JPH09127950A - Tuning method of keyboard musical instrument or the like and electronic musical instrument - Google Patents

Abstract

PROBLEM TO BE SOLVED: To tune a keyboard musical instrument, etc., to the scale having a beautiful chord sound and capable of being freely modulated. SOLUTION: The scale having the intervals of mi, fa, sol, 1a for constituting general chords close to just intonation is regarded as harmonically good scale. In order to form a scale free to modulate, each interval is required to have a relation represented by n-power root of 2. The general expression of interval from the prime of each scale sound is determined as shown in a selected drawing, setting whole tone to x-step, whole-tone scale semitone to y-step, and chromatic scale semitone to x/2 step. In the expression, when the scale is determined with (x), (y) satisfying √2<x/y<2, the intervals of mi, fa, sol, 1a become closer to just intonation than temperament.

Description

Detailed Description of the Invention

The present invention relates to an electronic musical instrument in which chords are well harmonized and can be transposed and tuned to a scale (diatonic scale).

[0002]

2. Description of the Related Art Scales used for musical instruments such as keyboard musical instruments that produce musical tones of a pre-tuned scale (hereinafter referred to as keyboard musical instruments, etc.) have traditionally been various such as pure temperament, intermediate temperament, equal temperament Things have been proposed.

The scale used for keyboard musical instruments and the like is a harmonic scale based on the fact that when a plurality of musical tones of different pitches are simultaneously pronounced, they are harmonized. This is an ideal harmony scale, unless target semitones (outside scale semitones) are taken into consideration. Fig. 19 shows the major and minor scales of just intonation. In the pure temperament scale, "1st note, 3rd note,
5th sound (Do Mi Sor), "4th sound, 6th sound, 8th sound (Far la Do)", "5th sound, 7th sound, 9th sound (So
The long 3 chords of "Shi-Le)" become a simple integer ratio of 4: 5: 6, and become chords without howling. Also, in the pure temperament scale, these sounds are short 3rd chords, and have an integer ratio of 10:12:15. Thus, in just intonation, the 3rd note, the 4th note,
The 5th and 6th notes are very well harmonized with the tonic (1st note), that is, 3rd major (short), 4th perfect, 5th perfect,
The long (short) 6 degrees resonate without groaning, so it has the characteristic that it sounds extremely beautiful. Further, when playing a musical instrument such as a voice or a stringed instrument that determines the pitch at the time of sounding, it has a characteristic that it naturally converges to this scale because it only needs to take a pitch of 0 beat.

However, in the case of transposing in just intonation, as described above, the relationship between the new tonic and other tones becomes completely different from that in just intonation. It was necessary to retune the scale notes of the new tones to new tones, and it was impossible to apply them to keyboard instruments.

Therefore, a large whole tone (9: 8 = 204 cents) and a small whole tone (10: 9 = 18) in the just intonation scale shown in FIG.
2 cents) are integrated, and all whole tones are set to 193 cents, which is the middle pitch between big whole notes and small whole notes, so that all major thirds become ideal 5: 4 (386 cents). Tuning was proposed. FIG. 20 shows the pitch of a scale note in the intermediate temperament. In this scale, all major thirds are accurate, so the sound of chords is kept beautiful and it can withstand some degree of modulation, but it is a semitone C #, D #, E, E #,
F #, G #, A #, B # and D ♭, E ♭, F ♭, F, G
♭, A ♭, B ♭, C has the drawback that it is different, G ♭
It was impossible to use F # in place of, C # in place of D ♭, and A ♭ in place of G #. Furthermore, it was impossible to set double sharp and double flat, which are rarely used. Therefore, practical use in this scale was close to the original key (C major), that is, only a few major keys with 1 or 2 # or ♭ and a few monotones.

[0006] As described above, the scales based on just intonation and mid-tone tuning have the disadvantage that the resonances are harmonized, but have the drawback that modulation is difficult or impossible.

A scale that solves the drawback that the modulation is difficult is a scale based on the 12-note temperament that is widely used at present. This is an approximate scale composed of octave-divided intervals. According to this, all tones are 2 ^1/6 intervals (200 cents), and half tones are all diatonic and semitones. It has a pitch of 2 ^1/12 (100 cents), and has the characteristic that the same major and minor scales can be configured even if any of the 12 semitones is the tonic. Therefore, if a keyboard instrument or the like is tuned to this scale, there is an advantage that any key can be transposed without retuning.

[0008]

However, in this 12-note temperament, perfect 5th and perfect 4th, which were strictly adhered to as the basis for scale division, are treated as irrational numbers. There is a deviation of 1.955 ... cents from the perfect 5th pitch 3/2 and the perfect 4th pitch 4/3 respectively. Moreover, the major third and minor third of the pure temperament are perfect 5.
It is said that there are things that appeal more beautifully to human senses than degrees and perfect fourths, and as mentioned above, this is a scale that allows maintaining this pitch (third major) even when transposing. 12 The difference between the major third and minor thirds of the equal temperament and the major third major pitch 5/4 and minor third major pitch 6/5 of the just intonation is -1 each.
3.6863 cents, 15.6413 cents, which is an order of magnitude larger than the difference at perfect 5 degrees and perfect 4 degrees. As described above, although the 12-tempered temperament is free to transpose, it cannot be said that the tone is beautiful because the pitch relation is an approximate one that includes an error.

This invention has a beautiful chord sound, and
An object of the present invention is to provide a tuning method for a keyboard musical instrument or the like that can be tuned to a scale that can be freely modulated, and an electronic musical instrument tuned to such a scale.

[0010]

According to the invention of claim 1 of this application, an arbitrary natural number x, y satisfying √2 <x / y <2 is determined, and n is calculated by a calculation formula n = 5x + 2y. The frequency of the octave is logarithmically divided into units of n steps, the pitch of a diatonic whole tone is x units, the pitch of a diatonic semitone is y units, and the pitch of a diatonic semitone is x / 2 units. It is characterized by tuning so that

According to the invention of claim 2 of this application, the frequency of one octave is logarithmically n (n = 5x + 2y (x, y is √).
2 <x / y <2 natural number)) units are divided evenly into diatonic scales of x units, diatonic semitones at y units, and diatonic semitones at x / 2. Frequency information storage means for storing frequency information to be a unit, performance information generation means for generating a plurality of scale pitch information, and performance information when the performance information generation means generates performance information, the performance information is included in the performance information. A tone forming means for reading frequency information corresponding to the scale pitch information and forming a tone at a frequency based on the frequency information.

The above invention will be described below. A general chord is composed of a combination of pitches of major 3rd, perfect 4th, perfect 5th, and major 6th, and a pitch close to the pitch of just intonation is a "good scale." Can be said. On the scale, Mi, Fa, So, and La are in the relation of major 3rd, perfect 4th, perfect 5th, and major 6th with respect to the tonic (do). It should be noted that minor thirds are often used for chords, but major thirds and perfect fives
If the degree is realized, the minor third is automatically realized along with it. In addition, in order for the scale to be freely transposed, it is necessary that the pitches of the scaled notes are equal, that is, the frequency relationships are proportional. Since the octave is 1: 2, each pitch is 2 to the nth power. It is necessary that the relationship be represented by roots.
Therefore, the number of units n that divides one octave is x units for all tones and y units for all diatonic semitones (x> y).
Is calculated (n = 5x + 2y), the octave frequency is logarithmically divided into n equal parts, and the pitch of one unit is calculated. Then, the pitch of this one unit is multiplied by x to obtain the pitch of a whole tone, and is multiplied by y to obtain the pitch of a diatonic semitone. Furthermore, one unit is multiplied by x / 2 to obtain the pitch of a chromatic scale semitone. The general formula of the pitch from the tonic of each scale note thus obtained is shown in FIG.
It is represented as The scale of the diatonic whole tone determined in this way is 2 ^{x / n} , and the pitch of the diatonic semitone is 2 ^{y / n} . Of the scales determined by generally applying the arbitrary x, y and n, the ones whose major third, complete four, complete five and major six are close to the pitch of just intonation, Major scale of the decided scale is 3 degrees, perfect 4 degrees, perfect 5 degrees,
It is the scale required by the present invention that the total error between the major 6th and the just intonation major 3rd, perfect 4th, perfect 5th and major 6th is less than 33.2 cents. This is √
It was realized when the scale was decided by x and y satisfying the condition of 2 <x / y <2.

[0013]

BEST MODE FOR CARRYING OUT THE INVENTION A scale that is a suitable embodiment of the present invention will be found. There are infinite combinations of x and y that satisfy x (whole tone)> y (semitone) unless the range of x is limited, but here, the range of 2 ≦ x ≦ 20 is set,
In this range, try to find an appropriate scale for x and y that satisfy the condition of x> y. Furthermore, it is natural that x (whole tone)> y (half tone), but it is unnatural that x: y becomes too large or too small, so this ratio is set to 4
The range is limited to / 3: 1 to 3: 1. When x and y satisfying 2 ≦ x ≦ 20 and x> y and 4/3 ≦ x / y ≦ 3 are calculated, the ratio between the pitches of whole tones and semitones is calculated and arranged in the order of the ratios. Like

3 to 7 show x: y = 3: 1, x: y = 3: 2, x: y = 4: from the combination of x and y.
It shows the pitch from the do of each unit with respect to 1, x: y = 5: 3, and x: y = 8: 5.
In these figures, the pitch CE is represented by the number of cents (octave = 1200 cents) that is the standard of the 12-note equal temperament in order to make it intuitively understandable. For example, in the scale of x: y = 3: 1 in FIG. 3, one unit is 70.
59 cents, and re is x = 3 from do
211.77 cents because it is on the unit. 42 mi from do because mi is 3 more units above
3.53 cents (The cent value is rounded to two decimal places, so each pitch may differ from a simple multiple of one unit.) Also, fa is from mi to y
= 1 unit above, so 494.12 cents above Do. In this way, a new scale is formed by setting a diatonic whole tone as a pitch obtained by multiplying a unit obtained by dividing an octave into n and multiplying a diatonic semitone by a unit obtained by multiplying the unit by y.

Here, the cent value of each scale in the just intonation is as shown in FIG. 19, and the closer the mi-fa-so-la pitch, which is the main pitch of the chord, to the just intonation It can be said that the pitch is good in voice.

In FIG. 8, x and y in the range of 4 / 3≤x / y≤3.
The total error in mi, fa, so, and la pitches in each scale composed of a combination of x: y = 2: 1 12-note equal temperament error total 3
Since it is 3.2 cents, a scale with a smaller total error than this is a scale (diatonic scale) required by the present invention. As shown in the figure, in the scale where the total error is less than 33.2, the x / y ratio (ratio) is 1.4167 (1
7:12) to 1.9000 (19:10), with 1.6364 (18: 1) in the center.
The total error of the scale of 1) is the smallest (16.
6 cents). This shows the result when x is limited to 20. If the value of x can be any value without limiting the range of x, √2 (≈1.414) can be obtained from the above result.
2) If the scale is determined by the combination of x and y satisfying the condition of <x / y <2, it can be easily imagined that the total error becomes less than 33.2. Therefore, √2 <x / y
The scale determined by the combination of x and y satisfying the condition <2 is the scale required by the present invention.

FIG. 9 shows the pitch from the tonic of each scale for the scale of x ≦ 20 satisfying the above conditions. As is clear from this figure, the pitches of mi, fa, fol, and ra, which are in the relation of major 3rd, perfect 4th, perfect 5th, and major 6th from the tonic (do), are sufficient no matter which scale is applied. It is practically usable.

In the tuning method of the present invention, the semitone semitone is set to x / 2, which is half the whole tone, regardless of the size of the diatonic halftone y. 10 to 15, using this chromatic scale semitone, x: y is 3: 2, 13: 8, 18:11,
♭ 1 to ♭ 6 for the scale of 12: 7, 7: 4, 9: 5
And the pitches of # 1 to # 6 (F major to F major and G major to C major on the basis of C major). Also, in the mid-tone tuning, ♭ 1 to ♭ 6 and #
FIG. 16 shows the scale tones in the case of transposing 1 to # 6. Here, CHROMATIC is the total number of cents of the pitch difference with respect to the 12-note primary key (key without the key signature (# or ♭)), and DIATONIC is the total number of cents of the interval difference with respect to the primary key of the scale note. is there. Also, mi, fa, sol
& La is 4 for major 3rd, perfect 4th, perfect 5th, and major 6th.
The total number of cents of the pitch difference with respect to the original tone of the sound, that is,
It is the total error mentioned above. As you can see in these figures,
It can be seen that the middle tune is very close to the original key up to 2 ♭ and 4 #, but if the number of key signatures exceeds this, the error will suddenly increase and it will be difficult to use as a scale. On the other hand, in the scale of the invention of the present application, it is understood that the error is within a certain level of error with respect to the original key, regardless of the number of key signatures. Therefore, in the middle tone tuning, the pitch shift becomes large and it becomes unusable, but in the scale of the present invention, it is possible to maintain the pitch enough for practical use even after the tuning, and the harmony of chords It can be seen that, although the performance is relatively good, it also has the characteristics of the equality of 12-note equal temperament.

FIG. 17 is a block diagram of an electronic musical instrument having the above tuning. This electronic musical instrument, when a key on the keyboard 4 is turned on, produces a musical tone of a pitch (frequency) corresponding to the key. A bus is connected to the CPU 1 as a control device, and a ROM 2, a RAM 3, a keyboard 4 and a sound source 5 are connected to the bus. A waveform memory 6 and a sound system 7 are connected to the sound source 5. In the waveform memory 6, musical tones having a predetermined pitch (for example, C3) are sampled and stored. The ROM 2 is provided with a program storage area 21, a frequency information storage area 22, and a tone color parameter storage area 23. The program storage area 21 stores a program for controlling the operation of this electronic musical instrument. The frequency information storage area 22 stores information about what frequency the musical tone is formed when the key of the keyboard 4 is turned on.

FIG. 18 illustrates the contents stored in the frequency information storage area 22. The frequency information storage area 22 stores a table storing the key code of the turned-on key and a multiplier corresponding to the key code and the pitch (sampling key) of the waveform data stored in the waveform memory 6. It consists of areas. The sampling key is stored as f number which is a unit of data proportional to the frequency. In this example, the pitch of the waveform data stored in the waveform memory 6 is C3. When a certain key is turned on, the multiplier corresponding to the key code of the key is read from the table, and this multiplier is set to f of the sampling key.
Sound source 5 as the f number of the musical sound to be produced by multiplying the number
Output to The above processing is performed by the CPU 1.

Returning to FIG. 17, the tone color parameter storage area 23 stores parameters used when the tone generator 5 reads out waveform data from the waveform memory 6 to form a musical tone. The parameter is, for example, a cutoff parameter of the filter. Registers are set in the RAM 3 for storing various data generated during performance. The sound source 5 reads the waveform data stored in the waveform memory 6 as described above to form a musical sound. The tone formation is performed based on the tone formation data sent from the CPU 1. This tone formation data is key-on data,
An f number multiplied by the multiplier, a tone color parameter, and the like. The sound source 5 reads the waveform data of the waveform memory 6 while advancing the address by using the f number as the increment value.
Then, the waveform is processed by the tone color parameter and output to the sound system 7. In the sound system 7, the input digital musical tone signal is converted into an analog signal, amplified, and then emitted as a musical tone.

In FIG. 18, the multiplier is a value in which the general formula of FIG. 1 is an index of 2. x, y, and n satisfy the above-mentioned conditions, for example, x = 13, y =
8, n = 21, x = 18, y = 11, n = 29 may be applied. By multiplying this by the f number, it is possible to form a scale note based on the above tuning.

[0023]

As described above, according to the present invention, it is possible to tune a chord with good reverberation and to keep the pitch of the chord even if it is transposed. By applying it to a musical instrument to be placed, it is possible to play a chord with a better resonance than the conventional equal temperament.

[Brief description of the drawings]

FIG. 1 is a general formula showing the pitch of each scale note in the tuning method of the present invention.

FIG. 2 is a diagram showing a ratio between a diatonic whole tone and a diatonic semitone when various values are applied to the general formula.

FIG. 3 is a diagram showing the pitch of each scale note when 3 is applied to x and 1 is applied to y in the above general formula.

FIG. 4 is a diagram showing the pitch of each scale tone when 3 is applied to x and 2 is applied to y in the above general formula.

FIG. 5 is a diagram showing a pitch of each scale tone when 4 is applied to x and 1 is applied to y in the above general formula.

FIG. 6 is a diagram showing the pitch of each scale tone when 5 is applied to x and 3 is applied to y in the above general formula.

FIG. 7 is a diagram showing the pitch of each scale note when 8 is applied to x and 5 is applied to y in the above general formula.

FIG. 8 is a diagram showing a pitch difference from a just intonation in tuning of various values.

FIG. 9 is a diagram showing the cent value of each scale tone in a case where the pitch difference from just intonation is smaller than that in equal temperament.

FIG. 10 is a diagram showing a change in pitch when modulation is repeated in the tuning when x = 3 and y = 2.

FIG. 11 is a diagram showing a change in pitch when a transposition is repeated in the tuning when x = 13 and y = 8.

FIG. 12 is a diagram showing a change in pitch when modulation is repeated in the tuning when x = 18 and y = 11.

FIG. 13 is a diagram showing a change in pitch when modulation is repeated in the tuning when x = 12 and y = 7.

FIG. 14 is a diagram showing a change in pitch when modulation is repeated in the tuning when x = 7 and y = 4.

FIG. 15 is a diagram showing a change in pitch when a transposition is repeated in the tuning when x = 9 and y = 5.

FIG. 16 is a diagram showing a change in pitch of each scale note in the case of repeating modulation in intermediate rhythm.

FIG. 17 is a block diagram of an electronic keyboard musical instrument that has been tuned.

FIG. 18 is a diagram showing stored contents of a tuning information storage area of the electronic keyboard instrument.

FIG. 19 is a diagram showing pitches of just intonation scales.

FIG. 20 is a diagram showing a pitch of a scale note of an intermediate rhythm.

[Explanation of symbols]

 5-sound source, 22-frequency information storage area

Claims (2)

[Claims] 1. An arbitrary natural number x, y satisfying √2 <x / y <2 is determined, and n is obtained by a calculation formula n = 5x + 2y, and a frequency of one octave is logarithmically divided into units of n stages. A keyboard instrument, etc. characterized in that the pitch of a diatonic tone is x units, the tone of a diatonic semitone is y units, and the tuning of a diatonic semitone is x / 2 units. Tuning method. 2. A frequency of one octave is logarithmically n (n
= 5x + 2y (where x and y are natural numbers satisfying √2 <x / y <2)), and the pitch of a whole note is x units, the pitch of a halftone is a y unit, a halftone. The frequency information storage means for storing the frequency information of the diatonic scale, which is constructed with the pitch of a semitone as x / 2 units, the performance information generating means for generating the performance information including the scale information, and the performance information generating means. An electronic musical instrument comprising: a musical tone forming unit that, when musical performance information is generated, reads frequency information corresponding to scale information included in the musical performance information, and forms a musical tone at a frequency based on the frequency information.