JPH0754433B2 - Music synthesis method - Google Patents

Description

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a musical tone synthesizing method used in electronic musical instruments and the like, and more particularly to a musical tone synthesizing method for synthesizing a musical tone signal by a modulation method.

[Conventional technology]

Conventionally, as a tone synthesis method for synthesizing tone signals by modulation calculation, a frequency modulation (FM) method as disclosed in Japanese Patent Publication No. 54-33525 is known. In the tone synthesis method using the frequency modulation method, the tone signal is synthesized by performing an operation based on the following equation, for example.

sin (θ + Ksinβ) = J0 (K) sinθ + J1 (K) {sin (θ + β) −sin (θ−β)} + J2 (K) {sin (θ + 2β) −sin (θ−2β)} + …… (1 ) However, θ = wct, wc; carrier angular frequency β = wmt, wm; modulated wave angular frequency K; modulation index J (K); coefficient based on Bessel function [Problems to be solved by the invention] FIG. 4 ( (B) is a diagram showing an example of the frequency spectrum of the waveform obtained by the calculation of the above equation (1), in which both the carrier frequency θ and the modulating wave frequency β are 100 Hz.
Is shown. As shown in this figure, the waveform of the equation (1) has a negative frequency component. Since sin (−α) = − sinα (2), the negative frequency component in FIG. 4 (a) is inverted and then folded back to the corresponding positive frequency component position. (B) is obtained. FIG. 4C shows the magnitude of each component in FIG. 4B. As is clear from FIG. 4 (c), the spectrum envelope (broken line E in FIG. 4 (c)) oscillates in the tone signal obtained by the calculation of equation (1). This tendency becomes more remarkable as the modulation index K is increased to obtain higher harmonic components. The occurrence of vibration in such a spectrum envelope is convenient for synthesizing musical sounds such as plucked string instruments, but is not preferable for synthesizing brass sounds or analog synthesizer musical sounds.

Therefore, an object of the present invention is to provide a musical tone synthesizing method capable of synthesizing a musical tone signal having a spectrum envelope that does not vibrate and has a smoothly changing spectrum envelope.

[Means for solving problems]

This invention converts musical tone signals to exp (K1 · F1 (wmt)) · F2 (wct + K2 · F3 (wmt))
(3) where: wc is the carrier angular frequency wm is the modulated wave angular frequency K1 and K2 are synthesized based on the formulas of the modulation index. Where the functions F1 (X), F2
(X) and F3 (X) are cosX or sinX, respectively. For example, F1 (X) = cosX, F2 (X) = cosX, F3 (x) = cosX, F1 (X) = sinX, F2 (X) = sinX, F3 (x) = sinX, F1 (X X) = cosX, F2 (X) = cosX, F3 (x) = sinX.

[Action]

No negative frequency component is generated in the calculation result of the equation (3), and the spectrum envelope of the side wave (harmonic wave) is smoothly increased or decreased, and no vibration is generated. FIGS. 5A to 5D show spectrum examples of the musical tone signal obtained by the calculation of the equation (3). In both of these figures, wm and wc in the formula exp (K1coswmt) · cos (wct + K2sinwmt) (4), which is one concrete example of the formula (3), are 2π, and the values of K1 and K2 are respectively. This is the case when the same values 1, 2, 4, and 8 are used. The numbers on the horizontal axis are the orders of harmonics, and the vertical axes are the amplitudes.

[Embodiment] When wct = θ and wmt = β are set in the above formula (4), the formula exp (K1cosβ) · cos (θ + K2sinβ) (5) is obtained.

The first embodiment shown in FIG. 1 is a circuit for synthesizing a tone signal based on the equation (5). That is, in FIG. 1, COS tables 1 and 2 are ROMs that output data cosx for input data x, SIN table 3 is a ROM that outputs data sinx for input data x, and e ^x
Table 5 is a ROM that outputs data e ^x with respect to input data x. Now, when the data β is applied to the COS table 1 and the SIN table 3, cos β and sin β are output from the COS table 1 and the SIN table 3, respectively, and applied to the multipliers 6 and 7. The multipliers 6 and 7 multiply cosβ and sinβ by K1 and K2, and output the multiplication results K1cosβ and K2sinβ, respectively. The K1cosβ output from the multiplier 6 is converted into ^eK1cosβ by the e ^x table 5 and supplied to the multiplier 9. On the other hand, K2sinβ output from the multiplier 7 is supplied to the adder 11, where θ is added, and the addition result (θ + K2sin
β) is supplied to COS table 2. COS table 2 is
Receives the output (θ + K2sinβ) of the adder 11 and outputs cos (θ + K2si
nβ) is output and supplied to the multiplier 9. The multiplier 9 multiplies the output of the e ^x table 5 by the output of the COS table 2 and outputs e ^K1cosβ · cos (θ + K2sinβ) (6) as a result of this multiplication. The output of this multiplier 9 is D / A (digital /
If analog conversion is performed, a tone signal based on the equation (5) can be obtained.

FIG. 2 is a block diagram showing the configuration of the second embodiment of the present invention. In the embodiment shown in this figure, logarithmic operation is used, and multiplication is performed by addition. In FIG. 2, LOG / COS tables 12 and 13 are a table (ROM) that outputs log (cos x) for input data x, LOG / SI.
N table 14 shows log (sin
x) is output, and the e ^x tables 15 to 17 are the same tables as the e ^x table 5 in FIG. L now
When β is supplied to the OG / COS table 12 and the LOG / SIN table 14, respectively, log (cos
β), log (sin β) are output and supplied to the adders 18 and 19. The adders 18 and 19 are log (cos β) and log (sin β), respectively.
LogK1, logK2 are added to, and the addition result log (K1cosβ),
log a (K2sinβ) respectively output to e ^x tables 15 and 16. e
^{The x} tables 15 and 16 convert log (K1cosβ) and log (K2sinβ) into K1cosβ and K2sinβ, and output them to the adders 21 and 22, respectively.
That, e ^x tables 15 and 16 serves to return the log data to the original linear data. The adder 22 adds θ to K2sinβ and outputs the addition result (θ + K2sinβ) to LOG ・ COS
Output to table 13. LOG / COS table 13 is (θ +
K2sinβ) is converted into log {cos (θ + K2sinβ)} and output to the adder 21. The output of the adder 21 is e ^x Table 15 K1cos
β and output of LOG / COS table 13 log {cos (θ + K2sin
β)} is added, and the addition result is output to the ^ex table 17. Here, since K1cosβ = log e ^K1cosβ (7), the output of the adder 21 becomes log {e ^K1cosβ · cos (θ + K2sinβ)} (8). e ^x Table 17 returns the output of the adder 21 (log data) to the original linear data. That is, the e ^x table 17 receives the data of the above formula (8) and outputs e ^{K1 cosβ} · cos (θ + K2sinβ) (9). By performing D / A conversion on the output of the table 17, a musical tone signal based on the equation (5) can be obtained.

In the above embodiment, the musical tone is synthesized based on the equation (5), but it is possible to synthesize a more complicated musical tone by using the following equation.

exp (jθ + K1e ^jβ1 + K2e ^jβ2 + ... Kne ^jβn ) ...
(10) exp {jθ1 + K1 (jθ2 + K2e ^jβ ) (11) The above are the first and second embodiments of the present invention. According to these embodiments, it is possible to synthesize a musical tone signal having a spectrum envelope in which the harmonic spectrum envelope does not vibrate and smoothly changes. The reason will be described below.

The equation (5) is obtained by ^{modifying the} basic equation exp (jθ + Ke ^jβ ) (12). That is, above (12)
When the formula is transformed by applying the formula e ^jX = cosX + j sinX e ^{X + jY} = e ^X (cosX + j sinY), exp (jθ + Ke ^jβ ) = e ^Kcosβ・ cos (θ + Ksinβ) + je ^Kcosβ・ sin (θ
+ Ksinβ) (13) The following equation is obtained. When a musical sound is formed by this formula, only the real part is audible. Therefore, even if a musical tone signal is formed based on the equation (12), even if a musical tone is formed based on the equation e ^Kcosβ · cos (θ + Ksinβ) (14), the same musical tone can be formed in terms of hearing. . Then, the above equation (5) is
Only the two values in equation 4) are different.

Now, by transforming the above equation (12), exp (jθ + Ke ^jβ ) = exp (jθ) · exp (Ke ^jβ ) ...
(15) becomes equation is obtained, in this equation, applying ^{e x = 1 + (X /} 1!) + (X 2/2!) + (X 3/3!) + ··· becomes the official, exp ( ^Jθ + Ke ^jβ ) = exp (jθ) + Ke ^{j (θ + β)} + {K ² e
^{j (θ + 2β)} / 2! + {K ³ e ^{j (θ + 3β)} / 3!} + ... (16) The following equation is obtained. As is clear from this equation, (1
No negative frequency component is generated in the calculation result of equation (2), and the side wave (harmonic) spectrum envelope smoothly increases and decreases according to the coefficient (K ⁿ / n!), Causing vibration. There is no. Then, the same spectrum characteristic can be obtained by the equation (5).

Next, an application example of the present invention will be described. FIG. 3 is a block diagram showing a configuration example of an electronic musical instrument to which the present invention is applied.
In this figure, a keyboard circuit 30 outputs a key code KC of a key pressed on a keyboard (not shown), and also outputs a key-on signal KON which becomes "1" while the key is pressed. The tone color selection circuit 31 has a plurality of tone color selection switches, and a tone code corresponding to the operation state of the switches.
Output TC. When the key code KC is supplied from the keyboard circuit 30, the phase data generation circuit 32 forms phase data that sequentially changes at a rate corresponding to the pitch of the key indicated by this key code KC, and this phase data is converted into the data β. Is output sequentially. The formation of the phase data is performed, for example, by accumulating frequency information numerical values compared with the pitch of the key in a constant cycle. The θ calculation circuit 33 calculates the data β according to the tone color indicated by the tone code TC (for example, constants determined according to the tone code TC (for example, “1”, “2” ...
“1/2”, “1/3”, etc.) are multiplied) and the result of this operation is output as data θ. Envelope generator 34
Changes according to the tone color indicated by the tone code TC, and
The modulation index K1 (t), K2 (t) (or its logarithmic data logK1 (t), logK2 (t)) and the amplitude data A (t) whose values change sequentially with the passage of time after the rise of the key-on signal KON It is a circuit that occurs.

The waveform calculation circuit 35 is the same circuit as that shown in FIG. 1 or FIG. 2, and the data β, θ, K1 (t), K2 (t) (or logK1
Based on (t), logK2 (t), musical tone waveform data e ^K1cosβ · cos (θ + K2sinβ) is formed and output to the multiplier 36. Here, COS in Fig. 1
The table 1, the SIN table 3, and the LOG / COS table 12 and the LOG / SIN table 14 shown in FIG. 2 will be further described. These tables 1, 3 or 12, 14 have COS wave, S
Digital sampling values obtained by sampling one cycle of the IN wave at fixed time intervals or logarithmic values thereof are stored in order from address 0. Therefore, when the above-mentioned data β is applied to these tables 1, 3 or 12, 14 as an address, the sampling value of the COS wave or its logarithmic value or the sampling value of the SIN wave is output from the table 1, 3 or 12, 14, respectively. Alternatively, its logarithmic value is sequentially output. The frequency of the waveform (COS wave or SIN wave) output from these tables 1, 3, 12, and 14 corresponds to the pitch frequency of the pressed key.

Next, the tone waveform data output from the above-mentioned waveform calculation circuit 35 is multiplied by amplitude data A (t) as an envelope waveform in a multiplier 36 (FIG. 3), and a DAC (digital / analog converter) 37. Is supplied to. The DAC 37 converts the output of the multiplier 36 into an analog musical tone signal and outputs it to the sound system 38. The sound system 38 amplifies the analog musical tone signal and outputs it as a musical tone from the speaker.

〔The invention's effect〕

As described above, according to the present invention, exp (K1 · F1 (wmt)) · F2 (wct + K2 · F3 (wmt)) where: F1 (X), F2 (X), and F3 (X) are cosX, respectively. Or s
Since the musical sound is synthesized based on the formula inX, there is an effect that a musical tone signal having a spectrum envelope in which the harmonic spectrum envelope changes smoothly without vibrating can be synthesized. It is suitable for use in. Further, according to the present invention, it is possible to easily generate a tone signal having a high level (amplitude) of high-order harmonics as compared with the conventional tone synthesis method by the FM method, and therefore, it is more complicated than the conventional method. There is also an effect that musical tones of various tones can be generated.

Furthermore, according to the present invention, the modulation indices K1 and K2 can be controlled independently of each other, whereby the spectrum envelope can be controlled in various ways, so that the tone color of the musical tone can be changed in various ways.

[Brief description of drawings]

FIG. 1 is a block diagram showing a configuration of a first embodiment of the present invention, FIG. 2 is a block diagram showing a configuration of a second embodiment of the present invention, and FIG. 3 is an electronic musical instrument to which the present invention is applied. FIG. 4 is a block diagram showing a configuration example, FIG. 4 is a diagram showing a characteristic example of a conventional tone synthesis method, and FIG. 5 is a diagram showing a characteristic example of a tone synthesis method according to the present invention. 1, 2 ...... COS table, 3 ...... SIN table 5 ...... e ^x table, 6, 7, 9 ...... multiplier, 11 ...... adder, 12, 13 ...... LO
G / COS table, 14 ... LOG / SIN table, 15 ... 17 ...
e ^x table, 18,19,21,22 ...... adder.

Claims (1)

[Claims] 1. A carrier wave angular frequency is wc, and a modulated wave angular frequency is wc.
m, modulation index K1, K2, exp (K1 · F1 (wmt)) · F2 (wct + K2 · F3 (wmt)) where: F1 (X), F2 (X), F3 (X) are cosX or s
A musical tone synthesizing method characterized by synthesizing musical tone signals by performing calculations based on the expression inX.