JP5935252B2 - Electronic keyboard instrument - Google Patents

Description

  The present invention relates to a technique for generating a musical sound signal that simulates a sound generated by an acoustic keyboard instrument.

  There is known a method of synthesizing a musical sound signal simulating a sound emitted from an acoustic piano by performing a simulation according to a physical model based on a sound generation mechanism of an acoustic piano. For example, Patent Document 1 discloses a technique for acquiring performance information corresponding to a key press amount and generating a musical sound signal that simulates a sound generated from a piano. According to this technique, each key of the keyboard unit is provided with a key position sensor that outputs information indicating the amount of pressing, and information obtained by converting the information indicating the amount of pressing of the key from an analog format to a digital format is periodically output. A musical tone signal is generated based on the output information.

In the calculation of the physical model for generating the musical sound signal, the damper effectiveness, that is, the degree to which the vibration of the string due to the damper is suppressed (hereinafter referred to as damper information) is changed according to the key depression amount, and the damper The amount “b _D e _D (nΔt)” corresponding to the viscosity coefficient of the damper determined according to the effect amount “e _D (nΔt)” is sequentially changed on the discrete time axis. As a result, as with an acoustic piano damper, it is possible to control natural and continuous stop sound and string resonance, and to generate a musical sound signal simulating various musical nuances.

JP 2011-013674 A

  As described in Patent Document 1, a key position sensor that continuously detects and outputs a key press amount and an AD converter for converting from an analog format to a digital format are relatively expensive. is there. For this reason, if the configuration is such that the key pressing amount is not continuously detected but is detected in several places in the movable range of the key (hereinafter referred to as the key pressing range), the key position (position in the key pressing range, The same can be applied to the sensor for detecting the same hereinafter. In many cases, an AD converter is also unnecessary. Therefore, it contributes to cost reduction. On the other hand, when the detection position in the key pressing range decreases, the detection accuracy of the key behavior decreases, and the accuracy of the damper effectiveness decreases. For this reason, as the key detection position in the key-pressing range is reduced, it has become difficult to apply to a device that generates a musical sound signal that reflects the effectiveness of the damper.

  The present invention has been made in view of the above circumstances, and in an electronic keyboard instrument that generates a musical tone signal in response to a key depression, even if the key detection position in the key depression range is reduced, it is reflected in the musical tone signal. It aims at suppressing the fall of the precision of the amount of effect of a damper.

In order to solve the above-described problem, the present invention includes an action body that excites vibration of a sounding body in response to an operation on a key, and a damper that exerts a force on the sounding body in response to the operation and suppresses the vibration. An electronic keyboard instrument that generates a musical sound signal that simulates a sound generated from an acoustic keyboard instrument, wherein the key is provided so as to be movable within a key pressing range that is predetermined according to an operation, and the key is moved to the key pressing range. Detecting means for detecting at a plurality of detection positions, state variable updating means for updating the state variable of the key based on the detection result by the detecting means, and exciting the vibration of the sounding body by the operating body Excitation information output means for outputting excitation information indicating parameters, and damper information output for outputting damper information indicating parameters for suppressing vibration of the sounding body by the damper Determining a stage, the excitation information to be the output based on the detection result and the state variables by the detection means, on the basis and the state variables, to the time when the key is detected at each detecting position by the detecting means Te, an output control means for determining a variant of the damper information the output, a tone signal indicating the sound corresponding to the vibration of the sounding body is determined based on the outputted the excitation information and the damper information There is provided an electronic keyboard instrument comprising a musical tone signal synthesis means for generating.

  In another preferable aspect, the musical sound signal synthesis means calculates first information indicating a force exerted on the sounding body by the damper using a damper viscosity coefficient calculated from the output damper information. The vibration of the sounding body is calculated based on the force that the operating body calculated from the output excitation information exerts on the sounding body and the equation of motion representing the vibration of the sounding body using the first information. Second information to be expressed is calculated, and the musical sound signal is generated based on the second information.

  In another preferable aspect, the detection means detects the key at a first position in the key pressing range and a second position closer to the rest position than the first position, and the output control means. Detects the second position from the detection time of the first position when the key is detected at the first position by the detecting means and then the key is detected at the second position. The change mode of the damper information is determined such that the degree of suppression of vibration of the sounding body increases faster as the elapsed time up to the time is shorter.

  In another preferred aspect, the output control means, after the detection of the key at the second position, after the holding time that has been determined to be shorter as the elapsed time is shorter, The change mode of the damper information is determined so as to increase the degree of suppressing the vibration of the sounding body.

  According to the present invention, in an electronic keyboard instrument that generates a tone signal in response to a key press, even if the key detection position in the key press range is reduced, a reduction in the accuracy of the damper effect amount reflected in the tone signal is suppressed. be able to.

It is a block diagram which shows the structure of the electronic musical instrument which concerns on embodiment of this invention. It is a figure explaining the structure of the key position sensor which concerns on embodiment of this invention. It is a figure explaining the relationship of the key event conversion part which concerns on embodiment of this invention, a pedal event conversion part, and a musical tone signal synthetic | combination part. It is a flowchart explaining the event conversion process which concerns on embodiment of this invention. It is a figure explaining the state table which concerns on embodiment of this invention. It is a state transition diagram explaining the state control process which concerns on embodiment of this invention. It is a figure explaining the change mode (in the case of action A4) of damper information concerning the embodiment of the present invention. It is a figure explaining the change mode (in the case of action A6) of damper information concerning the embodiment of the present invention. It is a figure explaining the relationship between the change of the position of the key which concerns on embodiment of this invention, and the change of damper information. It is a block diagram which shows the structure of the musical tone signal synthetic | combination part which concerns on embodiment of this invention. It is a block diagram which shows the structure of the musical tone signal synthetic | combination part which has a calculating part which concerns on embodiment of this invention. It is a figure explaining the detection position of the key by the key position sensor which concerns on the modification 1 of this invention. It is a state transition diagram explaining the state control process for damper information determination concerning the modification 1 of this invention. It is a state transition diagram explaining the state control process for excitation information determination which concerns on the modification 1 of this invention. It is a figure explaining the detection position of the key by the key position sensor which concerns on the modification 2 of this invention. It is a figure explaining the relationship between the change of the position of the key which concerns on the modification 3 of this invention, and the change of damper information. It is a state transition diagram explaining the state control process for damper information determination concerning the modification 3 of this invention. It is a figure explaining the content of the state in the state transition diagram of FIG. 17, an event, and an action. It is a figure explaining the structure of a standard grand piano. It is a figure explaining the change of the position of the key which concerns on a standard grand piano, the change of the value equivalent to damper information, and the envelope of the musical sound to generate | occur | produce.

<Embodiment>
[Configuration of electronic keyboard instrument 1]
FIG. 1 is a block diagram showing a configuration of an electronic keyboard instrument 1 according to an embodiment of the present invention. The electronic keyboard instrument 1 is an electronic piano, for example, and includes a control unit 11, a storage unit 12, a user operation unit 13, a performance operation unit 15, and a sound emission unit 17. These units are connected to each other via a bus 18.

  The control unit 11 includes a CPU (Central Processing Unit) 11a, a DSP 11b, other peripheral circuits (not shown), a ROM (Read Only Memory) 11c, a RAM (Random Access Memory) 11d, a signal interface 11e, and an internal bus 11f. A DMA (Direct Memory Access) controller and a video processor may be included as other peripheral circuits. The CPU 11a reads out a control program stored in the ROM 11c, loads it into the RAM 11d and executes it, thereby controlling each part of the electronic keyboard instrument 1 via the bus 18 and performing musical tone signal synthesis processing described later. The signal synthesis unit 100, the key event conversion unit 110 that performs processing for converting a key event into a signal that is input to the musical sound signal synthesis unit 100, and the processing that converts a pedal event into a signal that is input to the musical sound signal synthesis unit 100. The pedal event conversion unit 120 and the like are realized. The RAM 11d functions as a work area when the CPU 11a processes each data.

  The storage unit 12 is storage means such as a hard disk, for example, and stores musical tone control data such as MIDI (Musical Instrument Digital Interface) data, musical tone signals generated by musical tone signal synthesis processing described later, and the like. In this example, the musical tone control data includes data indicating a change in the key depression amount, the damper pedal depression amount, and the shift pedal depression amount (in addition, the hammer speed may be included) according to the time progress. Yes. These data may be loaded from an information storage medium DP (for example, a compact disk) or downloaded from a server via a network, and may not necessarily be stored in the storage unit 12.

  The user operation unit 13 includes an operation panel 13 a and a display unit 14. The operation panel 13a includes, for example, a mouse 13b, an operation switch 13c, a keyboard 13d, and the like. When the user operates the mouse 13b, the operation switch 13c, and the keyboard 13d, data representing the operation content is output to the control unit 11. As a result, the user gives an instruction to the electronic keyboard instrument 1. The display unit 14 is a display device such as a liquid crystal display that displays video on the screen, and is controlled by the control unit 11 to display various screens such as a menu screen. The menu screen may be automatically displayed when power is supplied to the electronic keyboard instrument 1.

  The performance operation unit 15 includes a keyboard unit 15 a and a pedal unit 16. The keyboard portion 15a corresponds to a keyboard portion such as an electronic piano, and includes a plurality of (for example, 88) keys (a black key 15b and a white key 15c, hereinafter referred to as a key 15bc unless otherwise distinguished). Has a keyboard arranged. Here, key numbers are assigned to the keys 15bc, and in this example, numbers are assigned in order from the key 15bc corresponding to the low pitch (key on the left side of the keyboard). Each of the plurality of keys 15bc in the keyboard portion 15a is provided with a key position sensor 15d as detection means for detecting the key position.

FIG. 2 is a diagram illustrating the configuration of the key position sensor 15d according to the embodiment of the present invention. FIG. 2 shows the configuration of the white key 15c and the key position sensor 15d when the white key 15c is viewed from the side along the direction in which the white keys 15c are arranged. The black key 15b is the same as that of the white key 15c, and the description thereof is omitted.
FIG. 2A shows a state in which the white key 15c is at the rest position, and FIG. 2B shows a state in which the white key 15c is pushed and moved to the end position. As shown in FIGS. 2A and 2B, the white key 15c moves around a key support portion 151c that supports the white key 15c in a swingable manner. This movable range is called a key pressing range DW. The white key 15c is configured to move toward the end position when pressed by the user, but to move toward the rest position so that the white key 15c returns toward the rest position when the user does not press the white key 15c.

A rubber dome 150d formed of rubber in a dome shape is fixed to the lower surface of the white key 15c. Projecting portions 151d and 152d formed in a cylindrical shape project downward from the upper surface of the inner surface of the rubber dome 150d. The protrusion 151d is formed longer than the protrusion 152d. The protrusion 151d is provided at a position closer to the key support 151c than the protrusion 152d.
The switch unit 153d is, for example, a membrane switch installed on a frame (not shown) or the like, and has contacts 153da and 153db. When the white key 15c is pushed, the rubber dome 150d is bent so as to be crushed, and the projecting portion 151d contacts the contact point 153da. As a result, the contact 153da is changed from the off state to the on state. When the white key 15c is further pressed, the rubber dome 150d is bent so as to be further crushed, the protruding portion 151d is bent, and the protruding portion 152d is in contact with the contact point 153db. As a result, the contact 153db changes from the off state to the on state. The position of the white key 15c where the protrusion 151d and the contact point 153da come into contact is referred to as a detection position DHA, and the position of the white key 15c where the protrusion 152d and the contact point 153db come into contact is referred to as a detection position DHB.

  When the white key 15c is pushed in and passes through the detection position DHA and the contact 153da changes from the off state to the on state, the keyboard unit 15a outputs the detection information KDHA. Conversely, when the white key 15c is moved from the pressed state toward the rest position and passes through the detection position DHA, and the contact point 153da changes from the on state to the off state, the keyboard portion 15a Detection information KDHA is output. In this way, the keyboard unit 15a outputs the detection information KDHA every time the white key 15c passes the detection position DHA. Similarly, the keyboard unit 15a outputs detection information KDHB every time the white key 15c passes the detection position DHB. Here, the detection information KDHA, KDHB output from the keyboard unit 15a is associated with information indicating a key number that identifies the key 15bc that has passed the detection positions DHA, DHB.

In this example, it is assumed that the information indicating the key number is included in the detection information KDHA and KDHB, but the information indicating the key number is not included in the detection information KDHA and KDHB, and the detection information KDHA and KDDHB and the key are included. Information indicating numbers may be output in association with each other. The information output from the keyboard unit 15a in this way is collectively referred to as a key event hereinafter.
The pushing amount for reaching the white key 15c to the detection position DHA and the pushing amount for reaching the black key 15b to the detection position DHA are set so as to match, but they do not necessarily match. Also good. The same applies to the detection position DHB.

Returning to FIG. 1, the description will be continued. The pedal portion 16 has a plurality of pedals corresponding to the damper pedal 16a and the shift pedal 16b. In addition, the damper pedal 16a and the shift pedal 16b are provided with a pedal position sensor 16c that outputs information indicating the depression amount of the pedal when the pedal is depressed. The pedal unit 16 periodically outputs information PS obtained by converting information representing the pedal depression amount from an analog format to a digital format to the signal interface 11e of the control unit 11 via the bus 18. The pedal unit 16 outputs the information PS in association with the information PC indicating the pedal that has been depressed. The pedal unit 16 may output information indicating the depression amount of the damper pedal 16a and information indicating the depression amount of the shift pedal 16b. The information output from the pedal unit 16 is collectively referred to as a pedal event hereinafter.
Thus, when the user performs a performance operation, the keyboard unit 15a outputs a key event, and the pedal unit 16 outputs a pedal event.

  The sound emitting unit 17 includes a digital / analog converter 17a, an amplifier (not shown), and a speaker 17b. A musical sound signal input under the control of the control unit 11 is converted from a digital format to an analog format in the digital / analog converter 17a, amplified by an amplifier, and output as a sound from the speaker 17b. In this example, this musical tone signal is generated as a result of musical tone signal synthesis processing described later. The above is the description of the configuration of the electronic keyboard instrument 1.

[Functional configuration overview]
Next, the musical tone signal synthesis unit 100, the key event conversion unit 110, and the pedal event conversion unit 120 that are realized by the control unit 11 executing the control program will be described. Note that some or all of the components in the tone signal synthesis unit 100, the key event conversion unit 110, and the pedal event conversion unit 120 described below are PIC (Peripheral Interface Controller), EG (Envelope Generator), DSP ( It may be realized by hardware using a digital signal processor).

The musical sound signal synthesis unit 100 uses the signals input from the key event conversion unit 110 and the pedal event conversion unit 120 to generate a musical sound signal that simulates a sound generated from a grand piano according to a physical model calculation. The physical model calculation is almost the same as that described in Patent Document 1 (Japanese Patent Laid-Open No. 2011-013674) described above, but details of the calculation will be described later.
In this example, a standard grand piano (acoustic piano) is used as the premise of the physical model calculation. This standard grand piano will be described.

[Configuration of Grand Piano 21]
FIG. 19 is a diagram illustrating the configuration of a standard grand piano 21. The grand piano 21 includes a keyboard 21b including 88 keys 21a, a hammer 21c connected to the key 21a via an action mechanism 21d, a string 21e, a damper 21f that can contact the string 21e, a damper pedal 21m, and a shift pedal 21n. Have. The string 21e is connected to a piece 21ea at one end and a bearing 21eb at the other end. Most of the key 21a, the hammer 21c, the action mechanism 21d, the string 21e, and the damper 21f are housed in the cabinet 21h. The number of strings 21e and the number of contact points of the damper 21f vary depending on the sound range. The cabinet 21h, the frame, the wooden frame, the piece 21ea, the bearing 21eb, and other vibration parts (soundboards, columns, etc.) that radiate piano sound constitute the main body 21j. In the following description, a string, a hammer, a damper, and a main body indicate a configuration in the standard grand piano 21, and do not indicate a configuration included in the electronic keyboard instrument 1.

FIG. 20 is a diagram for explaining the relationship between the change in the position of the key 21a related to the standard grand piano 21, the change in the value corresponding to the damper information, and the envelope of the generated musical sound. In the grand piano 21, when the key 21a is depressed in a state where the damper pedal 21m is not depressed, the positional relationship between the string 21e and the damper 21f changes according to the amount of depression.
As shown in the upper part of FIG. 20, when the position of the depressed key 21a is within a certain range (contact area La) from the rest position (rest), the damper 21f contacts the string 21e, and the string 21e The vibration is suppressed. When the position of the depressed key 21a is further within a certain range (intermediate region Lb) on the end position (end) side, the damper 21f gradually moves away from the string 21e as it approaches the end position, and the string 21e. The degree to which the vibrations are suppressed is decreasing. When the position of the depressed key 21a further approaches the end position and is within a certain range (non-contact region Lc) from the end position, the damper 21f is completely separated from the string 21e, and the string 21e The vibration is not suppressed.

The middle part of FIG. 20, as shown in the upper part of FIG. 20, is a value (e _D ^* () corresponding to damper information indicating the degree to which the damper 21f suppresses the vibration of the string 21e when the position of the key 21a is changed over time. t)) changes. When the position of the key 21a is in the contact area La, e _D ^* (t) = 1. When the position of the key 21a is in the intermediate area Lb, 0 <e _D ^* (t) <1. When the position of the key 21a is in the non-contact area Lc, e _D ^* (t) = 0.
The musical sound Env. FIG. 20 is a diagram showing an envelope (volume) of a musical sound generated from the grand piano 21 when time is changed as shown in the upper part of FIG. Note that the horizontal axis of each stage in FIG. 20 indicates time t.

When the position of the key 21a moves in the pattern P1, e _D ^* (t) = 1, and since the hammer 21c does not hit the string 21e, no musical sound is generated. When the position of the key 21a moves in the pattern P2, 0 <e _D ^* (t) <1, but no tone is generated because the hammer 21c does not hit the string 21e. When the position of the key 21a moves in the pattern P3, e _D ^* (t) = 0, but no music is generated because the hammer 21c does not hit the string 21e.
When the position of the key 21a moves in the pattern P4, e _D ^* (t) = 0, and the hammer 21c strikes the string 21e to generate a musical tone. After the sound is generated, e _D ^* (t) increases. Mute. When the position of the key 21a moves in the pattern P5, e _D ^* (t) = 0, and the hammer 21c strikes the string 21e, and a musical tone is generated. After the sound is generated, e _D ^* (t) increases. Mute. At this time, since e _D ^* (t) = 1 is not satisfied, the decrease in the musical tone is more gradual than in the case of the pattern P4. If the position of the key 21a to move in a pattern P6,7 _becomes a ^e D * (t) = 0 which is maintained and also the tone is generated because the hammer 21c strikes the string 21e, after pronunciation strings 21e The vibration is gently reduced without being suppressed by the damper 21f.
The above is the description of the standard grand piano 21 as a premise of the physical model calculation.

[Event conversion overview]
Next, the key event conversion unit 110 and the pedal event conversion unit 120 will be described with reference to FIG.

FIG. 3 is a diagram for explaining the relationship among the key event conversion unit 110, the pedal event conversion unit 120, and the musical tone signal synthesis unit 100 according to the embodiment of the present invention.
As shown in FIG. 3, the pedal event conversion unit 120 acquires a pedal event (information PC, PS) from the pedal unit 16, and generates damper pedal information (damper information based on damper pedal control instead of a key) according to the depression amount of the damper pedal. The pedal event is converted into a signal (hereinafter, referred to as an input signal 3 (e _P (nΔt))) input to the musical sound signal synthesis unit 100 and output. The pedal event conversion unit 120 represents shift pedal information corresponding to the amount of shift pedal depression, and a signal input to the musical sound signal synthesis unit 100 (hereinafter referred to as an input signal 4 (e _S (nΔt)) is Convert pedal events and output. At this time, the pedal event conversion unit 120 determines damper pedal information and shift pedal information from the pedal event using a predetermined conversion formula, table, and the like, and outputs an input signal 3 representing the determined damper pedal information. An input signal 4 representing the determined shift pedal information is output.

Here, the value that the input signal 3 (e _P (nΔt)) can take is in the range of “0” to “1”. When the damper pedal 16a is not depressed, it is “1”. When the damper pedal 16a is depressed by a certain amount, it starts to decrease from “1”. When the damper pedal 16a is fully depressed, it reaches “0” and is fully depressed. The pedal event is converted into the input signal 3 (e _P (nΔt)) by the pedal event conversion unit 120 so that becomes “0”. Similarly, the value that the input signal 4 (e _S (nΔt)) can take is in the range of “0” to “1”. It is “1” when the shift pedal 16b is not depressed, starts to decrease from “1” when depressed a certain amount, reaches “0” immediately before it is fully depressed, and is fully depressed The pedal event is converted into the input signal 4 (e _S (nΔt)) by the pedal event conversion unit 120 so that it becomes “0”.

Also, as shown in FIG. 3, the key event conversion unit 110 acquires a key event from the keyboard unit 15a, and uses the key event as an input signal 1 (e _K (nΔt)) and an input signal 2 (V _H (nΔt)). Convert to and output. The input signal 1 (e _K (nΔt)) represents the degree to which the value suppresses the vibration of the string caused by the damper, that is, the damper information, and is input to the musical sound signal synthesis unit 100. The input signal 2 (V _H (nΔt)) represents a hammer speed (excitation information) and is input to the musical sound signal synthesis unit 100.
At this time, the key event conversion unit 110 determines the damper information and the excitation information from the key event by using an event conversion process described later, outputs the input signal 1 representing the determined damper information, and outputs the determined excitation information. A representative input signal 2 is output. The key event conversion unit 110 outputs the input signal 1 and the input signal 2 in association with information (for example, key number) that can identify each key 15bc corresponding to these signals. That is, in the tone signal synthesis unit 100, the input signal 1 and the input signal 2 are input corresponding to each key 15bc.

The input signal 1, the input signal 2, the input signal 3, and the input signal 4 are respectively input to the musical tone signal synthesis unit 100 as signals on a discrete time axis (t = nΔt; n = 0, 1, 2,...). The In the following description, “nΔt” may be represented by “t” as a continuous value for convenience.
These four signals may be those obtained by the control unit 11 reading out the musical tone control data stored in the storage unit 12 and converted by the key event conversion unit 110 and the pedal event conversion unit 120.

[Configuration of Key Event Conversion Unit 110]
The key event conversion unit 110 includes a conversion control unit 111, a damper information output unit 112, an excitation information output unit 113, and a timer 114. With these configurations, the key event conversion unit 110 realizes a function of converting the key event into the input signal 1 and the input signal 2 and outputting them.
The damper information output unit 112 outputs the input signal 1 (e _K (nΔt)) to the musical sound signal synthesis unit 100 according to the control from the conversion control unit 111.
The excitation information output unit 113 outputs the input signal 2 (V _H (nΔt)) to the musical sound signal synthesis unit 100 according to the control from the conversion control unit 111.
The timer 114 is a free-run counter or the like, and outputs information indicating time to the conversion control unit 111. This information is used by the conversion control unit 111 to time the output interval of the key event from the keyboard unit 15a.

  The conversion control unit 111 performs an event conversion process, acquires a key event output from the keyboard unit 15a, determines a change mode and excitation information of the damper information based on the acquired key event, and determines the determined damper information and Based on the excitation information, the outputs from the damper information output unit 112 and the excitation information output unit 113 are controlled. This event conversion process is started when the function of the key event conversion unit 110 is realized. This event conversion process will be described.

[Event conversion processing]
FIG. 4 is a flowchart for explaining event conversion processing according to the embodiment of the present invention. First, the conversion control unit 111 constructs a state table in which key numbers and state variables are associated with each other, and initializes the state variables as “S1” for all key numbers (1 to 88) (step S110).

  FIG. 5 is a diagram illustrating a state table according to the embodiment of the present invention. In the state shown in FIG. 5, the state variables corresponding to the key numbers are all initialized to “S1”. In this example, state variables in the state table exist from “S1” to “S4”. This state variable corresponds to each state in the state transition diagram described below, and is updated according to the contents of detection information (KDHA, KDHB) output from the keyboard unit 15a. When all the keys 15bc are at the rest position, that is, when the user does not press any key 15bc, the state variable is “S1”.

  Returning to FIG. 4, the description will be continued. The conversion control unit 111 waits for the key event to be output from the keyboard unit 15a (step S120; No). When the key event is output (step S120; Yes), the key number indicated by the output key event. Is specified (step S130). Hereinafter, the specified key number is referred to as a specific key number.

The conversion control unit 111 refers to the state table, acquires a state variable corresponding to the specific key number (step S140), and determines whether the key event output from the keyboard unit 15a is the detection information KDHA or the detection information KDHB. Whether it exists is identified (step S150).
Subsequently, the conversion control unit 111 determines the content to be processed from the acquired state variable and the content of the specified detection information according to a predetermined algorithm (step S160), performs the determined processing, and performs this processing. Determine the state variables to be changed with Then, the conversion control unit 111 updates the state variable corresponding to the specific key number to the determined state variable (step S170). The algorithm for determining the contents to be processed and the state variable to be changed will be described using a state transition diagram.

FIG. 6 is a state transition diagram illustrating state control processing according to the embodiment of the present invention. First, a state is assumed in which the key 15bc is above the detection position DHA (for example, a rest position) (state S1). In the state S1, the conversion control unit 111 specifies the detection information KDHA from the key event output from the keyboard unit 15a (event E1) when the key 15bc is pushed and passes through the detection position DHA. Shift to S2. Along with the transition to the state S2, the conversion control unit 111 starts measuring time (starting time ta) and starts decreasing the damper information from “1” to “0” at a predetermined decrease time Tc. (Action A1). That is, the phenomenon that the damper 21f moves away from the string 21e is reproduced. Thereby, the conversion control unit 111 controls the damper information output unit 112 to output the input signal 1 in the determined change manner of the damper information.
As described above, when the input signal 1 is output, a specific key number is associated. Also, the conversion control unit 111 determines the state variable to be changed as “S2”, and updates the state variable corresponding to the specific key number to “S2” (step S170 in FIG. 4).

In the state S2, the conversion control unit 111 specifies the detection information KDHA from the key event output from the keyboard unit 15a (event E1) by the key 15bc starting to return toward the rest position and passing through the detection position DHA again. In the case, the state is shifted to S1. Along with the transition to the state S1, the conversion control unit 111 ends the time measurement, and determines that the damper information increases at a time corresponding to the time measurement result (elapsed time T _AA from the start time ta) (action A6). ). That is, when the key 15bc passes through the detection position DHA twice in succession, the damper 21f in the grand piano 21 is changed to the string 21e by predicting a temporal change mode of the subsequent damper information from the interval of the passage time. Reproduce the phenomenon of contact. Thereby, the conversion control unit 111 controls the damper information output unit 112 to output the input signal 1 in the determined change manner of the damper information.
When the input signal 1 is output, a specific key number is associated. Also, the conversion control unit 111 determines the state variable to be changed as “S1”, and updates the state variable corresponding to the specific key number to “S1” (step S170 in FIG. 4).

On the other hand, in the state S2, the conversion control unit 111 specifies the detection information KDHB (event E2) from the key event output from the keyboard unit 15a by further pressing the key 15bc and passing through the detection position DHB. Shifts to state S3. With the transition to the state S3, the conversion control unit 111 ends the time measurement and determines the excitation information according to the time measurement result (elapsed time T _AB from the start time ta) (action A2). That is, the phenomenon that the hammer 21c hits the string 21e is reproduced. Thereby, the conversion control part 111 controls the excitation information output part 113, and outputs the input signal 2 according to the determined excitation information.
When the input signal 2 is output, a specific key number is associated. Also, the conversion control unit 111 determines the state variable to be changed as “S3”, and updates the state variable corresponding to the specific key number to “S3” (step S170 in FIG. 4).

In the state S3, the conversion control unit 111 specifies the detection information KDHB (event E2) from the key event output from the keyboard unit 15a by the key 15bc starting to return toward the rest position and passing through the detection position DHB. Is shifted to state S4. Along with the transition to the state S4, the conversion control unit 111 starts timekeeping (starting time tb) (action A3).
Also, the conversion control unit 111 determines the state variable to be changed as “S4”, and updates the state variable corresponding to the specific key number to “S4” (FIG. 4, step S170).

In the state S4, the conversion control unit 111 specifies the detection information KDHB from the key event output from the keyboard unit 15a (event E2) by passing the detection position DHB again by pressing the key 15bc. Transition to state S3. With the transition to the state S3, the conversion control unit 111 ends the time measurement and determines the excitation information according to the time measurement result (elapsed time T _BB from the start time tb) (action A5). That is, the phenomenon in which the hammer 21c hits the string 21e again is reproduced. Thereby, the conversion control part 111 controls the excitation information output part 113, and outputs the input signal 2 according to the determined excitation information.
When the input signal 2 is output, a specific key number is associated. Also, the conversion control unit 111 determines the state variable to be changed as “S3”, and updates the state variable corresponding to the specific key number to “S3” (step S170 in FIG. 4).

On the other hand, in the state S4, the conversion control unit 111 specifies the detection information KDHA from the key event output from the keyboard unit 15a when the key 15bc further returns toward the rest position and passes through the detection position DHA (event E1). If so, the process proceeds to state S1. Along with the transition to the state S1, the conversion control unit 111 ends the time measurement and determines that the damper information increases at a time corresponding to the time measurement result (elapsed time T _BA from the start time ta) (action A4). ). That is, when the key 15bc passes through the detection position DHA after passing through the detection position DHB, the damper 21f in the grand piano 21 is predicted from the time interval of the subsequent damper information based on the interval of the passage time. Reproduces the phenomenon that the string contacts the string 21e. Thereby, the conversion control unit 111 controls the damper information output unit 112 to output the input signal 1 in the determined change manner of the damper information.
When the input signal 1 is output, a specific key number is associated. Also, the conversion control unit 111 determines the state variable to be changed as “S1”, and updates the state variable corresponding to the specific key number to “S1” (step S170 in FIG. 4).
This completes the description of the algorithm for determining the contents to be processed and the state variables to be changed. Next, a method for determining the change mode of the damper information in the actions A4 and A6 will be described.

FIG. 7 is a diagram illustrating a change mode (in the case of action A4) of damper information (value of input signal 1 (e _K (nΔt))) according to the embodiment of the present invention. Figure 7 (a), (b) , (c) , respectively, when the elapsed time _{T BA} coincides with the time _{T 0} previously determined, shorter than _{T 0,} the change of the damper information when longer than _{T 0} The horizontal axis indicates the time, and the vertical axis indicates the value of the input signal 1 (e _K (nΔt)), that is, the damper information. The time ta indicates the time when the key 15bc has passed the detection position DHA and the time measurement is finished in the action A4. Time tr indicates the increase start time of the damper information. This time tr is predicted as the time when the key 15bc reaches the intermediate area Lb. Therefore, after the timing is over, the damper information does not increase during the holding time T _ar (time tr−time ta).
Time te indicates the increase end time of the damper information. This time te is predicted as the time when the key 15bc reaches the boundary portion between the intermediate region Lb and the contact region Lb. Therefore, the damper information increases from “0” to “1” in the increase time T _re (time te−time tr).

As shown in FIG. 7 (a) (b) ( c), as the elapsed time _{T BA} is short, the holding time _{T ar} and increased time _{T re} are determined to be shorter. In this example, the maximum possible time is determined for the holding time T _ar and the increase time T _re . Accordingly, the hold time at the upper limit time T _ar and increased time T _re in the case the elapsed time T _BA is longer than the upper limit time determined in advance. As a result, it is possible to avoid such a situation that the damper information gradually increases so as to be impossible.

By being thus the relationship between the change mode of the elapsed time T _BA and damper information determined, when performing gently key release operation key 15bc was loosely key release operation in grand piano 21 Similarly to the case, the state where the damper 21f gradually increases the degree of suppressing the vibration of the string 21e is reproduced, and when the key release operation is performed suddenly, the state where the vibration of the string 21e is rapidly suppressed is reproduced. can do.

The holding time T _ar and the increase time T _re may be determined as the shortest possible time. In this case, the holding time T _ar and increased time T _re at lower time when the elapsed time T _BA is shorter than the lower limit time determined in advance. Note that the decrease time Tc described in the above-described action A1 may be any time, but is preferably equal to or less than the total time of the shortest time that can be taken by the holding time _Tar and the increase time _Tre. It is further desirable if the time _Tre is less than the shortest possible time.

FIG. 8 is a diagram for explaining a change mode (in the case of action A6) of damper information (value of input signal 1 (e _K (nΔt))) according to the embodiment of the present invention.
In this example, the change mode of the damper information in the case of action A6 is determined to be different from that in the case of action A4, as shown in FIGS. 8 (a), (b), and (c). In this example, as the elapsed time T _AA becomes shorter, the holding time T _ar becomes longer, while the increase time T _re becomes shorter, and the total time thereof (holding time T _ar + increased time T _re ) becomes shorter. It is decided so.
By being thus the relationship between the change mode of the elapsed time T _AA and damper information determined for the case of performing the key release operation after keystroke not force the key 15bc to the end position is also key depression It is possible to reproduce a state in which the degree to which the damper 21f suppresses the vibration of the string 21e is gradually increased according to the time until the key release operation.
Note that the change mode of the damper information in the case of action A6 may be determined as the same as that in the case of action A4.
Further, when the damper information is reduced by the process in action A1 and the process of action A6 is performed before reaching “0”, the damper information may be increased after the damper information reaches “0”. Then, even in the state before reaching “0”, the decrease may be switched to stop and increase, or the damper information may continue to decrease during the holding time _Tar .

FIG. 9 is a diagram for explaining the relationship between the change in the position of the key 15bc and the change in the damper information according to the embodiment of the present invention. FIG. 9 shows changes in damper information when the position of the key 15bc changes in the same pattern as the example (see FIG. 20) in the grand piano 21 described above. As shown in the upper part of FIG. 9, the detection positions DHA and DHB are provided at portions corresponding to the non-contact area Lc in the case of the grand piano 21. The middle part of FIG. 9 shows changes in the damper information (value of the input signal 1 (e _K (nΔt))) when the position of the key 15bc is changed with time as shown in the upper part of FIG.

  The damper information shown in FIG. 9 and the value corresponding to the damper information shown in FIG. 20 are close to each other as long as the pattern of change in the key position is the same as shown in each figure. Although there is a difference in the pattern P2, the difference is almost not in a pronounced state, and has little influence on the reproducibility of the musical sound. Further, although there is a difference in these values from the patterns P5 to P6, in such a case, it is often a gentle key release operation. For this reason, the sound is silenced while the damper information is gradually increasing, and in this case, the reproducibility of the musical tone is hardly affected. In addition, although the manner in which these values are reduced may differ depending on the manner in which the key is pressed, in most cases, the damper information is “0” at the timing of sound generation, so the reproducibility of the musical tone is almost not. Has no effect.

The key event conversion unit 110 has been described above. The key event conversion unit 110 may be provided corresponding to each key 15bc. In this case, the conversion control unit 111 only needs to store the state variable of the key number of the corresponding key 15bc, and is not necessary for specifying the key number in the event conversion process (step S130).
Next, the configuration of the tone signal synthesizer 100 will be described.

[Configuration of Music Signal Synthesis Unit 100]
FIG. 10 is a block diagram showing the configuration of the tone signal synthesizer 100. The musical sound signal synthesizing unit 100 synthesizes a musical sound signal indicating a pseudo piano sound by a physical model composed of a plurality of models (damper model, hammer model, string model, main body model, air model) described below. As described above, the grand piano 21 which is the premise of the physical model calculation has 88 keys 21a on the keyboard 21b. Corresponding to each key 21a, one hammer 21c, one to three strings 21e, and 0 to a plurality of dampers 21f (meaning that they contact the strings at a plurality of points) are provided. The number of strings 21e and the number of dampers 21f are different for each sound range.

  The musical tone signal synthesis unit 100 shown in FIG. 10 includes a comparison unit 101, damper model calculation units 102-1 and 102-2 that calculate a damper model for each corresponding string, a hammer model calculation unit 103 that calculates a hammer model, and a string model. String model calculation units 104-1 and 104-2 for calculating a string for each string, a body model calculation unit 105 for calculating a body model, and an air model calculation unit 106 for calculating an air model.

  The damper model calculation units 102-1 and 102-2 calculate the vibration of a certain string 21e using a damper model. The string model calculation units 104-1 and 104-2 calculate the vibration of a certain string 21e based on the string model. The hammer model calculation unit 103, the main body model calculation unit 105, and the air model calculation unit 106 calculate the vibration of a certain string 21e using the hammer model, the main body model, and the air model, respectively.

  The comparison unit 101 is connected to the damper model calculation units 102-1 and 102-2. The damper model calculation units 102-1 and 102-2 are connected to the string model calculation units 104-1 and 104-2, respectively. The hammer model calculation unit 103 is connected to both the string model calculation units 104-1 and 104-2. The string model calculation units 104-1 and 104-2 are connected to the main body model calculation unit 105. The main body model calculation unit 105 is connected to the air model calculation unit 106. The output signal in the tone signal synthesis unit 100 is a tone signal (hereinafter referred to as a tone signal (P (nΔt))) indicating a waveform of “sound pressure at an observation point in the air” output from the air model calculation unit 106. .

  The musical sound signal synthesis unit 100 shown in FIG. 10 shows a case where a physical model is used in the case where there are two corresponding strings 21e in a specific key 21a. That is, the musical tone signal obtained by the musical tone signal synthesizing process of the musical tone signal synthesizing unit 100 shown in FIG. 10 is based on a physical model in the case where there are two corresponding strings 21e in the specific key 21a. For this reason, string model calculation units 104-1 and 104-2 for calculating string models are connected in parallel to the body model calculation unit 105 for calculating the body model. Here, in the specific key 21a, if there are three or more corresponding strings 21e, the string model calculation unit 104-iw (iw = 3,4,. ..) And the damper model calculation unit 102-iw (iw = 3, 4,...) Connected to the string model may be increased.

Since there are a plurality of keys 21 a in the grand piano 21, the musical sound signal synthesis unit 100 actually corresponds to each key 21 a, the comparison unit 101, the damper model calculation unit 102, the hammer model calculation unit 103, and the string model. A string model calculation unit 104 having a set of calculation units 104 and corresponding to each key 21 a is connected to the main body model calculation unit 105. In FIG. 10, if all of these configurations are described, 88 sets are required, and the description becomes complicated. Therefore, the portion of the configuration focusing on a specific key 21a having two corresponding strings 21e is shown. The musical tone signal synthesis unit 100 with the extracted configuration is shown.
Since the input signals 1 and 2 described above are output from the key event conversion unit 110 corresponding to the key number, they are input to the comparison unit 101 and the hammer model calculation unit 103 corresponding to the key number.
Hereinafter, a physical model of the tone signal synthesis process will be described.

First, in the physical model of the musical tone signal synthesis process in the musical tone signal synthesis unit 100 in this example, the following 27 assumptions are made.
(Assumption 1) Gravity is ignored.
(Assumption 2) It is assumed that a string in a state where it is straightly stopped by receiving an axial force (hereinafter referred to as a static equilibrium state) has an elongated cylindrical shape.
(Assumption 3) The thickness of the string is assumed to be unchanged. That is, the beam theory is adopted.
(Assumption 4) The cross section perpendicular to the central axis of the chord is assumed to be flat after deformation and perpendicular to the central axis. That is, Bernoulli Euler's assumption is adopted.
(Assumption 5) The amplitude of the string is small but not necessarily very small.
(Assumption 6) The strings are assumed to be homogeneous.
(Assumption 7) The string stress is given as the sum of a component proportional to strain and a component proportional to strain rate. That is, it is assumed that internal viscous damping (also referred to as rigidity proportional viscous damping) acts on the string.
(Assumption 8) One end of the string is supported by a point on a bearing which is a part of the main body, and the other end is supported by a point on a piece which is a part of the main body. (The string shall not be constrained from rotating at the support end.)
(Assumption 9) The action / reaction between the string and air is ignored.
(Assumption 10) The shape of the portion in contact with the string of the hammer (hereinafter referred to as the tip of the hammer) is assumed to be cylindrical, the bottom radius of the cylinder is infinitely small, and the height of the cylinder is the other string To the extent that it does not interfere with.
(Assumption 11) When there are a plurality of strings corresponding to one hammer, the central axes of these strings in a static equilibrium state are on the same plane.
(Assumption 12) When there are a plurality of strings corresponding to one hammer, the one hammer has the same number of hammer tips as the number of the strings.
(Assumption 13) The direction of the central axis of the tip of the hammer (cylinder) is orthogonal to the direction of the central axis of the string (cylinder) in a static equilibrium state.
(Assumption 14) The center of gravity of the hammer moves only on one straight line.
(Assumption 15) The movement direction of the center of gravity of the hammer is orthogonal to both the direction of the central axis of the tip of the hammer (cylinder) and the direction of the central axis of the string (cylinder) in a static equilibrium state.
(Assumption 16) It is assumed that the direction in which the hammer deforms coincides with the movement direction of the center of gravity of the hammer.
(Assumption 17) The hammer compression force-compression amount relational expression is assumed to be given by a function whose exponent should be a positive real number.
(Assumption 18) It is assumed that there is no friction between the hammer tip and the string surface.
(Assumption 19) The action / reaction between the hammer and air is ignored.
(Assumption 20) For a string equipped with a damper, the resistance force by the damper that tries to stop the bending vibration of the string acts on a point on the central axis of the string (hereinafter referred to as a sound stop point). .
(Assumption 21) The resistance force-speed relational expression of the damper is given by a linear expression.
(Assumption 22) It is assumed that the amplitude of the main body is very small.
(Assumption 23) It is assumed that the main body can be approximately treated as a proportional viscous damping system.
(Assumption 24) The reaction that the main body receives from the air is ignored.
(Assumption 25) Air is assumed to be homogeneous.
(Assumption 26) It is assumed that the air pressure-volume strain relational expression is given by a linear expression.
(Assumption 27) It is assumed that the air has no vortex.

  Further, the right-handed system (x, y, z) is used to represent the object coordinates of the string in this example. Here, the x axis is aligned with the central axis of the string in a static equilibrium state, the bearing side support end is the origin (0, 0, 0), and the piece side support end is included in the region where x> 0. The direction of the x-axis is determined, and the direction of movement of the hammer center of gravity when struck is determined as the positive direction of the z-axis. Further, the right-handed system (X, Y, Z) is used to represent the body and air object coordinates. Time progress (time variable) is represented by t.

  Hereinafter, symbols representing each parameter described in this example will be described.

  The following “Equation 1” to “Equation 5” are information input in the calculation of each model. “Equation 1” is a parameter (time variation parameter) that varies with time. On the other hand, “Equation 2” to “Equation 5” are parameters that do not vary with the progress of time (time invariant parameters) and are preset.

  The following “Equation 1” indicates a parameter relating to performance, that is, a parameter corresponding to an input signal in the musical tone signal synthesis unit 100. Keys, strings, hammers, dampers, and main bodies indicate the components 21a, 21e, 21c, 21f, and 21j of the standard grand piano 21, respectively.

  The following “Equation 2” is a parameter relating to design.

  The following “Equation 3” is a parameter related to the design of the main body and the position of the observation point in the air.

  The following “Equation 4” is a parameter related to tuning.

  The following “Equation 5” is a parameter related to numerical calculation.

  The following “Equation 6” is information output by calculation of each model, that is, a musical tone signal.

  The following “Equation 7”, “Equation 8”, and “Equation 9” are other parameters necessary for calculation of each model.

Here, in the case where there is one string corresponding to one hammer, if Z _B , X _B , Y _B , and θ _H are given, β _k′k is uniquely determined. When there are a plurality of strings corresponding to one hammer, β _k′k is uniquely determined when Z _B , X _B , and Y _B are given.

  The following “Equation 10” is an explanation of an index described as a superscript in each parameter.

  Hereinafter, the processing contents of each unit of the tone signal synthesis unit 100 in this example will be described in order with reference to FIG. In the following description, if all the indexes are written, the formula becomes complicated and difficult to read.

In addition, “1” is set as an initial value (value at t = 0) in the variables e _K (t), e _P (t), and e _S (t). That is, the key (black key 15b, white key 15c) is not depressed, and the damper pedal 16a and shift pedal 16b are not depressed. Further, it is assumed that “0” is set as an initial value for all other variables relating to “t”.

The comparison unit 101 acquires the input signal 1 (e _K (nΔt)) and the input signal 3 (e _P (nΔt)), and outputs the smaller value as e _D (nΔt). Therefore, e _D (nΔt) = e _K (nΔt) when the damper pedal 16a is not depressed. This is expressed by the following formula (1). Note that the input signal 1 (e _K (nΔt)) is a signal output from the key event conversion unit 110 as described above, and its value corresponds to the damper information. The input signal 3 (e _P (nΔt)) is a signal output from the pedal event conversion unit 120.

[Damper model]
The damper model calculation unit 102 calculates the damper model calculation unit 102-1 that calculates the damper corresponding to the first string (iw = 1), and the damper model calculation that calculates the damper corresponding to the first string (iw = 2). Part 102-2. In the following description, only the index of the string is different, so that the damper model calculation unit 102 will be described. When there are three or more strings, as described above, the damper model calculation unit 102-iw (iw = 3,4,...) Is replaced with the string (iw = 3,4,...). It may be provided in correspondence.

  The string model calculation unit 104 includes a string model calculation unit 104-1 for calculating the first string (iw = 1) and a string model calculation unit 104-2 for calculating the first string (iw = 2). In the following description, the string model calculation unit 104 is described because only the string index is different. When there are three or more strings, the string model calculation unit 104-iw (iw = 3, 4,...) May be provided in parallel to the main body model 105 as described above. . (The calculation of the string model calculation unit 104 will be described later.)

The damper model calculation unit 102 outputs e _D (nΔt) output from the comparison unit 101 and u _k (x _D , nΔt) (k = 1, 3) output from the string model calculation unit 104 as described later. And using these, f _Dk (nΔt) obtained as a result of the following calculation is output to the string model calculation unit 104.

  Hereinafter, the calculation in the damper model calculation unit 102 will be described.

  The piano string in the initial state is in a state where vibration is suppressed by the damper. As the piano keys are pushed in, the corresponding dampers gradually move away from the corresponding strings and eventually the strings are completely released from the resistance of the dampers to prepare for hammering. In the piano, the degree of contact between the damper and the string can be changed not only by the key depression amount but also by the depression amount of the damper pedal, and the way of stopping the sound and the degree of string resonance can be finely controlled.

The mechanism of the damper in such a piano can be expressed concisely by the relational expression between the resistance force f _Dk (t) of the damper and the deformation amount u _k (x _D , t) of the damper shown in the following formula (2). it can.

In this example, by substituting e _D (nΔt) output from the comparison unit 101 into the equation (2), an amount “b _D e _D (nΔt)” corresponding to the viscosity coefficient of the damper is changed to a discrete time axis ( (t = nΔt; n = 0, 1, 2,...), the idea of sequentially changing the sound is to enable natural and continuous stop and string resonance control similar to a natural musical instrument piano.
The above is the description of the damper model calculation unit 102.

[Hama model]
The hammer model calculation unit 103 acquires the input signal 2 (V _H (nΔt)) and the input signal 4 (e _S (nΔt)), and outputs u ₁ output from the string model calculation unit 104 as described later. (X _H , nΔt) is acquired, and using these, f _H (nΔt) obtained as a result of the following calculation is output to the string model calculation unit 104. Note that the input signal 2 (V _H (nΔt)) is a signal output from the key event conversion unit 110 as described above. The input signal 4 (e _S (nΔt)) is a signal output from the pedal event conversion unit 120.

  Hereinafter, the calculation in the hammer model calculation unit 103 will be described.

  When Newton's law of motion is applied to the assumptions regarding the physical model described above, Hammer's equation of motion is written as shown in Equation (3).

  The relational expression between the force exerted by the hammer tip on the string surface and the amount of compression of the hammer is as shown in Expression (4).

  However, when the hammer tip is in contact with the string surface, the equation (5) is applied, and when the hammer tip is separated from the string surface, the equations (6) and (7) are applied.

When the hammer speed V _H (t) is given based on the excitation information obtained by the event conversion process in the key event conversion unit 110 as described above, under the condition that the hammer tip is away from the string surface, The state of the hammer may be initialized as w _H (t) = W _H , dw _H (t) / dt = V _H (t).

Now, what is the mechanism of a shift pedal in a piano? When you depress it, the position of the hammer shifts to the treble side, changing the part that contacts the string of the hammer, or incomplete contact between the hammer and some strings In this example, by substituting the input signal 4 (e _S ^[iS] (nΔt)) into the equation (4), the elastic coefficient of the hammer is controlled. The equivalent amount K _H e _S ^[iS] (nΔt) is sequentially changed on the discrete time axis (t = nΔt; n = 0, 1, 2,. It enables natural and continuous tone control. The above is the description of the hammer model calculation unit 103.

[String model]
The string model calculation unit 104 outputs f _Dk (nΔt) (k = 1, 3) output from the damper model calculation unit 102 and f _H (nΔt) output from the hammer model calculation unit 103, which are forces acting on the strings. In addition, as described later, u _Bk (nΔt) (k = 1, 2, 3) output from the main body model calculation unit 105 is acquired, and the results obtained by performing the following calculation using these are obtained. F _Bk (nΔt) (k = 1, 2, 3) is output to the main body model calculation unit 105, and u _k (x _D , nΔt) (k = 1, 3) is output to the damper model calculation unit 102. Then, u ₁ (x _H , nΔt) is output to the hammer model calculation unit 103.

  Hereinafter, calculation in the string model calculation unit 104 will be described.

  When the Newton's law of motion is applied to the assumptions regarding the physical model described above, the equation of motion of the string is written as in the equations (8), (9), and (10).

  However, in the equations (8) and (10), the nonlinear term due to the finite amplitude is omitted because the effect due to this is small. Similarly, in the formula (9), the force applied by the hammer in the chord axis direction is omitted because the effect of the force is small. Equation (8) is the bending vibration of the string corresponding to the movement direction of the hammer center of gravity, Equation (10) is the bending vibration of the string corresponding to the direction orthogonal to the movement direction of the hammer gravity center, and Equation (9) is Corresponds to the vertical vibration of the strings.

  Further, the string boundary condition is written as in the equations (11) and (12).

  Now, “string displacement” is expressed by the sum of “relative displacement with respect to a straight line connecting two support ends” and “displacement of a straight line connecting two support ends”, and further, “two support ends. "Relative displacement with respect to a straight line connecting the two" is expressed by "a finite Fourier sine series with an arbitrary time function as a coefficient". That is, “string displacement” is expressed by equation (13). Here, the sine function included in Expression (13) is nothing but the natural vibration mode of the string when the displacement at the string support end of the string center axis is constrained. Further, “a linear displacement connecting two support ends” means “a static displacement of a string due to a displacement of a string support end”.

At this time, the expression (13) satisfies the boundary condition expressions (11) and (12) for an arbitrary time t.
After substituting equation (13) into the partial differential equation (equations (8), (9), (10)), sin (ikπx / l) (ik = 1, 2,..., Mk; k = 1 , 2, 3) and integrating in the interval “0 ≦ x ≦ l”, the following second-order ordinary differential equations (Equations (14), (15), (16)) are derived.

  The relational expression between the force exerted by the string on the string support end and the support end displacement is written as in Expressions (25) and (26).

  Further, by substituting equation (13) into equations (25) and (26), equations (28) and (29) are derived. However, the terms related to nonlinear terms and rotational inertia were omitted.

  Further, the displacement of the string hitting point and the sound stopping point is written as in the equations (30) and (31) from the equation (13).

  The above is the description of the string model calculation unit 104.

[Body model]
The body model calculation unit 105 obtains f _Bk (nΔt) output from the string model calculation unit 104, and uses this to calculate A _C (nΔt) obtained as a result of the following calculation. 106, and u _Bk (nΔt) (k = 1, 2, 3) is output to the string model calculation unit 104.

  Hereinafter, the calculation in the main body model calculation unit 105 will be described.

  Based on the assumptions regarding the physical model described above, the equation of motion of the main body can be described as a second-order ordinary differential equation (equation (32)) for each mode as follows.

  By the way, the main body of the piano is made of wood, metal, etc. Among them, wood has the feature that “the vibration damping ability of the high frequency component is larger than the low frequency component”, and this is the piano ( It is also the cause of the “sound that is comfortable in the ears and warm” that is peculiar to a musical instrument whose main body is made of wood. Such acoustic properties of wood can be explained by modeling wood as “a material having three-dimensional orthotropic anisotropy in both elastic modulus and structural damping coefficient” (for example, Reference 1: Japan). The Society of Mechanical Engineers (ed.). Advanced Composite Materials, pp.68-70. Gihodo Publishing, 1990.).

The main body model configured to include “a material having three-dimensional orthogonal anisotropy in both elastic modulus and structural damping coefficient” is also called a general structural damping system (non-proportional structural damping system or general hysteresis damping system). Therefore, the attenuation matrix cannot be diagonalized by real eigenvalue analysis (Reference Document 2), but here, by ignoring the off-diagonal terms of the attenuation matrix, the proportional structure damping system ( It is also referred to as a proportional hysteresis damping system).
(Reference 2: Akio Nagamatsu. Modal analysis. Baifukan, 1985.)

Further, the proportional damping system is approximated by a proportional viscous damping system, that is, the mode damping ratio is expressed by “mode structure damping coefficient / 2”. At this time, the natural angular frequency, mode damping ratio, and natural vibration mode included in Equation (32) are calculated by performing real eigenvalue analysis using a commercial finite element method software on the body of an arbitrary three-dimensional shape. can do. Here, the mode damping ratio should be an approximate mode damping ratio, but here, it is simply referred to as a mode damping ratio for convenience.
The displacement of the string support end can be calculated by using the following formula (34).

  The above is the description of the main body model calculation unit 105.

[Following equations of motion]
Next, an example of solving the equation of motion in each of the above models will be described. In the following description, the equation of motion of the hammer (the above equation (3)), the equation of motion for each mode of the string (the above equations (14), (15), (16)), and the equation of motion for each mode of the main body (the above equation ( 32)) will be collectively referred to as “hammer-string-body motion equation”. By substituting the above equations (2), (4), (5), (6), (28), (29), (30), (31), (34) into these equations of motion, variables _{f Dk} that represents the interaction between the structure _{^{[iD] (t), f}} H [iW] (t), w e (t), f Bk [iB] (t), u 1 (x H, t), If u _k (x _D ^[iD] , t) and u _Bk ^[iB] (t) are deleted, the “hammer-string-body equation of motion” gives the displacement w _H (t) of the center of gravity of the hammer, each string Displacement A _k ^[mk] (t) (m _k = 1, 2,..., M _k ; k = 1, 2, 3) on the mode coordinates of the natural vibration mode, each natural vibration mode mode of the main body This is a simultaneous nonlinear ordinary differential equation related to the displacement A _C ^[m] (t) (m = 1, 2,..., M) on the coordinates. Now, by setting a state before performance, that is, a stationary state as an initial condition, the problem dealt with here can be considered as a so-called “initial value problem of simultaneous nonlinear ordinary differential equations”. The “initial value problem of simultaneous nonlinear ordinary differential equations” can be converted into a problem in which simultaneous nonlinear algebraic equations are sequentially solved on a discrete time axis by using some numerical integration method (reference document 3).
(Reference 3: The Japan Society of Mechanical Engineers. Fundamentals and applications of numerical integration. Corona, 2003.)
Below are some examples of solutions.

[How to solve the whole]
First, we show how to solve the equations of motion for the hammer model, string model, and body model all together. Applying the Newmark β method to the above “hammer-string-body motion equation” (simultaneous nonlinear ordinary differential equation), “hammer center of gravity acceleration or acceleration increment”, “mode coordinates of each natural vibration mode of the string Simultaneous accelerations and acceleration increments "and" acceleration or acceleration increments on the mode coordinates of each natural vibration mode of the main body "can be derived and simultaneous nonlinear algebraic equations can be derived. Here, the reason for writing “acceleration or acceleration increment” is that the numerical integration method known as the Newmark β method has two algorithms: an algorithm that makes acceleration an unknown quantity, and an algorithm that makes acceleration increment an unknown quantity. This is due to the existence of streets.

  The Newton method is applied to the simultaneous nonlinear algebraic equations, or the linear linear algebraic equations are derived by the interval linearization method (Reference 3), and then the direct method (for example, LU decomposition method) or the iterative method (for example, conjugate method). By applying the gradient method, the calculation unit 107 described below can sequentially determine the unknown amount on the discrete time axis. Thus, the structure in the case of calculating by the method which solves the whole collectively is demonstrated using FIG.

FIG. 11 is a block diagram showing a configuration of a musical tone signal synthesis unit 100A having the calculation unit 107 according to the embodiment of the present invention. The musical sound signal synthesis unit 100A that performs computation by a method that solves the whole collectively includes a comparison unit 101, a computation unit 107, and an air model calculation unit 106Z.
The operation unit 107 performs an operation using the “hammer-string-main body equation of motion” that summarizes the calculations in the damper model calculation unit 102, the hammer model calculation unit 103, the string model calculation unit 104, and the main body model calculation unit 105. Do. The computing unit 107 obtains e _D (nΔt) from the comparison unit 101, obtains the input signal 2 (V _H (nΔt)) and the input signal 4 (e _S (nΔt)). The above-mentioned unknown amount is sequentially calculated and determined by an operation using the “hammer-string-body motion equation”. Here, information (d / dt (A _C (nΔt))) indicating “the speed of each natural vibration mode of the main body on the mode coordinates” among the unknown quantities is output to the air model calculation unit 106Z. The air model calculation unit 106Z is different from the air model calculation unit 106 only in input information, and the air model calculation described below is performed in the same manner.

  Here, the “velocity on the mode coordinates of each natural vibration mode of the main body” is “the nth order derivative (n = 1, 2,... Regarding the time of displacement on the mode coordinates of each natural vibration mode of the main body”.・) 」. The velocity can be easily calculated as a numerical derivative of the displacement when the displacement is known and as a numerical integral of the acceleration when the acceleration is known.

[Method to solve for each partial structure]
Subsequently, a method of solving the equation of motion of the hammer model, the string model, and the body model for each partial structure (hereinafter, the hammer model calculation unit 103, the string model calculation unit 104, and the body model calculation unit 105 are collectively referred to as a partial structure). Indicates. In this method, the variables f _H ^[iW] (t), f _Bk ^[iB] (t), u ₁ representing the interaction between the substructures eliminated in the explanation of the “hammer-string-body motion equation” above. (X _H , t), u _k (x _D ^[iD] , t), u _Bk ^[iB] (t) values are calculated explicitly, and these values are transferred between the partial structures. The calculation is advanced every time.

  When this solution is used, when solving the equation of motion of the hammer (the above equation (3)), an unknown quantity relating to the string and the body is included, and the kinematic mode equation of motion (the above equations (14), (15), ( When solving 16)), unknown quantities related to the main body are included, but the unknown quantities related to the strings and the main body are extrapolated from past values, etc., and are calculated repeatedly. The calculation can be carried out stably. The following are three examples based on the difference in the numerical integration method.

A “method for deriving a difference equation” will be described as a first example.
The central difference method is applied to the equation of motion of the hammer (the above equation (3)), the equation of motion for each mode of the string (the above equations (14), (15), (16)) and the equation of motion of each mode of the main body. A series of difference equations is derived by applying the bilinear sz transformation method to (Equation (32) above). Each difference equation can be solved by a general second-order IIR filter operation. In this method, “displacement of the center of gravity of the hammer”, “displacement of each natural vibration mode of the string on the mode coordinates”, and “displacement of the natural vibration mode of the main body on the mode coordinates” are defined as unknown quantities. Is sequentially determined on the discrete time axis.

As a second example, the “Galarkin method” will be described.
For the equation of motion of the hammer (the above equation (3)), the equation of motion for each mode of the string (the above equations (14), (15), (16)) and the equation of motion for the mode of the main body (the above equation (32)) By applying the Galerkin method (Reference 4) using a cubic function related to time as a test function, the acceleration and jerk on the mode coordinates of each natural vibration mode of the string An algorithm is obtained in which “acceleration” and “acceleration and jerk on mode coordinates of each natural vibration mode of the main body” are unknown quantities and their values are sequentially determined on a discrete time axis. Here, when the Galerkin method using a quaternary function as a test function instead of a cubic function with respect to time is used, an algorithm having acceleration, jerk, and jerk as unknown quantities is obtained.
(Reference 4: Yukio Kagawa. Vibration / acoustic engineering by finite element method / Basics and applications. Baifukan, 1981.)

As a third example, the “Newmark β method” will be described.
For the equation of motion of the hammer (the above equation (3)), the equation of motion for each mode of the string (the above equations (14), (15), (16)) and the equation of motion for the mode of the main body (the above equation (32)) By applying the Newmark β method, “acceleration or acceleration increment of hammer center of gravity”, “acceleration or acceleration increment on mode coordinates of each natural vibration mode of string”, and “natural vibration mode of main body” An algorithm that sequentially determines the values on the discrete time axis with the acceleration or acceleration increment on the mode coordinates as an unknown quantity can be obtained.

[Intermediate method between solving the whole and solving each partial structure]
An intermediate method between the above-described “method of solving the whole as a whole” and “method of solving each partial structure” can also be used. For example, the hammer model and the string model may be collected together and the body model may be solved separately, or the hammer model may be solved first and the string model and the body model may be solved together.

  In addition, as described above, “displacement on the mode coordinate of each natural vibration mode of the main body”, “displacement on the mode coordinate of each natural vibration mode of the main body”, and “displacement on the mode coordinate of each natural vibration mode of the main body” which are unknown quantities For each of these displacements, there may be acceleration, jerk, etc. depending on the solution. Furthermore, considering that the velocity can be easily calculated as a numerical derivative of displacement or as a numerical integral of acceleration, “displacement of hammer center of gravity”, “displacement of each natural vibration mode of the string on the mode coordinates”, and Each displacement of “displacement on the mode coordinates of each natural vibration mode of the main body” may be an n-order derivative (n = 1, 2,...) Related to the time of displacement. The same can be said for other displacements. For example, the displacement of the string support end may be an nth derivative (n = 1, 2,...) Related to the time of the displacement.

[Air model (acoustic radiation calculation)]
The air model calculation unit 106 acquires A _C (nΔt) output from the main body model calculation unit 105, and outputs P (nΔt) obtained as a result of performing the following calculation using this.

  Hereinafter, calculation in the air model calculation unit 106 will be described.

  The unsteady sound pressure at an arbitrary observation point in the air radiated from the main body having an arbitrary three-dimensional shape is expressed by the following equation, that is, “the velocity and air on the mode coordinates of each natural vibration mode of the main body. Convolution integration of "impulse response function between sound pressures at the observation point in the middle" and "velocity on the mode coordinates of each natural vibration mode of the main body" is performed for each natural vibration mode of the main body, and the sum of them is calculated. It can be calculated by the method of

H ^{[iP] [iG]} (ω) included in the equation (37), that is, “the frequency response function between the velocity of each acoustic radiation element of the main body and the sound pressure at the observation point in the air” is arbitrary 3 It can be calculated by performing frequency response analysis using a commercial boundary element method software on a dimensional shape main body on a discrete frequency axis. Equation (36) can be calculated by a general IFFT (Inverse Fast Fourier Transform) operation, and the integral included in Equation (35) can be calculated by a general FIR (Finite Impulse Response) filter method.

Thus, Ac ^[m] (nΔt) (m = 1, 2,..., M) or Ac ^[m] (nΔt) (m = 1, 2,...) Output from the body model calculation unit 105. , M) using the derivative with respect to time, the output signal from the air model, that is, the sound pressure P ^[iP] (t = nΔt; n = 0, 1, 2,...) nΔt) (i _P = 1, 2,..., I _P ) can be calculated sequentially and output as a musical tone signal.

Here, by using a technique called fast convolution in which the convolution operation in the equation (35) is performed in the frequency domain instead of the time domain, the speed can be further dramatically increased. At this time, the IFFT calculation included in the high-speed convolution may be performed after taking the sum of the frequency domain convolution results for each main body natural vibration mode, and does not need to be performed for each natural vibration mode of the main body.
The above is the description of the configuration of the tone signal synthesizer 100.

In this way, the tone signal synthesis unit 100 has a rich and three-dimensional sound produced by three-dimensional vibration of the entire instrument, a ringing sound that can be heard when a string in the middle / low range is struck, a key press depth and a pedal. It is possible to generate a pseudo piano sound that realistically expresses the characteristics of a natural instrument piano sound, such as various musical nuances linked to the depth of depression. In addition, these characteristics can be controlled in the same way as a natural musical instrument piano.
At this time, even if the detection position of the key 15bc in the key pressing range DW is reduced, the effect of the damper to be reflected in the musical sound signal by predicting the temporal change mode of the damper information from the passage times of the plurality of detection positions. The decrease in accuracy can be suppressed. Therefore, even if such a key 15bc is used, various musical nuances can be expressed.

Specific examples of the realistic characteristics of the piano sound of a natural musical instrument include the following. For example, by changing parameters such as chord length (= distance between chord support points) or striking ratio (= “string length” / “distance between bearing side chord support end and strut point”), ringing sound It becomes possible to control the level. In the following, this ringing sound will be described in particular using equation (15). However, in order to make the explanation easy to understand, in the equation (15), the description will be made according to the equation (38) in which the displacement of the string support end, the displacement in the string y direction, and the internal viscosity damping coefficient of the string are omitted. .

Equation (38) is a motion equation of the longitudinal vibration second i _2-order natural vibration of the strings, by regarding the right and periodic external force, it can be thought of as the equation of motion of the single-degree-of-freedom viscous damping forced vibration system. As is well known, the general solution of this equation is composed of the sum of a damped free vibration solution (a general solution of homogeneous equations) and a sustained forced vibration solution (a special solution of inhomogeneous equations). The property of the forced vibration solution is that the system vibrates at a frequency of a periodic external force, the amplitude increases as the frequency approaches the natural frequency of the system, and resonates when they coincide. Now, it is assumed that each natural vibration related to the bending vibration of the string is a harmonic vibration, that is, it is written as in Expression (39).

  At this time, the inside of the right side {} of Expression (38) is derived as Expression (40).

Now, with i ₂ fixed, paying attention to the sequence created by the term cos2π (f ₁ ^[m1] + f ₁ ^{[m1 + i2]} ) t included in the equation (40), “the second (2m ₁ + i of this sequence) ₂ ) When the deviation of the secondary frequency f ₁ ^[m1] + f ₁ ^{[m1 + i2] from} the harmonic series frequency is calculated, when i ₂ is small, the value is “bending vibration number (2m ₁ + i ₂ )”. It can be confirmed that the frequency is about 1/4 of the deviation from the harmonic sequence frequency of the second natural frequency f ₁ ^{[2m1 + i2]} . By analyzing the piano sound of a natural instrument, it is known that "the partial sequence of piano has a sub-sequence whose frequency deviation from the harmonic sequence is about 1/4 of the main sequence" Therefore, the sequence created by the term applies to the subsequence. As i ₂ increases, this “deviation amount” gradually increases.

In addition, the sequence generated by the term cos2π (f ₁ ^[m1] + f ₁ ^[i2−m1] ) t included in the equation (40) also contributes to the formation of the subsequence, provided that the degree of contribution is It can be understood that it is smaller than the term.

The formula obtained by substituting the formula (40) into the formula (38) is that the (2m ₁ + i ₂ ) th order frequency f ₁ ^[m1] + f ₁ ^{[m1 + i2] of the} subsequence is the i th of the longitudinal vibration of the string. resonance phenomenon when matching the _secondary natural frequency represents that occur. This is a characteristic phenomenon of the piano sound of a natural instrument, “There are sub-sequences in the partial sequence of pianos whose frequency deviation from the harmonic sequence is about 1/4 of the main sequence” In addition, “when the frequency of the odd-order partial sound of the sub-sequence matches the odd-order natural frequency of the longitudinal vibration of the string, or the frequency of the even-order partial sound of the sub-sequence is When it matches the even-order natural frequency, the level of the sub-sequence partial sound increases and this becomes a ringing sound. When the sum of the natural frequencies matches the odd-order natural frequency of the longitudinal vibration of the string, or the sum of a set of odd-order natural frequencies of the bending vibration of the string, or a set of even-order natural frequencies Ringing sound when the sum of is equal to the even natural frequency of the longitudinal vibration of the string. For but generated "it (ref 5), is intended to provide a mathematical description.
(Reference 5: J. Ellis. Longitudinal model in piano strings: Results of new research. Piano Technicians journal, pp.16-23, May 1998.)

Furthermore, with respect to the roaring phenomenon such as “Rin Ling” and “Hin Hin”, for example, the frequency of the sub-sequence 15th (= 7 + 8 = 2 × 7 + 1) order and the sub-sequence 15th (= 6 + 9 = 2 × 6 + 3) order is Since it is slightly different, it can be explained that the difference in frequency produces a sag. The terms cos2π (f ₁ ^[m1] −f ₁ ^{[m1 + i2]} ) t and cos2π (f ₁ ^[m1] −f ₁ ^[i2−m1] ) t included in the equation (44) This indicates the presence of a partial sound having a frequency slightly higher than the natural frequency.

  Now, when the material constant of the string is fixed, the longitudinal vibration natural frequency of the string depends only on the string length from the equation (18). Note that this is not the case for wound strings (strings in which a copper wire is wound around a steel core wire) that is normally used in the bass range of a piano.

  In the range of about 30th to 40th keys of a standard 88-key piano, the frequency and string of the 15th (= 7 + 8 = 2 × 7 + 1) th sub-sequence are caused by the setting of the string length. In some cases, the fundamental natural frequency of the vertical vibration is close. Even in such a case, setting the stringing ratio to “7” or “8” can avoid an excessive increase in ringing sound level.

  This is because the 15th (= 7 + 8 = 2 × 7 + 1) th subsequence is a product of the 7th and 8th natural vibrations of the bending vibration, but the stringing ratio is “7” or “8”. This is because the “7” th order or “8th” order natural vibration of the bending vibration is lost, and the 15th (= 7 + 8 = 2 × 7 + 1) th subsequence is not generated. Even in this case, the fifteenth (= 6 + 9 = 2 × 6 + 3) order of the subsequence still exists, but these do not resonate with the fundamental natural vibration of the longitudinal vibration.

  As described above, the generation mechanism of ringing sound and the design factors (string length, string striking ratio) that control the level have been explained, but the vertical vibration of the string itself has little ability to radiate sound in the air. In order for the ringing sound to be heard as a sound, in addition to the “string non-linear (finite amplitude) vibration mechanism” just described, the “three-dimensional coupled vibration mechanism between the string and the body” (“attachment angle of the string to the body”) Needless to say, design factors such as “frame shape” are included) and “three-dimensional acoustic radiation mechanism of the main body” (including “frame shape” is also included).

  By the way, in the development field of natural instrument pianos, the improvement of piano sound is nothing but finding the overall optimal solution of a complex system called the piano. This is particularly inefficient for a huge acoustic structure having many design factors and error factors, such as pianos, which have variations in physical properties of natural materials and variations in work by humans such as sounding. Since the present invention quantitatively clarifies the causal relationship between the specification (cause) and the sound (result) of the piano, it contributes to the improvement of piano development efficiency as a design simulator. In addition to the above, an advantage of the musical sound synthesis method based on the physical model is that a supernatural effect (for example, a remarkably large piano that is difficult to produce in reality) can be virtually generated.

<Modification>
As mentioned above, although embodiment of this invention was described, this invention can be implemented in various aspects as follows.
[Modification 1]
In the embodiment described above, the detection position of the key 15bc in the key pressing range DW is two points of the detection positions DHA and DHB, and the damper information and the excitation information are determined by the passage of the key 15bc at the detection positions DHA and DHB. However, the two detection positions used for determining the damper information and the two detection positions used for determining the excitation information may be provided separately. In this case, there are four detection positions. In this case, the number of sets of protrusions and contacts in the key position sensor 15d may be four.

  FIG. 12 is a diagram for explaining the detection position of the key 15bc by the key position sensor 15d according to the first modification of the present invention. As shown in FIG. 12, the detection positions DA and DB used for determining the damper information in the conversion control unit 111 are provided in a portion corresponding to the non-contact area Lc in the case of the grand piano 21. Similarly, the detection positions HA and HB used for the determination of excitation information in the conversion control unit 111 are provided in a portion corresponding to the non-contact region Lc in the case of the grand piano 21. The four detection positions are arranged in the order of detection positions DA, HA, DB, and HB from the rest position side. It is assumed that detection information output when the key 15bc passes through the detection positions DA, DB, HA, and HB is KDA, KDB, KHA, and KHB, respectively.

In such a configuration, the conversion control unit 111 constructs a damper information determination state table and an excitation information determination state table, and determines damper information determination state control processing and excitation information determination state control processing. And in parallel. Specifically, it is performed as follows.
When the conversion control unit 111 acquires a state variable (FIG. 4, step S140), the conversion control unit 111 refers to each state table and acquires the state variable for each state control process. Then, in step S150 (FIG. 4), the conversion control unit 111 determines the processing content based on the state control process for determining the damper information when any of the detection information KDA and KDB is specified from the key event. (Step S160) On the other hand, when one of the detection information KHA and KHB is specified from the key event, the processing content is determined based on the state control processing for determining excitation information (Step S160). An algorithm for determining the processing contents based on the state control process for determining the damper information will be described with reference to the state transition diagram shown in FIG. Further, an algorithm for determining the processing content based on the state control processing for determining excitation information will be described with reference to the state transition diagram shown in FIG.

  FIG. 13 is a state transition diagram for explaining the state control process for determining damper information according to the first modification of the present invention. FIG. 14 is a state transition diagram illustrating state control processing for determining excitation information according to the first modification of the present invention. The state transition diagram shown in FIG. 13 is a configuration in which a portion related to damper information is extracted from the state transition diagram according to the embodiment shown in FIG. On the other hand, the state transition diagram shown in FIG. 14 is a configuration in which a portion related to excitation information is extracted from the state transition diagram according to the embodiment shown in FIG. Therefore, detailed description of these will be omitted.

As described above, the detection position for determining the damper information and the detection position for determining the excitation information are separately divided, so that the difference between the operation of the damper 21f and the operation of the hammer 21c according to the change in the position of the key 21a. Can be reproduced more accurately.
In the first modification, the four detection positions are arranged in the order of the detection positions DA, HA, DB, and HB from the rest position side, but in the order of the detection positions HA, DA, DB, and HB. Alternatively, the detection positions HA, DA, HB, and DB may be in this order, or the detection positions DA, HA, HB, and DB may be in this order. Moreover, the order of detection positions DA, DB, HA, and HB may be used, or the order of detection positions HA, HB, DA, and DB may be used. This may be set as appropriate depending on the type of musical instrument to be reproduced.

[Modification 2]
In the first modification described above, the four detection points DA and DB for determining the damper information and the detection positions HA and HB for determining the excitation information are used. These detection positions may be used.

FIG. 15 is a diagram for explaining the detection position of the key 15bc by the key position sensor 15d according to the second modification of the present invention. As shown in FIG. 15, for example, a detection position DBHA in which the detection position DB and the detection position HA in Modification 1 are made common may be provided. When the key 15bc passes, the detection information KDBHA is output. In the state control process in the first modification, the process when the detection information KDB and the detection information KHA are specified is performed when the detection information KDBHA is specified. To do so.
The combination to be shared may be another combination. That is, the detection position DA and the detection position HA may be shared, the detection position DB and the detection position HB may be shared, or the detection position DA and the detection position HB may be shared.

[Modification 3]
In the embodiment and the modification described above, the detection position of the key 15bc in the key pressing range DW is two points, and the damper information is determined by the passage of the key 15bc at the two detection positions. The damper information may be determined using the detected position. In Modification 3, a case will be described in which, in addition to the detection positions DA and DB in Modification 1, two detection positions DC and DD are added to provide four points. Here, when the key 15bc passes through the detection positions DC and DD, detection information KDC and KDD are output, respectively.

FIG. 16 is a diagram for explaining the relationship between the change in the position of the key 15bc and the change in the damper information according to the third modification of the present invention. FIG. 16 is a diagram corresponding to FIG. 9 described in the embodiment. As shown in the upper part of FIG. 16, the detection positions DC and DD are provided in a portion corresponding to the contact area La in the case of the grand piano 21, and the detection position DC exists on the rest position side from the detection position DD. The detection positions DA and DB are used in the same manner as in the first modification when the damper information is increased in principle. On the other hand, the detection positions DC and DD are used when the damper information is reduced in principle.
In such a configuration, an algorithm for determining the processing content based on the damper information determination state control processing in the conversion control unit 111 will be described with reference to state transition diagrams shown in FIGS. 17 and 18.

  FIG. 17 is a state transition diagram illustrating a state control process for determining damper information according to the third modification of the present invention. FIG. 18 is a diagram for explaining the contents of states, events, and actions in the state transition diagram of FIG. First, a state where the key 15bc is above the detection position DC (for example, a rest position) is assumed (state S1). In the state S1, the conversion control unit 111 specifies the detection information KDC from the key event output from the keyboard unit 15a (event E1) by passing the detection position DC by pressing the key 15bc. Shift to S2. Along with the transition to the state S2, the conversion control unit 111 starts measuring time (starting time tc) (action A1).

In the state S2, the conversion control unit 111 specifies the detection information KDC from the key event output from the keyboard unit 15a (event E1) by the key 15bc starting to return toward the rest position and passing through the detection position DC again. In the case, the state is shifted to S1. With the transition to the state S1, the conversion control unit 111 ends the time measurement (action A3).
On the other hand, in the state S2, the conversion control unit 111 specifies the detection information KDD from the key event output from the keyboard unit 15a (event E2) by further pressing the key 15bc and passing through the detection position DD. Shifts to state S3. With the transition to the state S3, the conversion control unit 111 ends the time measurement, determines that the damper information is decreased at a time corresponding to the time measurement result (elapsed time T _CD from the start time tc), and measures the time again. Is started (start time td) (action A2). Here, the shorter the elapsed time T _CD, determined as the damper information is reduced in a short time. That is, when the key 15bc passes through the detection position DD after passing through the detection position DC, the damper 21f in the grand piano 21 is predicted from the time interval of the subsequent damper information from the interval of the passage time. Reproduces the phenomenon of the alienating from the string 21e.

When the key 15bc returns toward the rest position and passes through the detection position DD in the state S3, the conversion control unit 111 specifies the detection information KDD from the key event output from the keyboard unit 15a (event E2). Shifts to state S8. With the transition to the state S8, the conversion control unit 111 ends the time measurement, determines that the damper information increases at a time corresponding to the time measurement result (elapsed time T _DD from the start time td), and measures the time again. Is started (set to start time td). (Action A5). Here, it is determined that the damper information increases in a shorter time as the elapsed time T _DD is shorter. That is, when the key 15bc passes the detection position DD from the rest position side and again passes the detection position DD from the end position side, the temporal change mode of the subsequent damper information is predicted from the interval of the passage time. Then, the phenomenon that the damper 21f of the grand piano 21 contacts the string 21e is reproduced. In action A5, conversion control unit 111 may determine that the damper information increases at a predetermined time regardless of elapsed time T _DD .
On the other hand, in the state S3, the conversion control unit 111 specifies the detection information KDA (event E3) from the key event output from the keyboard unit 15a by further pressing the key 15bc and passing through the detection position DA. Shifts to state S4. Along with the transition to the state S4, the conversion control unit 111 once ends the time measurement started in the actions A2 and A8, and starts again (sets to the start time ta) (action A1).

When the key 15bc returns toward the rest position and passes through the detection position DA in the state S4, the conversion control unit 111 specifies the detection information KDA from the key event output from the keyboard unit 15a (event E3). Shifts to state S7. With the transition to the state S7, the conversion control unit 111 finishes timing, determines that the damper information increases at a time corresponding to the timing result (elapsed time T _AA from the start time ta), and again counts time. Is started (start time ta) (action A6). Here, the change mode of the damper information may be the same as that shown in FIG.
On the other hand, in the state S4, the conversion control unit 111 specifies the detection information KDB from the key event output from the keyboard unit 15a (event E4) by further pressing the key 15bc and passing through the detection position DB. Shifts to state S5. With the transition to the state S5, the conversion control unit 111 ends the time measurement (action A3).

  In the state S5, the conversion control unit 111 specifies the detection information KDB from the key event output from the keyboard unit 15a (event E4) by returning the key 15bc toward the rest position and passing through the detection position DB. Shifts to state S6. Along with the transition to this state S6, the conversion control unit 111 starts timekeeping (starting time tb) (action A1).

In the state S6, the conversion control unit 111 specifies the detection information KDB from the key event output from the keyboard unit 15a (event E4) when the key 15bc is pushed in again and passes through the detection position DB. The state is shifted to S5. With the transition to the state S5, the conversion control unit 111 ends the time measurement (action A3).
On the other hand, the conversion control unit 111 specifies the detection information KDA from the key event output from the keyboard unit 15a when the key 15bc further returns toward the rest position and passes through the detection position DA in the state S6 (event E3). If so, the process proceeds to state S7. With the transition to the state S7, the conversion control unit 111 ends the time measurement, determines that the damper information increases at a time corresponding to the time measurement result (elapsed time T _BA from the start time tb), and measures the time again. Is started (start time ta) (action A4). Here, the change mode of the damper information may be the same as that shown in FIG.

In the state S7, the conversion control unit 111 specifies the detection information KDA (event E3) from the key event output from the keyboard unit 15a by pressing the key 15bc again and passing through the detection position DA. Transition to state S4. Along with the transition to the state S4, the conversion control unit 111 ends the time measurement, determines that the damper information is decreased by a time corresponding to the time measurement result (elapsed time T _AA from the start time ta), and measures the time again. Is started (start time ta) (action A7). Here, as the elapsed time _TAA is shorter, the damper information is determined to decrease in a shorter time. That is, when the key 15bc passes the detection position DA from the end position side and again passes the detection position DA from the rest position side, the temporal change mode of the subsequent damper information is predicted from the interval of the passage time. Then, the phenomenon that the damper 21f in the grand piano 21 is separated from the string 21e is reproduced. Note that in action A7, conversion control section 111, the elapsed regardless of the time T _AA, may be determined so as to reduce the time that the damper information is determined in advance.
On the other hand, the conversion control unit 111 specifies the detection information KDD from the key event output from the keyboard unit 15a when the key 15bc further returns toward the rest position and passes through the detection position DD in the state S7 (event E2). If so, the process proceeds to state S8. Along with the transition to this state S8, the conversion control unit 111 once ends the timing started in actions A4 and A6, and starts again (sets to the start time td) (action A1).

In the state S8, the conversion control unit 111 specifies the detection information KDB from the key event output from the keyboard unit 15a (event E2) by the key 15bc being pushed in again and passing through the detection position DB. Transition to state S3. Along with the transition to the state S3, the conversion control unit 111 finishes timing, determines that the damper information is decreased in a time corresponding to the timing result (elapsed time T _DD from the start time td), and again counts time. (Start time td) is started (action A8). Here, as the elapsed time T _DD is shorter, the damper information is determined to decrease in a shorter time. That is, when the key 15bc passes the detection position DD from the end position side and passes the detection position DD from the rest position side again, a temporal change mode of the subsequent damper information is predicted from the interval of the passage time. Then, the phenomenon that the damper 21f in the grand piano 21 is separated from the string 21e is reproduced. Note that in action A8, conversion control section 111, the elapsed regardless of the time T _DD, it may be determined so as to reduce the time that the damper information is determined in advance.
On the other hand, the conversion control unit 111 specifies the detection information KDC from the key event output from the keyboard unit 15a when the key 15bc further returns toward the rest position and passes through the detection position DC in the state S8 (event E1). If so, the process proceeds to state S1. With the transition to the state S1, the conversion control unit 111 ends the time measurement (action A3).

  This completes the description of the algorithm for determining the processing content based on the damper information determination state control processing in the third modification. Note that an algorithm for determining the processing content based on the state control process for determining excitation information in the third modification may be the same as that in the first modification.

[Modification 4]
In the embodiment described above, when the detection position DHA is located at the boundary portion between the intermediate region Lb and the non-contact region Lc shown in FIG. 9, the holding time _Tar shown in FIGS. 7 and 8 is set to “0”. Also good. The same applies to the detection position DA in the modified example.
In the embodiment, the detection position DHA is preferably closer to the end position than the boundary portion between the intermediate region Lb and the non-contact region Lc when the reproduction of the operation of the hammer 21c is mainly designed, while the operation of the damper 21f When the reproduction is mainly designed, it is often desirable to be close to the boundary. Therefore, the detection position DHA is configured to be present on the end position side with respect to the boundary portion between the intermediate region Lb and the non-contact region Lc, and the holding time _Tar is included in the prediction of the damper information. On the other hand, when it is not necessary to consider such a situation, the detection position DHA can be positioned at the boundary between the intermediate region Lb and the non-contact region Lc as in the present modification.

[Modification 5]
In the embodiment described above, as shown in FIGS. 7 and 8, the manner in which the damper information increases at the increase time _Tre is expressed by a mode in which the damper information increases linearly with a constant slope, that is, by a linear function related to time. However, it may be increased in a curve as represented by a function of quadratic or higher, or may be an aspect in which the slope of the straight line changes during the increase time _Tre . Then, parameters such as coefficients used for these functions may be changed according to the elapsed time.

[Modification 6]
In the embodiment and the modification described above, the detection position of the key 15bc in the non-contact area Lc in the key pressing range DW is two points, and the degree to which the damper information is increased passes the key 15bc at the two detection positions. However, it may be determined using detection positions of more points. In this case, the conversion control unit 111 may perform the process of action A4 (see FIG. 6) in the embodiment based on the time measurement result using the two detection positions closest to the rest position.

Further, in the embodiment, the elapsed time between two points is used, but the elapsed time between two points among three or more detection positions is timed in a plurality of combinations, and the damper information according to the time measurement result. The change mode may be determined. That is, in the elapsed time measurement result obtained from the combination of one detection position, the moving speed of the key 15bc can be calculated, while using the elapsed time measurement results obtained from a plurality of combinations, the key 15bc Acceleration, jerk, etc. can be calculated. Therefore, it is possible to improve the accuracy of predicting the change mode of the damper information by predicting the change mode of the damper information in consideration of the acceleration and jerk rather than predicting the change mode of the damper information based only on the speed of the key 15bc. . For example, the prediction accuracy of the holding time _Tar and the increase time _Tre can be improved. Moreover, the change mode in the increase time _Tre can be predicted as various modes as shown in the fifth modification.

[Modification 7]
In the embodiment described above, the conversion control unit 111 uses the two detection positions DHA and DHB in the determination of excitation information. However, only one of the detection positions may be used. For example, when the key 15bc passes the detection position DHB, predetermined excitation information may be determined.

[Modification 8]
In the embodiment described above, the position of the key 15bc is detected by the mechanical structure using the protrusions 151d and 152d and the contacts 153da and 153db. However, the key 15bc is detected at a plurality of detection positions. As long as the position can be detected, the key position sensor 15d may be realized by other configurations such as an optical detection configuration. For example, for optical detection, a plurality of sets of light emitting units such as LEDs and light receiving units such as optical sensors provided on the optical path of light from the LEDs (Light Emitting Diodes) are provided, and the key 15bc is pushed in. If the optical path is blocked one by one each time the detection position is reached, the position of the key 15bc can be detected from the presence or absence of light reception by the light receiving unit.

[Modification 9]
In the embodiment described above, the electronic keyboard instrument 1 has the damper pedal 16a and the shift pedal 16b, but either one or both may not be present. If the damper pedal 16a is not present, the input signal 3 (e _P (nΔt)) = 1 may be treated as needed. Further, when there is no shift pedal 16b, the input signal 4 (e _S (nΔt)) = 1 may be treated as needed.

[Modification 10]
In the above-described embodiment, for example, in order to function as the electronic keyboard instrument 1 that generates sound in response to the operation of the keyboard unit 15a and the pedal unit 16, the tone signal synthesis processing is performed in real time, but according to the tone control data. For example, in the case of generating a sound, non-real time processing may be used. In this case, the musical tone control data may include information indicating the timing at which the key 15bc passes the detection positions DHA and DHB instead of the key pressing amount.

  In this case, for example, using the musical tone control data for one song, the “speed data on the time axis for each natural vibration mode of the instrument main body” is calculated first, and the data and the “natural vibration of the main body” are calculated. It can also be said that the convolution operation with “impulse response or frequency response data between the mode and the observation point in the air” is performed later. This means that tone synthesis can be easily performed when only the position of the observation point is changed.

[Modification 11]
In the embodiment described above, the tone signal synthesis process is a synthesis process of a tone signal simulating the sound of the grand piano 21. However, the tone generator such as a string that vibrates and vibrates, and a string by operating a key. A musical tone signal that simulates the sound of any keyboard instrument is synthesized as long as it is a keyboard instrument having an action body such as a hammer that excites vibration by striking it and a damper that applies vibration to the string and suppresses vibration. It may be a thing. For example, harpsichord, celesta and the like can be mentioned. The harpsichord has a string as a sounding body, a plectorum (a claw that plays the string) as an action body, and a damper that suppresses vibration of the string. The Celesta has a sound plate of a metal piece as a sounding body, a hammer that strikes a sound plate as an action body, and a damper that suppresses vibration of the sound plate.

[Modification 12]
In the above-described embodiment, the tone signal synthesis unit 100 performs the tone signal synthesis process for generating the tone signal by the physical model calculation. However, even if the tone signal synthesis unit 100 generates the tone signal by a configuration other than the physical model calculation. Good. For example, the tone signal may be generated by a configuration used for a PCM (pulse code modulation) sound source, an FM (Frequency Modulation) sound source, or the like. In this case, the tone signal synthesizer 100 controls parameters that reproduce the state of suppressing the vibration of the sounding body according to the value (damper information) of the input signal 1 (e _K (nΔt)) that is input. For example, the cutoff frequency, gain, volume level, etc. of the filter may be controlled.

[Modification 13]
The control program in the above-described embodiment is provided in a state stored in a computer-readable recording medium such as a magnetic recording medium (magnetic tape, magnetic disk, etc.), an optical recording medium (optical disk, etc.), a magneto-optical recording medium, or a semiconductor memory. Can do. Further, the electronic keyboard instrument 1 may download the control program via a network.

DESCRIPTION OF SYMBOLS 1 ... Electronic keyboard instrument, 11 ... Control part, 11a ... CPU, 11b ... DSP, 11c ... ROM, 11d ... RAM, 11e ... Signal interface, 11f ... Internal bus, 12 ... Memory | storage part, 13 ... User operation part, 13a ... Operation panel, 13b ... mouse, 13c ... operation switch, 13d ... keyboard, 14 ... display unit, 15 ... performance operation unit, 15a ... keyboard unit, 15b ... black key, 15c ... white key, 15d ... key position sensor, 151c ... Key support part, 150d ... Rubber dome, 151d, 152d ... Projection part, 153d ... Switch part, 153da, 153db ... Contact, 16 ... Pedal part, 16a ... Damper pedal, 16b ... Shift pedal, 16cc ... Pedal position sensor, 17 ... Release Sound part, 17a ... digital / analog converter, 17b ... speaker, 18 ... bus, 21 ... grand piano, 2 a ... key, 21b ... keyboard, 21c ... hammer, 21d ... action mechanism, 21e ... string, 21ea ... piece, 21eb ... bearing, 21f ... damper, 21h ... cabinet, 21j ... main body, 21m ... damper pedal, 21n ... shift pedal, DESCRIPTION OF SYMBOLS 100,100A ... Music signal synthesis | combination part, 101 ... Comparison part, 102-1, 102-2 ... Damper model calculation part, 103 ... Hammer model calculation part, 104-1, 104-2 ... String model calculation part, 105 ... Main body Model calculation unit 106, 106Z ... Air model calculation unit 107 ... Calculation unit 110 ... Key event conversion unit 111 ... Conversion control unit 112 ... Damper information output unit 113 ... Excitation information output unit 114 ... Timer 120 ... Pedal event converter

Claims (5)

A musical tone signal simulating a sound generated from an acoustic keyboard instrument having an action body that excites vibration of a sounding body in response to an operation on a key and a damper that applies force to the sounding body in accordance with the operation and suppresses the vibration An electronic keyboard instrument that generates
A key provided to be movable within a predetermined key pressing range according to the operation;
Detecting means for detecting the key at a plurality of detection positions in the key pressing range;
State variable update means for updating the state variable of the key based on the detection result by the detection means;
Excitation information output means for outputting excitation information indicating parameters for exciting vibration of the sounding body by the acting body;
Damper information output means for outputting damper information indicating parameters for suppressing vibration of the sounding body by the damper;
The detection result by the detecting means and on the basis of said state variable to determine the excitation information to be the output, and the state variable, based on the time when the key is detected at each detecting position by the detecting means, wherein Output control means for determining a change mode of the output damper information ;
An electronic keyboard instrument comprising: a tone signal synthesis means for generating a tone signal indicating a sound corresponding to the vibration of the sounding body determined based on the output excitation information and the damper information. The musical sound signal synthesis means includes:
Using the damper viscosity coefficient calculated from the output damper information, the first information indicating the force exerted on the sounding body by the damper is calculated,
Based on a force applied to the sounding body by the operating body calculated from the output excitation information and a motion equation representing the vibration of the sounding body using the first information, 2 information,
The electronic keyboard instrument according to claim 1, wherein the musical tone signal is generated based on the second information. The detection means detects the key at a first position in the key pressing range and a second position closer to the rest position than the first position,
The output control means detects the key at the first position by the detecting means and then detects the key at the second position, and then detects the second from the detection time of the first position. The change mode of the damper information is determined so that the degree of suppression of vibration of the sounding body increases faster as the elapsed time until the position detection time is shorter. Electronic keyboard instrument described in 1. The output control means includes
After the detection of the key at the second position, after the holding time that has been determined to be shorter as the elapsed time is shorter, to increase the degree of suppressing the vibration of the sounding body, The electronic keyboard instrument according to claim 3, wherein a change mode of the damper information is determined. The detection position of the key in the detection result used by the output control means for determining the excitation information is different from the detection position of the key at the time used by the output control means for determining the change mode of the damper information. Have
The electronic keyboard instrument according to any one of claims 1 to 4, wherein

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