresponding displacement yb (xf) is specified with respect to x). The displacement yb (xf) specified by the first calculation unit 311 is used by the second calculation unit 312 as an initial value of the displacement yb (x) of the lip ML in the equation of motion B, as in the first embodiment. In this modification, it does not matter whether the elasticity value e changes nonlinearly with respect to the input value v. Similarly to the fourth embodiment, the relationship between the bending stiffness Stiff (x) and the displacement y0 (xf) and the relationship between the spring constant distribution klip (x) and the displacement yb (xf) are the instructions from the user. A configuration edited or created accordingly is also preferably employed.

It is a block diagram of a musical tone synthesis apparatus according to an embodiment of the present invention. It is a conceptual diagram which shows the vicinity of the lead of the wind instrument which a lead simulation part simulates. It is a schematic diagram of the contact between the lips and the reed when the wind instrument is played. It is a block diagram of a lead simulation part. It is a conceptual diagram explaining the discretization of the position of a X direction. It is a block diagram of an elasticity value specific | specification part. It is a schematic diagram of the structure which measures the elasticity value (spring constant) of a lip sample. It is a graph which shows the relationship between the external force which acts on a lip sample, and a spring constant. It is a schematic diagram of the structure which measures the elastic value (spring constant) of a lead sample. It is a block diagram of a parameter converter. It is a block diagram of the elastic value specific | specification part in 2nd Embodiment. It is a graph which shows the relationship between the position in a lead sample, and bending rigidity. It is a block diagram of the elastic value specific | specification part in 3rd Embodiment. It is a block diagram of the elastic value specific | specification part in 4th Embodiment.

Explanation of symbols

100 …… Musical sound synthesizer, 10 …… Calculation processing unit, 12 …… Setting unit, 14 …… Synthesis unit, 20 …… Elasticity value specifying unit, 22 (22A, 22B, 22C) …… Specifying unit, 23 …… Selection unit, 24... Control unit, 26... Parameter conversion unit, 31... Lead simulation unit, 311... First calculation unit, 312. Fourth computing unit, 32... Range limiting unit, 33... Tube simulation unit, 42... Storage device, 44 .. input device, 46.

Claims (8)

First specifying means for specifying an elastic value of each position of the lead so as to change nonlinearly with respect to a longitudinal position of the lead of the wind instrument ;
A tone synthesizer comprising: a tone synthesizer for synthesizing a tone of the wind instrument based on a plurality of variables corresponding to the elasticity value specified by the first specifying means. The musical tone synthesizer according to claim 1, wherein the relationship between the first input value and the elastic value specified by the first specifying means is set based on an actual measurement value. Selecting means for selecting one of a plurality of types of relationships set for the first input value and the elastic value specified by the first specifying means;
The musical tone synthesis apparatus according to claim 1, wherein the first specifying unit specifies an elasticity value of the lead corresponding to the first input value in the relationship selected by the selection unit. The musical tone synthesis according to any one of claims 1 to 3, further comprising control means for variably controlling a relationship between the first input value and the elastic value specified by the first specifying means in accordance with an instruction from a user. apparatus. A second specifying means for specifying an elastic value of each position of the lip so as to change nonlinearly with respect to a position in a longitudinal direction of the lead on a player's lip contacting the lead;
2. The musical tone synthesizing unit synthesizes a musical tone based on a plurality of variables according to the elasticity value of the lead specified by the first specifying unit and the elastic value of the lip specified by the second specifying unit. The musical tone synthesizer according to claim 4.   Parameter conversion means for calculating a distribution of internal resistance in the longitudinal direction of the lead from the elastic value of each position of the lead specified by the first specifying means,
  The musical tone synthesizing unit synthesizes the musical tone of the wind instrument based on a plurality of variables including an internal resistance distribution calculated by the parameter converting unit.
  6. The musical tone synthesizer according to any one of claims 1 to 5.   Parameter conversion means for calculating the distribution of the internal resistance of the lips in the longitudinal direction of the lead from the elastic value of each position of the lips specified by the second specifying means;
  The musical tone synthesizing unit synthesizes the musical tone of the wind instrument based on a plurality of variables including an internal resistance distribution calculated by the parameter converting unit.
  The musical tone synthesizer according to claim 5. A first specifying process for specifying an elastic value at each position of the lead so as to change nonlinearly with respect to a position in a longitudinal direction of the lead of the wind instrument ;
A program for causing a computer to execute a tone synthesis process for synthesizing a tone of the wind instrument based on a plurality of variables corresponding to an elasticity value specified in the first specifying process.

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