WO2022036883A1 - Antisymmetric temperament sequence generation method oriented to pythagorean temperament - Google Patents

Antisymmetric temperament sequence generation method oriented to pythagorean temperament Download PDF

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WO2022036883A1
WO2022036883A1 PCT/CN2020/128037 CN2020128037W WO2022036883A1 WO 2022036883 A1 WO2022036883 A1 WO 2022036883A1 CN 2020128037 W CN2020128037 W CN 2020128037W WO 2022036883 A1 WO2022036883 A1 WO 2022036883A1
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temperament
sequence
law
antisymmetric
frequency
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PCT/CN2020/128037
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陈根方
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陈根方
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
    • G10G—REPRESENTATION OF MUSIC; RECORDING MUSIC IN NOTATION FORM; ACCESSORIES FOR MUSIC OR MUSICAL INSTRUMENTS NOT OTHERWISE PROVIDED FOR, e.g. SUPPORTS
    • G10G1/00—Means for the representation of music

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  • the invention belongs to the field of modern music industry, and particularly relates to a method for generating antisymmetric temperament oriented to Pythagorean temperament.
  • rhythm is one of the main contents of music practice and music research.
  • Pythagorean rhythm is a rhythm system of rhythm.
  • Most musical instruments use the method of Pythagorean law, which has made great contributions to the inheritance and development of the music industry of all centuries.
  • Figure 1 shows the temperament structure diagram of the commonly used Pythagorean derived temperament method. Its basic rule is: the frequency of the initial temperament is artificially given, for example, the frequency of the central C of the musical tone system is usually 261.63Hz, as The starting frequency is used to generate the temperament in two directions: the upward perfect fifth and the downward perfect fifth.
  • the upward perfect fifth is the frequency of the current temperament multiplied by or If the frequency of the current temperament is multiplied by If not more than 2 times the frequency of the initial temperament, the frequency of the next temperament is the frequency of the current temperament multiplied by otherwise multiply by
  • the upper line (1) in Figure 1 indicates that starting from the center C, according to the law of perfect fifth ascending, by multiplying by or Get the next one.
  • the descending perfect fifth is the frequency of the current temperament multiplied by or If the frequency of the current temperament is multiplied by If not more than 2 times the frequency of the initial temperament, the frequency of the next temperament is the frequency of the current temperament multiplied by otherwise multiply by
  • the next line (2) in Figure 1 shows that starting from the center C, according to the descending law of perfect fifths, by multiplying by or Get the next one. Although this method constrains the generated temperament to be within 2 times of the frequency of the initial temperament, the multiplication factor must be selected for each calculation. For the frequency of the tone b, the frequencies of the four tones g, d, a, and e must be calculated separately.
  • the present invention provides a technical solution for a method for generating an antisymmetric law sequence oriented to the Pythagorean law.
  • the method for generating an antisymmetric law sequence oriented to the Pythagorean law is characterized in that it includes a generating system, the generating system includes an input module, a calculation module and an output module, and the calculation module includes a multiplication-by-three method unit, a division-by-three method unit and merge unit, the specific steps are:
  • the number sequence F is obtained by multiplying the three-method unit: multiply the current temperament frequency by or Obtain the next temperament frequency, so that the generated temperament frequency is constrained between the numerical interval [f 0 , 2 ⁇ f 0 ], and the new temperament frequency can be generated in a continuous chain multiple times, and the sequence F is obtained, and the sequence F is an antisymmetric temperament sequence the right end part of ⁇ ;
  • ⁇ i ⁇ log 2 3 ⁇ represents the value of the fractional part of the value i ⁇ log 2 3
  • the method for generating an antisymmetric law sequence oriented to the Pythagorean law is characterized in that the output module is a display screen.
  • the present invention has the following advantages:
  • the invention obtains the antisymmetric temperament sequence by using the calculation unit, can conveniently represent the twelve tones of Western music, and can directly calculate the frequencies of the seven temperaments, which greatly facilitates the calculation of the temperament;
  • the invention provides the construction method of the antisymmetric law sequence of the Pythagorean law, provides the temperament calculation formula of the Pythagorean law, realizes the method that can calculate the temperament frequency of any given temperament number, and furthermore It can realize the purpose of applying polyphonic temperament to music software;
  • the invention combines the temperament calculation formula with the music application software, uses the input module to input the frequency of the center temperament, the number of the left end temperament and the number of the right end temperament, uses the calculation module to calculate the corresponding antisymmetric temperament sequence, and then outputs it through the output module for display.
  • the output antisymmetric temperament can be further played out by various musical instrument software, so as to be used by music practitioners.
  • Fig. 1 is the musical rhythm structure diagram of the Pythagorean derived rhythm method in the prior art
  • Fig. 2 is the flow chart of the present invention
  • FIG. 3 is a schematic diagram of the circuit relationship of the generation system in the present invention.
  • FIG. 4 is a schematic diagram of a sequence structure of an antisymmetric law sequence in the present invention.
  • FIG. 5 is a schematic diagram showing the relationship between the antisymmetric law sequence and the heptatone in the present invention.
  • a method for generating antisymmetric law sequences oriented to Pythagorean law including a generating system, the generating system includes an input module 1, a calculation module 2 and an output module 3, and the calculation module 1 includes a multiplication by three
  • the method unit 20, the division-by-three method unit 21 and the merging unit 22, the specific steps are:
  • the number sequence F is obtained by multiplying the three-method unit 20: using the current temperament frequency to multiply by or Obtain the next temperament frequency, so that the generated temperament frequency is constrained between the numerical interval [f 0 , 2 ⁇ f 0 ], and the new temperament frequency can be generated in a continuous chain multiple times, and the sequence F is obtained, and the sequence F is an antisymmetric temperament sequence the right end part of ⁇ ;
  • the division-by-three method unit 21 obtains the number sequence F': multiply by the current rhythm frequency or Obtain the next temperament frequency, so that the generated temperament frequency is constrained between the numerical interval [f 0 , 2 ⁇ f 0 ], and new temperament frequencies can be generated in a continuous chain multiple times, and the sequence F' is obtained.
  • the sequence F' is antisymmetric the left part of the law column ⁇ ;
  • the multiplication-by-three temperament calculation formula and the division-by-third temperament calculation formula can be unifiedly expressed as: where Z represents an integer.
  • Z represents an integer.
  • the Pythagorean-oriented antisymmetric tempered sequence ⁇ described in the present invention can conveniently represent the twelve tones of Western music, such as the C major that constitutes the heptatonic scale is the continuous antisymmetric tempered sequence ⁇ .
  • the key of #F with six sharps is fk, 5 ⁇ k ⁇ 11
  • the key of #C with seven sharps is fk, 6 ⁇ k ⁇ 12 ; thus, for the key with m sharps , which is composed of seven tones of f k , -1+m ⁇ k ⁇ 5+m.
  • the method for producing the rhythm of the present invention facing the Pythagorean rhythm can conveniently utilize the formula For calculation, for any key, as long as the value range of the independent variable k corresponding to each temperament that constitutes the key is determined, the frequency of the seven temperaments of this key can be calculated using the formula. And the traditional Pythagorean method of calculating temperament, they use the multiplicative factor method factor and To calculate, starting from the artificially specified starting temperament frequency, the required temperament is generated multiple times according to different temperaments. Each time a new temperament is generated, human judgment is required to select which multiplication factor to use, and to calculate any temperament, it is necessary to start from the Start the calculation from the beginning temperament.
  • the method for producing the musical rhythm of the present invention facing the Pythagorean rhythm can conveniently utilize the formula To calculate the temperament frequency at any specified position k in the antisymmetric temperament sequence ⁇ , the temperament frequency can be directly obtained by only one calculation.
  • the traditional Pythagorean temperament calculation method needs to calculate all the temperaments from the starting temperament to the specified position k.
  • the present invention greatly improves computing efficiency.
  • the output module 3 in the present invention is a display screen, and the present invention can be applied to a PC terminal or a mobile phone terminal, taking the computer terminal as an example, the input module 1 is a keyboard, the calculation module 2 is a computer application program, and the output module 3 is a computer display screen.
  • the input module 1 is a keyboard
  • the calculation module 2 is a computer application program
  • the output module 3 is a computer display screen.
  • open the application program of this method on the computer and then input any center-rhythm frequency f 0 through the keyboard, input N as the number of temperaments in the left end part of the antisymmetric law column ⁇ , and input M as the right end part of the antisymmetric law column ⁇ .
  • the calculation module 2 calculates the corresponding antisymmetric temperament ⁇ , and displays it on the computer screen.
  • Fig. 4 shows the sequence structure of the antisymmetric law sequence of the present invention, which unifies the two generation methods of the ascending perfect fifth and the descending perfect fifth of the commonly used Pythagorean law into a musical temperament calculation formula: where Z represents an integer.
  • Z represents an integer.
  • the range of the independent variable in Fig. 4 is -6 to 11, and the frequency of the corresponding 18 musical tones can be calculated by using the formula.
  • Multiplication by three method unit 20 it corresponds to the upward pure fifth method of the commonly used Pythagorean law, and it generates the required temperament from the initial law to upward generation, and the present invention provides the temperament calculation formula of the multiplication by three method, Temperament can be calculated directly without the need to select the multiplicative factor used with the usual methods.
  • the independent variable in Fig. 4 is greater than 0, the corresponding temperament calculation method is the multiplication method.
  • the division-by-three method unit 21 it corresponds to the descending pure fifth method of the commonly used Pythagorean law, and it generates the required temperament from the starting temperament to the descending generation.
  • the present invention provides the temperament calculation formula of the division-by-three method, Temperament can be calculated directly without the need to select the multiplicative factor used with the usual methods.
  • the independent variable in Fig. 4 is less than 0, the corresponding temperament calculation method is the division-by-three method.
  • Merging unit 22 Combine the temperaments generated by the multiplying-by-three unit 20 and the three-division unit 21 with the initial temperament as the center to obtain an antisymmetric temperament sequence.
  • the temperament generated by the multiply-by-three unit 20 is at the right end of the initial temperament
  • the temperament generated by the division-by-three unit 21 is at the left end of the initial temperament. Then, unify the temperament calculation formulas of the multiply-by-three method unit 20 and the division-by-three method unit 21, and obtain the Pythagorean temperament calculation formula:
  • Fig. 5 is a kind of relationship between the antisymmetric temperament and the heptatone tones facing the Pythagorean law according to the present invention, and seven consecutive temperaments are selected from the antisymmetric temperament to form the tones corresponding to the scale, and the tone
  • the name is the sound name of the second temperament in seven consecutive temperaments.
  • the G key selects seven consecutive temperaments of c, g, d, a, e, b, and # f in the antisymmetric temperament sequence to form a scale, and the name of the second temperament is the name of the key.
  • the present invention combines the temperament calculation formula with the music application software, uses the input module to input the central temperament frequency f 0 , inputs N as the temperament number of the left end part of the antisymmetric temperament column ⁇ , and input M as the temperament of the right end part of the antisymmetric temperament sequence ⁇
  • the corresponding antisymmetric temperament is calculated by the calculation module, and then output and displayed through the output module.
  • the output antisymmetric temperament can be further played with various musical instrument software, so as to be used by music practitioners.
  • the invention provides the construction method of the antisymmetric law sequence of the Pythagorean law, provides the temperament calculation formula of the Pythagorean law, realizes the method that can calculate the temperament frequency of any given temperament number, and furthermore It can realize the purpose of applying polyphonic temperament to music software.
  • the invention provides the temperament calculation formula of the Pythagorean temperament, which is as simple and easy to understand as the twelve equal temperament. Therefore, the invention will greatly promote the diversified use of temperament in the digital music era, and enrich digital music products.
  • the industrial ecology provides technical support.

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Abstract

An antisymmetric temperament sequence generation method oriented to the Pythagorean temperament. The method specifically involves inputting, by means of an input module, a central temperament frequency, the number of left-end temperaments and the number of right-end temperaments, then calculating a corresponding antisymmetric temperament sequence by using a calculation module, and then outputting same by means of an output module and displaying same. The twelve tones of western music can be conveniently represented, and the frequencies of seven temperaments can also be directly calculated, such that temperament calculation is greatly facilitated, and the aim of music software applying a multi-temperament temperament system can also be achieved.

Description

一种面向毕达哥拉斯律的反对称律列产生方法An Antisymmetric Law Sequence Generation Method Oriented to Pythagorean Law 技术领域technical field
本发明属于现代音乐工业领域，具体涉及一种面向毕达哥拉斯律的反对称律列产生方法。The invention belongs to the field of modern music industry, and particularly relates to a method for generating antisymmetric temperament oriented to Pythagorean temperament.
背景技术Background technique
在音乐艺术领域，音律是音乐实践和音乐研究的主要内容之一，毕达哥拉斯律是一种音律的律制，在现代中国常常被称为五度相生律，在古代中国被称为三分损益律，它是分别由古希腊时期的毕达哥拉斯学派和中国先秦时期的音乐家各自独立提出的，已有二千多年的历史，在世界各地广为使用，存见的大多数乐器的都采用毕达哥拉斯律为定律的方法，毕达哥拉斯律为全人类的音乐事业的传承与发展做出了巨大贡献。In the field of music art, rhythm is one of the main contents of music practice and music research. Pythagorean rhythm is a rhythm system of rhythm. The law of three points of profit and loss, which was independently proposed by the Pythagoreans in ancient Greece and the musicians in the pre-Qin period in China, has a history of more than 2,000 years and is widely used all over the world. Most musical instruments use the method of Pythagorean law, which has made great contributions to the inheritance and development of the music industry of all mankind.
但是，现代世界已经进入了数字音乐时代，国际流行的毕达哥拉斯律仍然采用毕达哥拉斯学派提出的古老的生律方法，已经不适合于数字音乐的飞速发展。图1示出常用的毕达哥拉斯学派生律方法的音律结构图，它的基本规则是：人为给定起始律的频率，如通常以乐音体系的中央C的频率为261.63Hz，作为起始频率，按上行纯五度和下行纯五度两个方向链式生成音律。上行纯五度，就是当前音律的频率乘以
Figure PCTCN2020128037-appb-000001
或
Figure PCTCN2020128037-appb-000002
如果当前音律的频率乘以
Figure PCTCN2020128037-appb-000003
不超过起始律频率的2倍，则下一律的频率为当前音律频率乘以
Figure PCTCN2020128037-appb-000004
否则乘以
Figure PCTCN2020128037-appb-000005
图1中的上一行(1)表示从中央C出发，按纯五度上行生律，通过乘以
Figure PCTCN2020128037-appb-000006
或
Figure PCTCN2020128037-appb-000007
得到下一律。下行纯五度，就是当前音律的频率乘以
Figure PCTCN2020128037-appb-000008
或
Figure PCTCN2020128037-appb-000009
如果当前音律的频率乘以
Figure PCTCN2020128037-appb-000010
不超过起始律频率的2倍，则下一律的频率为当前音律频率乘以
Figure PCTCN2020128037-appb-000011
否则乘以
Figure PCTCN2020128037-appb-000012
图1中的下一行(2)表示从中央C出发，按纯五度下行生律，通过乘以
Figure PCTCN2020128037-appb-000013
或
Figure PCTCN2020128037-appb-000014
得到下一律。这个 方法虽然把生成的音律约束在了起始律频率的2倍以内，但是每计算一律都要选择乘法因子，同时，为了计算某一音律，必须先计算出它前面的各个音律，如要计算乐音b的频率，必须先分别计算出g、d、a、e等四个乐音的频率。 However, the modern world has entered the era of digital music, and the internationally popular Pythagorean rhythm still adopts the ancient method of biological rhythm proposed by the Pythagorean school, which is no longer suitable for the rapid development of digital music. Figure 1 shows the temperament structure diagram of the commonly used Pythagorean derived temperament method. Its basic rule is: the frequency of the initial temperament is artificially given, for example, the frequency of the central C of the musical tone system is usually 261.63Hz, as The starting frequency is used to generate the temperament in two directions: the upward perfect fifth and the downward perfect fifth. The upward perfect fifth is the frequency of the current temperament multiplied by
Figure PCTCN2020128037-appb-000001
or
Figure PCTCN2020128037-appb-000002
If the frequency of the current temperament is multiplied by
Figure PCTCN2020128037-appb-000003
If not more than 2 times the frequency of the initial temperament, the frequency of the next temperament is the frequency of the current temperament multiplied by
Figure PCTCN2020128037-appb-000004
otherwise multiply by
Figure PCTCN2020128037-appb-000005
The upper line (1) in Figure 1 indicates that starting from the center C, according to the law of perfect fifth ascending, by multiplying by
Figure PCTCN2020128037-appb-000006
or
Figure PCTCN2020128037-appb-000007
Get the next one. The descending perfect fifth is the frequency of the current temperament multiplied by
Figure PCTCN2020128037-appb-000008
or
Figure PCTCN2020128037-appb-000009
If the frequency of the current temperament is multiplied by
Figure PCTCN2020128037-appb-000010
If not more than 2 times the frequency of the initial temperament, the frequency of the next temperament is the frequency of the current temperament multiplied by
Figure PCTCN2020128037-appb-000011
otherwise multiply by
Figure PCTCN2020128037-appb-000012
The next line (2) in Figure 1 shows that starting from the center C, according to the descending law of perfect fifths, by multiplying by
Figure PCTCN2020128037-appb-000013
or
Figure PCTCN2020128037-appb-000014
Get the next one. Although this method constrains the generated temperament to be within 2 times of the frequency of the initial temperament, the multiplication factor must be selected for each calculation. For the frequency of the tone b, the frequencies of the four tones g, d, a, and e must be calculated separately.
因此，迫切需要一种能方便计算的音律计算公式和音律产生***，从而解决数字音乐时代毕达哥拉斯律的广泛应用问题。Therefore, there is an urgent need for a temperament calculation formula and a temperament generation system that can be easily calculated, so as to solve the problem of wide application of the Pythagorean temperament in the digital music era.
发明内容SUMMARY OF THE INVENTION
为了弥补现有技术的不足，本发明提供一种面向毕达哥拉斯律的反对称律列产生方法技术方案。In order to make up for the deficiencies of the prior art, the present invention provides a technical solution for a method for generating an antisymmetric law sequence oriented to the Pythagorean law.
所述的一种面向毕达哥拉斯律的反对称律列产生方法，其特征在于包括产生***，产生***包括输入模块、计算模块和输出模块，计算模块包括乘三法单元、除三法单元和合并单元，其具体步骤为：The method for generating an antisymmetric law sequence oriented to the Pythagorean law is characterized in that it includes a generating system, the generating system includes an input module, a calculation module and an output module, and the calculation module includes a multiplication-by-three method unit, a division-by-three method unit and merge unit, the specific steps are:
1)通过输入模块输入按实际需要人为给定的频率f 0，频率f 0作为中心律，输入N作为反对称律列Ω左端部分的音律个数，输入M作为反对称律列Ω右端部分的音律个数； 1) Input the frequency f 0 artificially given according to actual needs through the input module, the frequency f 0 is used as the central law, the input N is the number of temperaments at the left end of the antisymmetric law column Ω, and the input M is the right end part of the antisymmetric law column Ω. number of melody;
2)通过乘三法单元得到数列F：利用当前音律频率乘以
Figure PCTCN2020128037-appb-000015
或
Figure PCTCN2020128037-appb-000016
得到下一个音律频率，使得生成的音律频率约束在数值区间[f 0,2×f 0]之间，可以连续多次链式生成新的音律频率，得到数列F，数列F是反对称律列Ω的右端部分； 2) The number sequence F is obtained by multiplying the three-method unit: multiply the current temperament frequency by
Figure PCTCN2020128037-appb-000015
or
Figure PCTCN2020128037-appb-000016
Obtain the next temperament frequency, so that the generated temperament frequency is constrained between the numerical interval [f 0 , 2×f 0 ], and the new temperament frequency can be generated in a continuous chain multiple times, and the sequence F is obtained, and the sequence F is an antisymmetric temperament sequence the right end part of Ω;
3)除三法单元得到数列F'：利用当前音律频率乘以
Figure PCTCN2020128037-appb-000017
或
Figure PCTCN2020128037-appb-000018
得到下一个音律频率，使得生成的音律频率约束在数值区间[f 0,2×f 0]之间，可以连续多次链式生成新的音律频率，得到数列F'，数列F'是反对称律列Ω的左端部分； 3) Divide three method unit to get number sequence F': use the current temperament frequency to multiply by
Figure PCTCN2020128037-appb-000017
or
Figure PCTCN2020128037-appb-000018
Obtain the next temperament frequency, so that the generated temperament frequency is constrained between the numerical interval [f 0 , 2×f 0 ], and new temperament frequencies can be generated in a continuous chain multiple times, and the sequence F' is obtained. The sequence F' is antisymmetric the left part of the law column Ω;
4)通过合并单元得到反对称律列Ω：把数列F、数列F’和中心起始律放在一起；4) Obtain the antisymmetric law sequence Ω through the merging unit: put the sequence F, the sequence F' and the central onset law together;
5)通过输出模块输出反对称律列Ω。5) Output the antisymmetric law column Ω through the output module.
所述的一种面向毕达哥拉斯律的反对称律列产生方法，其特征在于所述步骤2)中，乘三法单元音律计算公式是：
Figure PCTCN2020128037-appb-000019
其中{i×log 23}表示取数值i×log 23的小数部分值，利用此公式计算M个音律的频率，把计算得到的M个音律的频率，按下标i的大小，从小到大排列，得到数列F，即F＝<f 1,…,f i-1,f i,…,f M>。 Described a kind of antisymmetric law sequence generation method facing Pythagorean law, it is characterized in that in described step 2), multiplying three method unit temperament calculation formula is:
Figure PCTCN2020128037-appb-000019
Wherein {i×log 2 3} represents the value of the fractional part of the value i×log 2 3, use this formula to calculate the frequencies of the M temperaments, and use the calculated frequencies of the M temperaments to denote the size of i, from small to Large permutation to obtain a sequence F, that is, F=<f 1 ,...,f i-1 ,f i ,...,f M >.
所述的一种面向毕达哥拉斯律的反对称律列产生方法，其特征在于所述步骤3)中，除三法单元音律计算公式是：
Figure PCTCN2020128037-appb-000020
其中{-j×log 23}表示取数值-j×log 23的小数部分值，利用此公式计算N个音律的频率,把计算得到的N个音律的频率，按下标j的大小，从大到小排列，得到数列F’，即F'＝<f′ N,f′ N-1,…,f′ j+1,f′ j,…,f 1'>。 Described a kind of antisymmetric law sequence generation method oriented to Pythagorean law, it is characterized in that in described step 3), divide three method unit temperament calculation formula is:
Figure PCTCN2020128037-appb-000020
Wherein {-j×log 2 3} means to take the value of the fractional part of the value -j×log 2 3, use this formula to calculate the frequencies of N temperaments, and press the calculated frequencies of the N temperaments to the size of j, Arrange from big to small to get the sequence F', that is, F'=<f' N ,f' N-1 ,...,f' j+1 ,f' j ,...,f 1 '>.
所述的一种面向毕达哥拉斯律的反对称律列产生方法，其特征在于所述步骤4)中，数列F、数列F’和中心起始律的组成方法为Ω＝<F'f 0F>＝<f′ N,f′ N-1,…,f′ j…,f 1',f 0,f 1,…,f i,…,f M-1,f M>。 Described a kind of antisymmetric law sequence generation method oriented to Pythagorean law, it is characterized in that in described step 4), the composition method of sequence F, sequence F' and central onset law is Ω=<F' f 0 F>=<f′ N ,f′ N-1 ,…,f′ j …,f 1 ′,f 0 ,f 1 ,…,f i ,…,f M-1 ,f M >.
所述的一种面向毕达哥拉斯律的反对称律列产生方法，其特征在于所述输出模块为显示屏。The method for generating an antisymmetric law sequence oriented to the Pythagorean law is characterized in that the output module is a display screen.
与现有技术相比，本发明有以下优点：Compared with the prior art, the present invention has the following advantages:
本发明利用计算单元得到反对称律列，能够方便地表示西方音乐的十二个调，还能直接计算七个音律的频率，极大地方便了音律的计算；The invention obtains the antisymmetric temperament sequence by using the calculation unit, can conveniently represent the twelve tones of Western music, and can directly calculate the frequencies of the seven temperaments, which greatly facilitates the calculation of the temperament;
本发明给出了毕达哥拉斯律的反对称律列的构造方法，给出了毕达哥拉斯律的音律计算公式，实现了能计算任意给定音律数量的音律频率的方法，进而可实现音乐软件应用多音律律制的目的；The invention provides the construction method of the antisymmetric law sequence of the Pythagorean law, provides the temperament calculation formula of the Pythagorean law, realizes the method that can calculate the temperament frequency of any given temperament number, and furthermore It can realize the purpose of applying polyphonic temperament to music software;
本发明将音律计算公式与音乐应用软件相结合，利用输入模块输入中心律频率、左端音律个数和右端音律个数，利用计算模块算出相应的反对称律列，再将其通过输出模块输出显示，利用本发明可进一步的将输出的反对称律列用各种乐 器软件播放出来，以便音乐从业人员使用。The invention combines the temperament calculation formula with the music application software, uses the input module to input the frequency of the center temperament, the number of the left end temperament and the number of the right end temperament, uses the calculation module to calculate the corresponding antisymmetric temperament sequence, and then outputs it through the output module for display. , by using the present invention, the output antisymmetric temperament can be further played out by various musical instrument software, so as to be used by music practitioners.
附图说明Description of drawings
图1为现有技术中毕达哥拉斯学派生律方法的音律结构图；Fig. 1 is the musical rhythm structure diagram of the Pythagorean derived rhythm method in the prior art;
图2为本发明流程图；Fig. 2 is the flow chart of the present invention;
图3为本发明中产生***的电路关系示意图；3 is a schematic diagram of the circuit relationship of the generation system in the present invention;
图4为本发明中反对称律列的数列结构示意图；4 is a schematic diagram of a sequence structure of an antisymmetric law sequence in the present invention;
图5为本发明中反对称律列与七声音调的关系示意图。FIG. 5 is a schematic diagram showing the relationship between the antisymmetric law sequence and the heptatone in the present invention.
具体实施方式detailed description
下面结合附图对本发明作进一步说明。The present invention will be further described below in conjunction with the accompanying drawings.
如图2、3所示，一种面向毕达哥拉斯律的反对称律列产生方法，包括产生***，产生***包括输入模块1、计算模块2和输出模块3，计算模块1包括乘三法单元20、除三法单元21和合并单元22，其具体步骤为：As shown in Figures 2 and 3, a method for generating antisymmetric law sequences oriented to Pythagorean law, including a generating system, the generating system includes an input module 1, a calculation module 2 and an output module 3, and the calculation module 1 includes a multiplication by three The method unit 20, the division-by-three method unit 21 and the merging unit 22, the specific steps are:
1)通过输入模块1输入按实际需要人为给定的频率f 0，频率f 0作为中心律，输入N作为反对称律列Ω左端部分的音律个数，输入M作为反对称律列Ω右端部分的音律个数； 1) Input the artificially given frequency f 0 through the input module 1, the frequency f 0 is used as the central law, the input N is the number of temperaments in the left part of the antisymmetric law column Ω, and the input M is the right end part of the antisymmetric law column Ω The number of melody;
2)通过乘三法单元20得到数列F：利用当前音律频率乘以
Figure PCTCN2020128037-appb-000021
或
Figure PCTCN2020128037-appb-000022
得到下一个音律频率，使得生成的音律频率约束在数值区间[f 0,2×f 0]之间，可以连续多次链式生成新的音律频率，得到数列F，数列F是反对称律列Ω的右端部分； 2) The number sequence F is obtained by multiplying the three-method unit 20: using the current temperament frequency to multiply by
Figure PCTCN2020128037-appb-000021
or
Figure PCTCN2020128037-appb-000022
Obtain the next temperament frequency, so that the generated temperament frequency is constrained between the numerical interval [f 0 , 2×f 0 ], and the new temperament frequency can be generated in a continuous chain multiple times, and the sequence F is obtained, and the sequence F is an antisymmetric temperament sequence the right end part of Ω;
3)除三法单元21得到数列F'：利用当前音律频率乘以
Figure PCTCN2020128037-appb-000023
或
Figure PCTCN2020128037-appb-000024
得到下一个音律频率，使得生成的音律频率约束在数值区间[f 0,2×f 0]之间，可以连续多次链式生成新的音律频率，得到数列F'，数列F'是反对称律列Ω的左端部分； 3) The division-by-three method unit 21 obtains the number sequence F': multiply by the current rhythm frequency
Figure PCTCN2020128037-appb-000023
or
Figure PCTCN2020128037-appb-000024
Obtain the next temperament frequency, so that the generated temperament frequency is constrained between the numerical interval [f 0 , 2×f 0 ], and new temperament frequencies can be generated in a continuous chain multiple times, and the sequence F' is obtained. The sequence F' is antisymmetric the left part of the law column Ω;
4)通过合并单元22得到反对称律列Ω：把数列F、数列F’和中心起始律放在一起；4) Obtain the antisymmetric law column Ω through the merging unit 22: put the sequence F, the sequence F' and the central starting law together;
5)通过输出模块3输出反对称律列Ω。5) The antisymmetric law column Ω is output through the output module 3 .
所述步骤2)中，乘三法单元20音律计算公式是：
Figure PCTCN2020128037-appb-000025
其中{i×log 23}表示取数值i×log 23的小数部分值，利用此公式计算M个音律的频率，把计算得到的M个音律的频率，按下标i的大小，从小到大排列，得到数列F，即F＝<f 1,…,f i-1,f i,…,f M>。 In described step 2), multiplying three method unit 20 musical temperament calculation formula is:
Figure PCTCN2020128037-appb-000025
Wherein {i×log 2 3} represents the value of the fractional part of the value i×log 2 3, use this formula to calculate the frequencies of the M temperaments, and use the calculated frequencies of the M temperaments to denote the size of i, from small to Large permutation to obtain a sequence F, that is, F=<f 1 ,...,f i-1 ,f i ,...,f M >.
所述步骤3)中，除三法单元21音律计算公式是：
Figure PCTCN2020128037-appb-000026
其中{-j×log 23}表示取数值-j×log 23的小数部分值，利用此公式计算N个音律的频率,把计算得到的N个音律的频率，按下标j的大小，从大到小排列，得到数列F’，即F'＝<f′ N,f′ N-1,…,f′ j+1,f′ j,…,f 1'>。 Described step 3) in, divide by three method unit 21 temperament calculation formula is:
Figure PCTCN2020128037-appb-000026
Wherein {-j×log 2 3} means to take the value of the fractional part of the value -j×log 2 3, use this formula to calculate the frequencies of N temperaments, and press the calculated frequencies of the N temperaments to the size of j, Arrange from big to small to get the sequence F', that is, F'=<f' N ,f' N-1 ,...,f' j+1 ,f' j ,...,f 1 '>.
所述步骤4)中，数列F、数列F’和中心起始律的组成方法为Ω＝<F'f 0F>＝<f′ N,f′ N-1,…,f′ j…,f 1',f 0,f 1,…,f i,…,f M-1,f M>。 In the step 4), the composition method of the sequence F, the sequence F' and the central onset law is Ω=<F'f 0 F>=<f' N , f' N-1 ,...,f' j ..., f 1 ',f 0 ,f 1 ,…,f i ,…,f M-1 ,f M >.
由于{-j×log 23}＝{(-j)×log 23}，因此，可以把乘三法音律计算公式和除三法音律计算公式统一表示为：
Figure PCTCN2020128037-appb-000027
其中Z表示整数。这样，当k＝0时，就可得到中心起始律f 0,当k>0时，就可得到数列F,当k<0时，就可得到数列F'。 Since {-j×log 2 3}={(-j)×log 2 3}, the multiplication-by-three temperament calculation formula and the division-by-third temperament calculation formula can be unifiedly expressed as:
Figure PCTCN2020128037-appb-000027
where Z represents an integer. In this way, when k=0, the central starting law f 0 can be obtained, when k>0, the sequence F can be obtained, and when k<0, the sequence F' can be obtained.
因为对于任何下标i，都满足
Figure PCTCN2020128037-appb-000028
乘积是常数2，因此数列F和数列F'是反对称关系，也即反对称律列Ω是反对称数列。 because for any subscript i,
Figure PCTCN2020128037-appb-000028
The product is a constant 2, so the sequence F and the sequence F' are antisymmetric, that is, the antisymmetric law sequence Ω is an antisymmetric sequence.
本发明的优点如下：The advantages of the present invention are as follows:
1.本发明所述的面向毕达哥拉斯律的反对称律列Ω，能方便地表示西方音乐的十二个调，如组成七声音阶的C调的为反对称律列Ω的连续七个音律f k,-1≤k≤5，带一个升号的G调为f k,0≤k≤6，带二个升号的D调为f k,1≤k≤7，带三个升号的A调为f k,2≤k≤8，带四个升号的E调为f k,3≤k≤9，带五个升号的B调为f k,4≤k≤10，带六个升号的 #F调为f k,5≤k≤11，带七个升号的 #C调为f k,6≤k≤12；从而，对于带m个升号的调，它是由f k,-1+m≤k≤5+m七个音律构成。 1. The Pythagorean-oriented antisymmetric tempered sequence Ω described in the present invention can conveniently represent the twelve tones of Western music, such as the C major that constitutes the heptatonic scale is the continuous antisymmetric tempered sequence Ω. Seven tones f k , -1≤k≤5, G with one sharp is f k , 0≤k≤6, D with two sharps is f k , 1≤k≤7, with three A with 1 sharps is fk, 2≤k≤8 , E with four sharps is fk, 3≤k≤9 , B with five sharps is fk, 4≤k≤ 10. The key of #F with six sharps is fk, 5≤k≤11 , and the key of #C with seven sharps is fk, 6≤k≤12 ; thus, for the key with m sharps , which is composed of seven tones of f k , -1+m≤k≤5+m.
同样，对于带m个降号方向的调，它是由f k,-1-m≤k≤5-m七个音律构成。 Similarly, for a key with m flat directions, it is composed of seven tones of f k , -1-m≤k≤5-m.
2.本发明所述的面向毕达哥拉斯律的音律产生方法，可方便地利用公式
Figure PCTCN2020128037-appb-000029
进行计算，如对任意一个调，只要把组成调的各音律对应的自变量k的取值范围确定了，就能利用公式计算出此调的七个音律的频率。而传统的毕达哥拉斯学派的音律计算方法，它们利用乘法因子法因子
Figure PCTCN2020128037-appb-000030
和
Figure PCTCN2020128037-appb-000031
来计算，从人为指定的起始律频率开始，按不同音律多次生成所需要的音律，每次生成新音律需要人为判断来选择利用哪个乘法因子，而且计算任何一个音律，都需要先从起始律开始进行计算，如计算带七个升号的 #C调的七个音律，需要从起始律开始，一个音律一个音律顺次计算出，即按这样的顺序进行计算，f 0→f 1→f 2→f 3→f 4→f 5→f 6→f 7→f 8→f 9→f 10→f 11→f 12，然后选取最后的七律构成 #C调。本发明所述的面向毕达哥拉斯律的音律产生方法，利用音律计算公式，直接计算七个音律的频率即可，极大地方便了音律的计算。 2. The method for producing the rhythm of the present invention facing the Pythagorean rhythm can conveniently utilize the formula
Figure PCTCN2020128037-appb-000029
For calculation, for any key, as long as the value range of the independent variable k corresponding to each temperament that constitutes the key is determined, the frequency of the seven temperaments of this key can be calculated using the formula. And the traditional Pythagorean method of calculating temperament, they use the multiplicative factor method factor
Figure PCTCN2020128037-appb-000030
and
Figure PCTCN2020128037-appb-000031
To calculate, starting from the artificially specified starting temperament frequency, the required temperament is generated multiple times according to different temperaments. Each time a new temperament is generated, human judgment is required to select which multiplication factor to use, and to calculate any temperament, it is necessary to start from the Start the calculation from the beginning temperament. For example, to calculate the seven temperaments in the key of # C with seven sharps, you need to start from the beginning temperament, and calculate one temperament by one temperament in sequence, that is, calculate in this order, f 0 →f 1 → f 2 → f 3 → f 4 → f 5 → f 6 → f 7 → f 8 → f 9 → f 10 → f 11 → f 12 , and then choose the final seven law to form the key of # C. The Pythagorean temperament-oriented method of the present invention can directly calculate the frequencies of the seven temperaments by using the temperament calculation formula, which greatly facilitates the calculation of the temperament.
3.本发明所述的面向毕达哥拉斯律的音律产生方法，可以方便地利用公式
Figure PCTCN2020128037-appb-000032
计算反对称律列Ω中任意指定位置k的音律频率，只需要计算一次即可直接得到音律频率。而传统的毕达哥拉斯学派的音律计算方法需要计算从起始律开始到指定位置k的所有音律。本发明极大地提高了计算效率。 3. The method for producing the musical rhythm of the present invention facing the Pythagorean rhythm can conveniently utilize the formula
Figure PCTCN2020128037-appb-000032
To calculate the temperament frequency at any specified position k in the antisymmetric temperament sequence Ω, the temperament frequency can be directly obtained by only one calculation. The traditional Pythagorean temperament calculation method needs to calculate all the temperaments from the starting temperament to the specified position k. The present invention greatly improves computing efficiency.
本发明中的输出模块3为显示屏，本发明可应用于PC端或手机端，电脑端为例，输入模块1为键盘，计算模块2为电脑的应用程序，输出模块3为电脑显示屏，操作时，在电脑上打开本方法的应用程序，然后通过键盘输入任意中心律频率f 0，输入N作为反对称律列Ω左端部分的音律个数，输入M作为反对称律列Ω右端部分的音律个数，然后计算模块2计算出相应的反对称律列Ω，并将其显示于电脑显示屏上。 The output module 3 in the present invention is a display screen, and the present invention can be applied to a PC terminal or a mobile phone terminal, taking the computer terminal as an example, the input module 1 is a keyboard, the calculation module 2 is a computer application program, and the output module 3 is a computer display screen. During operation, open the application program of this method on the computer, and then input any center-rhythm frequency f 0 through the keyboard, input N as the number of temperaments in the left end part of the antisymmetric law column Ω, and input M as the right end part of the antisymmetric law column Ω. Then the calculation module 2 calculates the corresponding antisymmetric temperament Ω, and displays it on the computer screen.
图4示出本发明的反对称律列的数列结构，它把常用的毕达哥拉斯律的上行 纯五度和下行纯五度两种生成方法统一为音律计算公式：
Figure PCTCN2020128037-appb-000033
其中Z表示整数。只要给定自变量k的值，利用此公式能计算出对应的音律。图4中自变量的范围为-6～11，利用公式可计算出对应的18个乐音的频率。 Fig. 4 shows the sequence structure of the antisymmetric law sequence of the present invention, which unifies the two generation methods of the ascending perfect fifth and the descending perfect fifth of the commonly used Pythagorean law into a musical temperament calculation formula:
Figure PCTCN2020128037-appb-000033
where Z represents an integer. As long as the value of the independent variable k is given, the corresponding temperament can be calculated using this formula. The range of the independent variable in Fig. 4 is -6 to 11, and the frequency of the corresponding 18 musical tones can be calculated by using the formula.
乘三法单元20：它对应常用的毕达哥拉斯律的上行纯五度方法，它产生从起始律开始上行生成所需的音律，本发明通过给出乘三法的音律计算公式，不需要选择利用常用方法时的乘法因子，就能直接计算音律。图4中自变量大于0时，对应的音律计算方法即是乘三法。Multiplication by three method unit 20: it corresponds to the upward pure fifth method of the commonly used Pythagorean law, and it generates the required temperament from the initial law to upward generation, and the present invention provides the temperament calculation formula of the multiplication by three method, Temperament can be calculated directly without the need to select the multiplicative factor used with the usual methods. When the independent variable in Fig. 4 is greater than 0, the corresponding temperament calculation method is the multiplication method.
除三法单元21：它对应常用的毕达哥拉斯律的下行纯五度方法，它产生从起始律开始下行生成所需的音律，本发明通过给出除三法的音律计算公式，不需要选择利用常用方法时的乘法因子，就能直接计算音律。图4中自变量小于0时，对应的音律计算方法即是除三法。The division-by-three method unit 21: it corresponds to the descending pure fifth method of the commonly used Pythagorean law, and it generates the required temperament from the starting temperament to the descending generation. The present invention provides the temperament calculation formula of the division-by-three method, Temperament can be calculated directly without the need to select the multiplicative factor used with the usual methods. When the independent variable in Fig. 4 is less than 0, the corresponding temperament calculation method is the division-by-three method.
合并单元22：把乘三法单元20和除三法单元21生成的音律，以起始律为中心组合起来，得到反对称律列。图4中乘三法单元20生成的音律在起始律的右端，除三法单元21生成的音律在起始律的左端。然后再把乘三法单元20和除三法单元21的音律计算公式统一起来，得到了毕达哥拉斯律音律计算公式：
Figure PCTCN2020128037-appb-000034
Merging unit 22: Combine the temperaments generated by the multiplying-by-three unit 20 and the three-division unit 21 with the initial temperament as the center to obtain an antisymmetric temperament sequence. In FIG. 4, the temperament generated by the multiply-by-three unit 20 is at the right end of the initial temperament, and the temperament generated by the division-by-three unit 21 is at the left end of the initial temperament. Then, unify the temperament calculation formulas of the multiply-by-three method unit 20 and the division-by-three method unit 21, and obtain the Pythagorean temperament calculation formula:
Figure PCTCN2020128037-appb-000034
图5为本发明所述的一种面向毕达哥拉斯律的反对称律列与七声音调的关系，从反对称律列中选取连续的七个音律，构成的音阶对应的音调，调名就是连续七个音律中第二个音律的音名。如图5中G调选取了反对称律列中c、g、d、a、e、b、 #f连续的七个音律组成音阶，其第二个音律的音名即是调名。 Fig. 5 is a kind of relationship between the antisymmetric temperament and the heptatone tones facing the Pythagorean law according to the present invention, and seven consecutive temperaments are selected from the antisymmetric temperament to form the tones corresponding to the scale, and the tone The name is the sound name of the second temperament in seven consecutive temperaments. As shown in Figure 5, the G key selects seven consecutive temperaments of c, g, d, a, e, b, and # f in the antisymmetric temperament sequence to form a scale, and the name of the second temperament is the name of the key.
本发明将音律计算公式与音乐应用软件相结合，利用输入模块输入中心律频率f 0，输入N作为反对称律列Ω左端部分的音律个数，输入M作为反对称律列Ω右端部分的音律个数，利用计算模块算出相应的反对称律列，再将其通过输出模块 输出显示，利用本发明可进一步的将输出的反对称律列用各种乐器软件演奏出来，以便音乐从业人员使用。本发明给出了毕达哥拉斯律的反对称律列的构造方法，给出了毕达哥拉斯律的音律计算公式，实现了能计算任意给定音律数量的音律频率的方法，进而可实现音乐软件应用多音律律制的目的。 The present invention combines the temperament calculation formula with the music application software, uses the input module to input the central temperament frequency f 0 , inputs N as the temperament number of the left end part of the antisymmetric temperament column Ω, and input M as the temperament of the right end part of the antisymmetric temperament sequence Ω The corresponding antisymmetric temperament is calculated by the calculation module, and then output and displayed through the output module. Using the present invention, the output antisymmetric temperament can be further played with various musical instrument software, so as to be used by music practitioners. The invention provides the construction method of the antisymmetric law sequence of the Pythagorean law, provides the temperament calculation formula of the Pythagorean law, realizes the method that can calculate the temperament frequency of any given temperament number, and furthermore It can realize the purpose of applying polyphonic temperament to music software.
在数字音乐时代，音乐软件几乎能为所有的音乐活动服务，无论是设计音乐采样器、音乐效果器、音乐音色库，还是在音乐创作时，都需要用到音律计算，为了计算方便，大多数的音乐软件往往采用十二平均律，十二平均律计算简单，容易理解，其计算公式为：
Figure PCTCN2020128037-appb-000035
但是从音乐理论角度看，十二平均律是不和谐的音律律制。在人类的漫长的音乐实践中，毕达哥拉斯律是使用最广泛的音律，但是毕达哥拉斯律常用的生律方法需要有一定的音乐知识才能理解，而且其音律计算方法比十二平均律复杂，所以大大压缩了它的使用范围。 In the era of digital music, music software can serve almost all music activities. Whether it is designing music samplers, music effects, music tone libraries, or when creating music, it is necessary to use temperament calculation. For the convenience of calculation, most Music software often uses twelve well-tempered, twelve well-tempered calculations are simple and easy to understand, and the calculation formula is:
Figure PCTCN2020128037-appb-000035
But from the perspective of music theory, the twelve equal temperament is a dissonant temperament system. In the long musical practice of human beings, the Pythagorean temperament is the most widely used temperament, but the commonly used physical temperament method of the Pythagorean temperament requires a certain degree of musical knowledge to understand, and its temperament calculation method is more than ten The two-average law is complex, so its scope of use is greatly reduced.
本发明提供了毕达哥拉斯律的音律计算公式，计算和十二平均律一样简单，也容易理解，因此，本发明将极大地推动数字音乐时代音律的多样性使用，为丰富数字音乐产品的产业生态化提供了技术支撑。The invention provides the temperament calculation formula of the Pythagorean temperament, which is as simple and easy to understand as the twelve equal temperament. Therefore, the invention will greatly promote the diversified use of temperament in the digital music era, and enrich digital music products. The industrial ecology provides technical support.
最后应说明的是：以上各实施例仅用以说明本发明的技术方案，而非对其限制；尽管参照前述各实施例对本发明进行了详细的说明，本领域的普通技术人员应当理解：其依然可以对前述各实施例所记载的技术方案进行修改，或者对其中部分或者全部技术特征进行等同替换；而这些修改或者替换，并不使相应技术方案的本质脱离本发明各实施例技术方案的范围。Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, but not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: The technical solutions described in the foregoing embodiments can still be modified, or some or all of the technical features thereof can be equivalently replaced; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the technical solutions of the embodiments of the present invention. Scope.

Claims (5)

  1. 一种面向毕达哥拉斯律的反对称律列产生方法，其特征在于包括产生***，产生***包括输入模块(1)、计算模块(2)和输出模块(3)，计算模块(2)包括乘三法单元(20)、除三法单元(21)和合并单元(22)，其具体步骤为：A method for generating antisymmetric law sequences oriented to Pythagorean law, characterized by comprising a generating system, wherein the generating system comprises an input module (1), a calculation module (2) and an output module (3), and the calculation module (2) It comprises a multiplying three method unit (20), a three dividing method unit (21) and a merging unit (22), and its specific steps are:
    1)通过输入模块(1)输入按实际需要人为给定的频率f 0，频率f 0作为中心律，输入N作为反对称律列Ω左端部分的音律个数，输入M作为反对称律列Ω右端部分的音律个数； 1) Input the artificially given frequency f 0 according to the actual needs through the input module (1), the frequency f 0 is used as the central law, the input N is the number of temperaments in the left end of the anti-symmetric law column Ω, and the input M is the anti-symmetric law column Ω The number of temperaments in the right end part;
    2)通过乘三法单元(20)得到数列F：利用当前音律频率乘以
    Figure PCTCN2020128037-appb-100001
    或
    Figure PCTCN2020128037-appb-100002
    得到下一个音律频率，使得生成的音律频率约束在数值区间[f 0,2×f 0]之间，可以连续多次链式生成新的音律频率，得到数列F，数列F是反对称律列Ω的右端部分；     2) The number sequence F is obtained by multiplying the three-method unit (20): multiply the current temperament frequency by
    Figure PCTCN2020128037-appb-100001
    or
    Figure PCTCN2020128037-appb-100002
    Obtain the next temperament frequency, so that the generated temperament frequency is constrained between the numerical interval [f 0 , 2×f 0 ], and the new temperament frequency can be generated in a continuous chain multiple times, and the sequence F is obtained, and the sequence F is an antisymmetric temperament sequence the right end part of Ω;
    3)除三法单元(21)得到数列F′：利用当前音律频率乘以
    Figure PCTCN2020128037-appb-100003
    或
    Figure PCTCN2020128037-appb-100004
    得到下一个音律频率，使得生成的音律频率约束在数值区间[f 0,2×f 0]之间，可以连续多次链式生成新的音律频率，得到数列F′，数列F′是反对称律列Ω的左端部分；     3) The division-by-three method unit (21) obtains the sequence F′: multiply the current temperament frequency by
    Figure PCTCN2020128037-appb-100003
    or
    Figure PCTCN2020128037-appb-100004
    Get the next temperament frequency, so that the generated temperament frequency is constrained between the numerical interval [f 0 , 2×f 0 ], and the new temperament frequency can be generated in a continuous chain multiple times, and the sequence F′ is obtained. The sequence F′ is antisymmetric the left part of the law column Ω;
    4)通过合并单元(22)得到反对称律列Ω：把数列F、数列F’和中心起始律放在一起；4) Obtain the antisymmetric law sequence Ω through the merging unit (22): put the sequence F, the sequence F' and the central onset law together;
    5)通过输出模块(3)输出反对称律列Ω。5) Output the antisymmetric law column Ω through the output module (3).
  2. 根据权利要求1所述的一种面向毕达哥拉斯律的反对称律列产生方法，其特征在于所述步骤2)中，乘三法单元(20)音律计算公式是：
    Figure PCTCN2020128037-appb-100005
    其中{i×log 23}表示取数值i×log 23的小数部分值，利用此公式计算M个音律的频率，把计算得到的M个音律的频率，按下标i的大小，从小到大排列，得到数列F，即F＝<f 1,…,f i-1,f i,…,f M>。     A kind of antisymmetric law sequence generation method oriented to Pythagorean law according to claim 1, is characterized in that in described step 2), multiplying three method unit (20) temperament calculation formula is:
    Figure PCTCN2020128037-appb-100005
    Wherein {i×log 2 3} represents the value of the fractional part of the value i×log 2 3, use this formula to calculate the frequencies of the M temperaments, and use the calculated frequencies of the M temperaments to denote the size of i, from small to Large permutation to obtain a sequence F, that is, F=<f 1 ,...,f i-1 ,f i ,...,f M >.
  3. 根据权利要求2所述的一种面向毕达哥拉斯律的反对称律列产生方法，其特征在于所述步骤3)中，除三法单元(21)音律计算公式是：
    Figure PCTCN2020128037-appb-100006
    其中{-j×log 23}表示取数值-j×log 23的小数部分值，利用此公式计算N个音律的频率,把计算得到的N个音律的频率，按下标j的大小，从大到小排列，得到数列F’，即F′＝<f′ N,f′ N-1,…,f′ j+1,f′ j,…,f′ 1>。     A kind of antisymmetric law sequence generation method oriented to Pythagorean law according to claim 2, it is characterized in that in described step 3), divide by three method unit (21) temperament calculation formula is:
    Figure PCTCN2020128037-appb-100006
    Wherein {-j×log 2 3} means to take the value of the fractional part of the value -j×log 2 3, use this formula to calculate the frequencies of N temperaments, and press the calculated frequencies of the N temperaments to the size of j, Arrange from large to small to obtain a sequence F', that is, F'=<f' N ,f' N-1 ,...,f' j+1 ,f' j ,...,f' 1 >.
  4. 根据权利要求3所述的一种面向毕达哥拉斯律的反对称律列产生方法，其特征在于所述步骤4)中，数列F、数列F’和中心起始律的组成方法为Ω＝<F′f 0F>＝<f′ N,f′ N-1,…,f′ j…,f′ 1,f 0,f 1,…,f i,…,f M-1,f M>。 A method for generating an antisymmetric law sequence oriented to Pythagorean law according to claim 3, characterized in that in the step 4), the composition method of the sequence F, sequence F' and the central onset law is Ω ＝<F′f 0 F>=<f′ N ,f′ N-1 ,…,f′ j …,f′ 1 ,f 0 ,f 1 ,…,f i ,…,f M-1 ,f M >.
  5. 根据权利要求1所述的一种面向毕达哥拉斯律的反对称律列产生方法，其特征在于所述输出模块(3)为显示屏。A method for generating antisymmetric law sequences oriented to Pythagorean law according to claim 1, characterized in that the output module (3) is a display screen.
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