CN105374347A - A mixed algorithm-based computer-aided composition method for popular tunes in regions south of the Yangtze River - Google Patents

Abstract

Translated fromChinese

本发明公开了一种基于混合算法的江南小调计算机辅助作曲的方法，具体步骤包括建立江南小调音乐素材库、建立江南小调作曲知识规则库、制定遗传算法的关键规则、提取遗传算法的初始种群和生成江南小调旋律，建立94首的江南小调音乐素材库，用于特征参数提取。本发明通过知识规则库来定义编码规则、遗传算子及适应度函数，利用适应度函数评判机制，从而实现江南小调计算机自动作曲功能，将江南小调的知识规则库用于建立遗传算法中的适应度函数，既可以避免交互式遗传算法的复杂性，还大大提高了适应度函数的准确性，从而提高了整个计算机辅助作曲系统的准确性。

The invention discloses a computer-aided composing method of Jiangnan minor tune based on a hybrid algorithm. The specific steps include establishing a Jiangnan minor tune music material database, establishing a Jiangnan minor tune composition knowledge rule base, formulating key rules of a genetic algorithm, extracting the initial population of the genetic algorithm and Generate Jiangnan minor melody, and build a Jiangnan minor music material library of 94 songs for feature parameter extraction. The invention defines coding rules, genetic operators and fitness functions through the knowledge rule base, utilizes the fitness function evaluation mechanism, thereby realizing the computer automatic composing function of Jiangnan Minor, and uses the knowledge rule base of Jiangnan Minor to establish the adaptation in the genetic algorithm. The degree function can not only avoid the complexity of the interactive genetic algorithm, but also greatly improve the accuracy of the fitness function, thereby improving the accuracy of the entire computer-aided composition system.

Description

Translated fromChinese

一种基于混合算法的江南小调计算机辅助作曲的方法A Method of Computer-Aided Composition in Jiangnan Minor Based on Hybrid Algorithm

技术领域technical field

本发明涉及计算机应用技术领域，具体是一种基于混合算法的江南小调计算机辅助作曲的方法。The invention relates to the technical field of computer application, in particular to a method for computer-aided composition of Jiangnan minor tune based on a hybrid algorithm.

背景技术Background technique

随着计算机技术在音乐创作上的应用，计算机音乐应运而生。计算机音乐作为一门新兴的学科，其主要目的是应用计算机来模仿人们对音乐的认知，进行辅助创作和设计。探索计算机辅助作曲问题一方面可以了解和模拟作曲家在从事音乐创作这一特定过程中的思维方式；另一方面，基于计算机辅助作曲研究技术而开发的作曲系统所创作出的不同形式的音乐作品可以起到对作曲家的有益补充。With the application of computer technology in music creation, computer music came into being. As an emerging discipline, computer music is mainly aimed at using computers to imitate people's cognition of music and assist in creation and design. Exploring the problem of computer-aided composition can understand and simulate the way of thinking of composers in the specific process of music creation on the one hand; Can play a useful supplement to the composer.

目前计算机辅助作曲技术在国外相对成熟，总结来看主要的算法包括马尔克夫(Markov)转换表(或称马尔克夫链)、算法作曲研究中的知识库系统、音乐文法、人工神经网络技术和遗传算法。At present, computer-aided composition technology is relatively mature in foreign countries. In summary, the main algorithms include Markov (Markov) conversion table (or Markov chain), knowledge base system in algorithmic composition research, music grammar, artificial neural network technology and genetic algorithm.

马尔克夫(Markov)转换表就像一个函数。其自变量是当前的音符，而函数值则是下一个要出现音符的可能性。针对某一特定(如某一作曲家或某一时期)风格的音乐作品进行收集和统计，就可以构造出相应的转换表。该算法目前存在的问题是很难判断生成音乐的质量，此外随机生成的片段，与标准的完整音乐之间还是存在差距。A Markov transition table is like a function. Its argument is the current note, and the function value is the probability that the note will occur next. A corresponding conversion table can be constructed by collecting and counting music works of a certain style (such as a certain composer or a certain period). The current problem with the algorithm is that it is difficult to judge the quality of the generated music. In addition, there is still a gap between the randomly generated fragments and the standard complete music.

基于规则的知识库系统的算法作曲是一种很自然的选择，特别是在已定义完善的领域内建立模型或者是介绍清晰的结构或规则时尤其如此。其主要优点是：它们具有清晰的推理，并能够为行为的选择做出解释。该算法的缺点是知识引导机制的建立既困难又费时，对于较为规范的音乐容易总结规则，但是对于即兴多变的旋律，很难找到规范。Algorithmic composition of rule-based knowledge base systems is a natural choice, especially when modeling within well-defined domains or introducing clear structures or rules. Their main advantage is that they have clear reasoning and can explain the choice of behavior. The disadvantage of this algorithm is that it is difficult and time-consuming to establish a knowledge guidance mechanism. It is easy to summarize the rules for more standardized music, but it is difficult to find norms for impromptu and changeable melodies.

正如语言有文法一样，音乐也是有音乐文法的。结合统计的方法，使用音乐文法可以匹配(或捕获)现有作品中的各种音乐事件(如音程、节奏等)的概率分布，并能基于这些特征生成出类似风格的作品。但是该算法对于即兴创作的音乐很难找到范畴文法，进而很难进行音符的分解与重组，生成新的音乐。Just as language has a grammar, music has a musical grammar. Combined with statistical methods, the use of music grammar can match (or capture) the probability distribution of various musical events (such as intervals, rhythms, etc.) in existing works, and can generate works of similar styles based on these features. However, it is difficult for the algorithm to find a category grammar for improvised music, and it is difficult to decompose and recombine notes to generate new music.

在感知和认知方面，人工神经网络能够从一个样板集合中学习，以避免需要对规则的形式化。特别是递归神经网络能够成功获取一个旋律经过句的表层结构，并以这样获取的知识为基础，产生出新的旋律。但是所生成的旋律缺乏音乐的全局连贯性，即它无法获取较高级的音乐特征。从原理上讲，人工神经网络技术通常更适合用于分析音乐作品而不是创作。In terms of perception and cognition, ANNs are able to learn from a set of templates, avoiding the need to formalize rules. In particular, recurrent neural networks are able to successfully capture the surface structure of a melodic passing sentence and generate new melodies based on the knowledge thus acquired. But the generated melody lacks the global coherence of music, that is, it cannot capture higher-level musical features. In principle, artificial neural network techniques are often better suited for analyzing musical compositions than for composing them.

遗传算法是模拟达尔文的遗传选择和自然淘汰的生物进化过程的计算模型，是一种通过模拟自然进化过程搜索最优解的方法。遗传算法使用适应函数来演化候选者(染色体)，从而得到近似最优解。但是在使用遗传算法进行自动作曲的研究时，适应度函数其实是很难准确定义的。于是出现了让人代替适应度函数来直接评估染色体的一种方法，即交互式的遗传算法IGA。然而目前交互式遗传算法的有效性较差，用户必须听到所有可能潜在的解，才能做出具有普遍性的评估。Genetic Algorithm is a computational model that simulates Darwin's genetic selection and natural elimination process of biological evolution, and is a method of searching for the optimal solution by simulating the natural evolution process. Genetic algorithms use fitness functions to evolve candidates (chromosomes) to obtain near-optimal solutions. However, when using genetic algorithms for automatic composition research, the fitness function is actually difficult to define accurately. So there is a method to directly evaluate the chromosome by human instead of the fitness function, that is, the interactive genetic algorithm IGA. However, the effectiveness of interactive genetic algorithms is poor at present, and users must hear all possible potential solutions in order to make a generalized assessment.

综上所述，各种作曲算法各有其自身的优点和存在的问题。建立一种混合算法的计算机辅助作曲系统可以扬长避短，以最优化的方式进行计算机辅助作曲。此外，由于国内关于计算机作曲系统的研究起步较晚，目前并没有成熟的针对于中国民族音乐的算法作曲技术。因此将国际上现有的算法作曲技术进行整合，应用到中国民族音乐的分析和创作中，并建立有自己民族特色的计算机作曲系统是十分必要的。To sum up, each composition algorithm has its own advantages and problems. Establishing a computer-aided composition system with mixed algorithms can make use of its strengths and circumvent its weaknesses, and perform computer-aided composition in an optimal way. In addition, due to the relatively late start of domestic research on computer composition systems, there is currently no mature algorithmic composition technology for Chinese folk music. Therefore, it is very necessary to integrate the existing international algorithm composition technology, apply it to the analysis and creation of Chinese national music, and establish a computer composition system with its own national characteristics.

发明内容Contents of the invention

本发明的目的在于提供一种适应度函数准确性高、使用方便的基于混合算法的江南小调计算机辅助作曲的方法，以解决上述背景技术中提出的问题。The object of the present invention is to provide a method for computer-aided composition of Jiangnan minor tune based on hybrid algorithm with high accuracy of fitness function and easy to use, so as to solve the problems raised in the above-mentioned background technology.

为实现上述目的，本发明提供如下技术方案：To achieve the above object, the present invention provides the following technical solutions:

一种基于混合算法的江南小调计算机辅助作曲的方法，具体步骤如下：A method for computer-aided composition of Jiangnan minor tune based on hybrid algorithm, the specific steps are as follows:

(1)建立江南小调音乐素材库：建立94首的江南小调音乐素材库，用于特征参数提取；(1) Establish Jiangnan minor music material database: establish 94 Jiangnan minor music material databases for feature parameter extraction;

(2)建立江南小调作曲知识规则库：提取声学特征和旋律特征，建立知识规则库，用于遗传算法关键技术的制定；(2) Establish a knowledge rule base for Jiangnan minor composition: extract acoustic features and melody features, establish a knowledge rule base, and use it to formulate key technologies of genetic algorithms;

(3)制定遗传算法的关键规则：对江南小调素材厍进行特征参数计算及旋律特征的统计分析，根据提取的特征制定遗传算法的编码规则、遗传算子和适应度函数；(3) Formulate the key rules of the genetic algorithm: calculate the characteristic parameters and statistical analysis of the melody characteristics of the materials of Jiangnan Minor Tune, and formulate the coding rules, genetic operators and fitness functions of the genetic algorithm according to the extracted features;

(4)提取遗传算法的初始种群：根据用户选择的调式和速度，从素材库挑选对应的旋律，并提取旋律的第一小节作为遗传算法的初始种群；(4) Extract the initial population of the genetic algorithm: select the corresponding melody from the material library according to the mode and speed selected by the user, and extract the first bar of the melody as the initial population of the genetic algorithm;

(5)生成江南小调旋律：通过计算适应度函数，开始进行选择、交叉和变异的遗传计算，经过多次迭代直到达到终止的条件，再进行下一小节的遗传计算，最终生成12小节的江南小调的旋律。(5) Generating the melody of Jiangnan Minor: By calculating the fitness function, the genetic calculation of selection, crossover and mutation is started. After multiple iterations until the termination condition is reached, the genetic calculation of the next section is performed, and finally 12 sections of Jiangnan are generated. melody in minor key.

作为本发明进一步的方案：所述步骤(4)中的调式分别是G徵调、A羽调和C宫调，速度分别为中慢速和中快速。As a further solution of the present invention: the tone modes in the step (4) are respectively G-shaped tone, A-yu tone and C-gong tone, and the speeds are medium-slow and medium-fast respectively.

作为本发明进一步的方案：所述步骤(2)中建立江南小调作曲知识规则库时，分别提取江南小调的声学特征参数和旋律特征参数建，提取声学特征参数采用时频计算的方法，提取与音色、音高和调性相关的11个特征参数，计算频谱时所使用的傅立叶变换长度为8192个采样点，频率分辨率为5.38Hz，75％的重叠，得到的频谱为线性幅度谱，使用TrueEnvelope的方法来计算信号波形包络，所有声学特征参数均为帧平均值，帧时窗为0.05s，半重叠；旋律特征参数通过统计分析的方法获得，旋律特征参数共7个，包括特殊的旋律行进、节奏型和音程，旋律特征参数的统计概率计算公式如下：As a further scheme of the present invention: when setting up the Jiangnan Minor composition knowledge rule storehouse in the described step (2), extract respectively the acoustic feature parameter and the melody feature parameter of the Jiangnan Minor to build, extract the acoustic feature parameter and adopt the method of time-frequency calculation, extract and There are 11 characteristic parameters related to timbre, pitch and tonality. The Fourier transform length used to calculate the spectrum is 8192 sampling points, the frequency resolution is 5.38Hz, and the overlap is 75%. The obtained spectrum is a linear amplitude spectrum. Use The TrueEnvelope method is used to calculate the signal waveform envelope. All acoustic feature parameters are frame average values, and the frame time window is 0.05s, which is semi-overlapped. The melody feature parameters are obtained by statistical analysis. There are 7 melody feature parameters, including special The formula for calculating the statistical probability of melody progression, rhythm pattern and interval, and melody feature parameters is as follows:

作为本发明进一步的方案：所述步骤(3)中的适应度函数分两步进行，首先对生成的每个小节进行评判，然后对整个旋律进行适应度函数的评判，小节的适应度函数如下所示：As a further scheme of the present invention: the fitness function in the step (3) is carried out in two steps, at first each section generated is judged, and then the whole melody is judged on the fitness function, and the fitness function of the section is as follows Shown:

$\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span><span><span>=</span>=</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>N</span>N</span>}}\mathrm{<span><span>P</span>P</span>}\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>c</span>c</span>}\mathrm{<span><span>h</span>h</span>}<span><span>(</span>(</span>\mathrm{<span><span>j</span>j</span>}<span><span>)</span>)</span><span><span>/</span>/</span>\mathrm{<span><span>N</span>N</span>}<span><span>+</span>+</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>N</span>N</span>}}\mathrm{<span><span>D</span>D.</span>}\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>a</span>a</span>}\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>o</span>o</span>}\mathrm{<span><span>n</span>no</span>}<span><span>(</span>(</span>\mathrm{<span><span>j</span>j</span>}<span><span>)</span>)</span><span><span>/</span>/</span>\mathrm{<span><span>N</span>N</span>}<span><span>+</span>+</span>\frac{\mathrm{<span><span>I</span>I</span>}\mathrm{<span><span>n</span>no</span>}\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>e</span>e</span>}\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>v</span>v</span>}\mathrm{<span><span>a</span>a</span>}\mathrm{<span><span>l</span>l</span>}\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>\mathrm{<span><span>m</span>m</span>}}<span><span>+</span>+</span>\mathrm{<span><span>M</span>m</span>}\mathrm{<span><span>e</span>e</span>}\mathrm{<span><span>l</span>l</span>}\mathrm{<span><span>o</span>o</span>}\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>y</span>the\; y</span>}\mathrm{<span><span>3</span>3</span>}<span><span>+</span>+</span>\mathrm{<span><span>M</span>m</span>}\mathrm{<span><span>e</span>e</span>}\mathrm{<span><span>l</span>l</span>}\mathrm{<span><span>o</span>o</span>}\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>y</span>the\; y</span>}\mathrm{<span><span>4</span>4</span>}<span><span>+</span>+</span>\mathrm{<span><span>R</span>R</span>}\mathrm{<span><span>h</span>h</span>}\mathrm{<span><span>y</span>the\; y</span>}\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>h</span>h</span>}\mathrm{<span><span>m</span>m</span>}$

(公式2)，(Formula 2),

其中i表示第i个小节，j表示第i个小节中的第j个音符，N表示小节中音符的个数，m表示该小节中音程量≥48的旋律音程个数；Wherein i represents the i-th bar, j represents the j-th note in the i-th bar, N represents the number of notes in the bar, and m represents the number of melody intervals with an interval amount ≥ 48 in the bar;

整个旋律的适应度函数如下所示：The fitness function of the whole melody is as follows:

$F=\underset{i=1}{\overset{12}{\&Sigma;}}f\left(i\right)+Interval2$(公式3)。$f=\underset{i=1}{\overset{12}{\&Sigma;}}f\left(i\right)+I\mathrm{no}terval2$ (Formula 3).

作为本发明再进一步的方案：所述步骤(5)中采用遗传算法生成江南小调的旋律时，初始种群为10个，以小节为迭代单元，设定适应度函数得分小于4分的小节下一轮迭代舍弃，生成12个小节的江南小调旋律，采用整个旋律的适应度函数进行评判，将得分最高的旋律视为生成的旋律。As a further scheme of the present invention: when adopting genetic algorithm to generate the melody of Jiangnan Minor in the described step (5), the initial population is 10, with the subsection as the iterative unit, and the next subsection whose fitness function score is set to be less than 4 points After rounds of iterations are discarded, 12 bars of Jiangnan minor melody are generated, and the fitness function of the entire melody is used for evaluation, and the melody with the highest score is regarded as the generated melody.

与现有技术相比，本发明的有益效果是：Compared with prior art, the beneficial effect of the present invention is:

本发明通过知识规则库来定义编码规则、遗传算子及适应度函数，利用适应度函数评判机制，从而实现江南小调计算机自动作曲功能，将江南小调的知识规则库用于建立遗传算法中的适应度函数，既可以避免交互式遗传算法的复杂性，还大大提高了适应度函数的准确性，从而提高了整个计算机辅助作曲系统的准确性。The present invention defines coding rules, genetic operators and fitness functions through the knowledge rule base, and utilizes the fitness function evaluation mechanism to realize the computer automatic composing function of Jiangnan Minor, and uses the knowledge rule base of Jiangnan Minor to establish the adaptation in the genetic algorithm. The degree function can not only avoid the complexity of the interactive genetic algorithm, but also greatly improve the accuracy of the fitness function, thereby improving the accuracy of the entire computer-aided composition system.

附图说明Description of drawings

图1为本发明的流程示意图。Fig. 1 is a schematic flow chart of the present invention.

图2为本发明中建立适应度函数的流程示意图。Fig. 2 is a schematic flow chart of establishing a fitness function in the present invention.

图3为本发明中实施例1生成的G徵调、中慢速的江南小调旋律谱图。Fig. 3 is the Jiangnan minor melody spectrogram generated in embodiment 1 of the present invention in G key and medium-slow speed.

具体实施方式detailed description

下面结合具体实施方式对本专利的技术方案作进一步详细地说明。The technical solution of this patent will be described in further detail below in conjunction with specific embodiments.

请参阅图1-2，一种基于混合算法的江南小调计算机辅助作曲的方法，具体步骤如下：Please refer to Figure 1-2, a computer-aided composition method based on a hybrid algorithm in Jiangnan Minor, the specific steps are as follows:

(1)建立江南小调音乐素材库：建立94首的江南小调音乐素材库，用于特征参数提取；(1) Establish Jiangnan minor music material database: establish 94 Jiangnan minor music material databases for feature parameter extraction;

(2)建立江南小调作曲知识规则库：提取声学特征和旋律特征，建立知识规则库，用于遗传算法关键技术的制定；(2) Establish a knowledge rule base for Jiangnan minor composition: extract acoustic features and melody features, establish a knowledge rule base, and use it to formulate key technologies of genetic algorithms;

(3)制定遗传算法的关键规则：对江南小调素材库进行特征参数计算及旋律特征的统计分析，根据提取的特征制定遗传算法的编码规则、遗传算子和适应度函数；(3) Formulate the key rules of the genetic algorithm: calculate the characteristic parameters and statistical analysis of the melody characteristics of the Jiangnan minor tune material database, and formulate the coding rules, genetic operators and fitness functions of the genetic algorithm according to the extracted features;

(4)提取遗传算法的初始种群：根据用户选择的调式和速度，从素材库挑选对应的旋律，并提取旋律的第一小节作为遗传算法的初始种群；(4) Extract the initial population of the genetic algorithm: select the corresponding melody from the material library according to the mode and speed selected by the user, and extract the first bar of the melody as the initial population of the genetic algorithm;

(5)生成江南小调旋律：通过计算适应度函数，开始进行选择、交叉和变异的遗传计算，经过多次迭代直到达到终止的条件，再进行下一小节的遗传计算，最终生成12小节的江南小调的旋律。(5) Generating the melody of Jiangnan Minor: By calculating the fitness function, the genetic calculation of selection, crossover and mutation is started. After multiple iterations until the termination condition is reached, the genetic calculation of the next section is performed, and finally 12 sections of Jiangnan are generated. melody in minor key.

建立江南小调音乐素材库时，建立94首江南小调的素材库，音频格式包含MIDI和Wave格式两类，MIDI格式用来提取旋律特征，Wave格式用来提取声学特征参数，该素材库中共包含三类调式，分别是G徵调、A羽调和C宫调，演奏速度从50bpm至160bpm，以90bpm为限，将低于90bpm的速度定义为中慢速，高于90bpm的速度定义为中快速。When building the Jiangnan minor music material library, a material library of 94 Jiangnan minor tunes was established. The audio formats include MIDI and Wave formats. The MIDI format is used to extract melody features, and the Wave format is used to extract acoustic feature parameters. The material library contains three Class mode, respectively G sign, A feather and C palace, the playing speed is from 50bpm to 160bpm, limited to 90bpm, the speed lower than 90bpm is defined as medium-slow speed, and the speed higher than 90bpm is defined as medium-fast.

所述的建立江南小调作曲知识规则库时，分别提取江南小调的声学特征参数和旋律特征参数建，提取声学特征参数采用时频计算的方法，提取与音色、音高和调性相关的11个特征参数，如表1所示：When the described Jiangnan minor composition knowledge rule base is established, the acoustic characteristic parameters and melody characteristic parameters of the Jiangnan minor are respectively extracted to build, and the acoustic characteristic parameters are extracted using the method of time-frequency calculation to extract 11 parameters related to timbre, pitch and tonality. Feature parameters, as shown in Table 1:

表1计算的声学特征参数Acoustic characteristic parameters calculated in Table 1

计算频谱时所使用的傅立叶变换长度为8192个采样点，频率分辨率为5.38Hz，75％的重叠，得到的频谱为线性幅度谱，使用TrueEnvelope的方法来计算信号波形包络，所有声学特征参数均为帧平均值，帧时窗为0.05s，半重叠。The length of the Fourier transform used to calculate the spectrum is 8192 sampling points, the frequency resolution is 5.38Hz, and the overlap is 75%. The obtained spectrum is a linear amplitude spectrum, and the TrueEnvelope method is used to calculate the signal waveform envelope. All are frame averages, the frame time window is 0.05s, and half overlaps.

旋律特征参数通过统计分析的方法获得，旋律特征参数共7个，包括特殊的旋律行进、节奏型和音程，通过统计94首江南小调中各个旋律特征所占的比例而建立旋律特征规则库，旋律特征参数的统计概率计算公式如下：The melody feature parameters are obtained through statistical analysis. There are 7 melody feature parameters in total, including special melody progression, rhythm pattern and interval. The melody feature rule library is established by counting the proportion of each melody feature in 94 Jiangnan minor tunes. The statistical probability calculation formula of the characteristic parameters is as follows:

计算的旋律特征参数如表2所示：The calculated melody feature parameters are shown in Table 2:

表2江南小调的旋律特征参数Table 2 The melodic characteristic parameters of Jiangnan Minor

序号serial number旋律特征参数Melody feature parameters11乐曲速度music tempo22调式debug33音符时长note duration44特殊节奏型Special Rhythm55特色旋法-音程向量Characteristic rotation-interval vector66旋律音程的音程量Interval volume of melodic intervals77乐曲结束旋法ending melody

遗传算法生成江南小调的计算步骤如下：The calculation steps of the genetic algorithm to generate Jiangnan Minor are as follows:

1、设定初始种群：系统得到用户需求后，自动在素材库中随机挑选符合条件的乐曲，并将乐曲的第一小节提取出来作为初始种群，采用现有的乐段，而不是计算机随机生成乐段，目的让作曲系统较快的搜索到最优解，遗传算法的迭代单元为小节，这样可以尽可能的保持完整的乐思，遗传算法种群设置为10。1. Set the initial population: After the system obtains the user's needs, it will automatically randomly select the music that meets the requirements in the material library, and extract the first bar of the music as the initial population, using the existing music section instead of randomly generated by the computer Music section, the purpose is to allow the composition system to quickly search for the optimal solution. The iteration unit of the genetic algorithm is a section, so that the complete music idea can be kept as much as possible. The population of the genetic algorithm is set to 10.

2、设定遗传算法编码规则：根据知识规则库设定编码规则，编码规则是对每个音符进行编码，包括时值、音高和强弱。2. Set the genetic algorithm coding rules: set the coding rules according to the knowledge rule base. The coding rules are to code each note, including duration, pitch and strength.

(1)音符时值：按照4分音符为1拍进行时值编码，如表3所示：(1) Note duration: the duration coding is carried out according to the quarter note as 1 beat, as shown in Table 3:

表3时长的编码规则Table 3 Encoding rules for duration

(2)音符音高：音高共包含三个八度，分别是小字组、小字一组和小字二组。以小字组c的音高设为0，其余音的编码值以一个半音为分辨率依次递增1，音高的编码规则如表4所示：(2) Note pitch: The pitch consists of three octaves, which are respectively the small word group, the small word group and the small word group two. The pitch of the small character group c is set to 0, and the encoding value of the remaining tones is incremented by 1 at a resolution of one semitone. The encoding rules of the pitch are shown in Table 4:

表4音高的编码规则Table 4 Encoding rules for pitch

音名musical alphabetC3C3D3D3E3E3G3G3A3A3休止符pause编码coding0022447799-48-48音名musical alphabetC4C4D4D4E4E4G4G4A4A4编码coding121214141616191921twenty one音名musical alphabetC5C5D5D5E5E5G5G5A5A5编码coding24twenty four2626282831313333

(3)音符强度：2/4拍包含音的强度是强拍和弱拍，休止符的力度为0，强拍的力度为127，弱拍的力度为100。(3) Note strength: 2/4 beat contains sound strength of strong beat and weak beat, the strength of rest is 0, the strength of strong beat is 127, and the strength of weak beat is 100.

3、设定遗传算子方式：遗传算子包括选择、交叉和变异。3. Set the genetic operator mode: genetic operators include selection, crossover and mutation.

(1)选择算子：采用锦标赛选择算法。(1) Selection operator: The tournament selection algorithm is adopted.

(2)交叉算子：对小节内时长为一拍的旋律段进行交叉，交叉概率为0.6。随机选择两个小节，计算每个小节音符的时值，累积时值等于1时为交叉位置。(2) Crossover operator: crossover the melody segments with a duration of one beat in a measure, and the crossover probability is 0.6. Randomly select two measures, calculate the time value of the note in each measure, and when the cumulative time value is equal to 1, it is the crossing position.

(3)变异算子：变异算子包括音程变异，音符分裂和音符合并三种变异。按照小节进行变异，并且按照30％的概率进行，即10个小节中随机选择3个小节变异，1个小节进行音程变异，1个小节进行音符合并，最后1个小节进行音符分裂，具体某个小节中哪个音符变异，除了首尾音符不变异以外，其他音符随机变异：(3) Variation operator: The variation operator includes interval variation, note splitting and note merging. Variation is carried out according to the measure, and it is carried out according to the probability of 30%, that is, 3 measures are randomly selected from 10 measures to be mutated, 1 measure is subjected to interval variation, 1 measure is performed to merge notes, and the last measure is subjected to note splitting. Which note in the measure is mutated, except the first and last notes are not mutated, other notes are randomly mutated:

A、音程变异：改变某个音符的音高，从而影响该音符的前后音程值。发生音程变异时，改变前后音程的概率如下表5所示。A. Interval Variation: Change the pitch of a note, thereby affecting the interval value before and after the note. When interval variation occurs, the probability of changing intervals before and after is shown in Table 5 below.

产生[0，1]的随机数，如果随机数位于[0，0.947]内，在产生新音程间隔均为5内的音符中选取，如果随机数位于(0.947，0.973]，在产生前音程间隔≤5且后音程间隔＞5的音符中选取；如果随机数位于(0.973，0.999]，在产生前音程间隔＞5且后音程间隔≤5的音符中选取；如果随机数位于(0.999，1]，在产生前音程间隔＞5且后音程间隔＞5的音符中选取。如果在某个区间内没有符合条件的音符出现，则变异直接结束。Generate a random number of [0, 1], if the random number is in [0, 0.947], select from the notes that generate new intervals within 5, if the random number is in (0.947, 0.973], the interval before the generation ≤5 and the interval between intervals>5; if the random number is at (0.973, 0.999], select among the notes that generate intervals before intervals>5 and intervals after intervals≤5; if the random number is at (0.999,1] , select among the notes that produce the interval of the previous interval > 5 and the interval of the subsequent interval > 5. If there is no qualified note in a certain interval, the mutation will end directly.

表5音程变异的概率分布Table 5 Probability distribution of interval variation

B、音符分裂：将一个音符分裂成两个音符，且仅变异时长为0.5，1，2的音符。如果音符时长为0.5，音长变异分配方案如表6所示，两个音符之间的音程关系生成概率如表7所示：B. Note splitting: Split a note into two notes, and only mutate the notes whose duration is 0.5, 1, and 2. If the duration of the note is 0.5, the distribution scheme of the variation of the sound length is shown in Table 6, and the generation probability of the interval relationship between two notes is shown in Table 7:

表6音符时长为0.5时音长变异方案Table 6 Note length variation scheme when the note duration is 0.5

分配方案distribution plan1/2+1/21/2+1/21/4+3/41/4+3/43/4+1/43/4+1/4概率probability0.80.80.10.10.10.1

其中第一行的数据表示所占音符时长的比例。The data in the first line represents the proportion of the note duration.

表7两个音符之间的音程关系生成概率Table 7 Interval relation generation probability between two notes

如果音符时长为1或2，则音长变异分配方案如表8所示，两个音符之间的音程关系生成概率仍参考表7。If the note length is 1 or 2, the sound length variation allocation scheme is shown in Table 8, and the interval relationship generation probability between two notes still refers to Table 7.

表8音符时长为1或2时音长变异方案Table 8 note length is 1 or 2 when sound length variation scheme

分配方案distribution plan1/2+1/21/2+1/21/4+3/41/4+3/43/4+1/43/4+1/41/8+7/81/8+7/87/8+1/87/8+1/8概率probability0.80.80.080.080.080.080.020.020.020.02

C、音符合并：将两个音符合并成一个音，合并的音符时长与原来两个音的时长相同，步骤如下：以随机的音符取代这两个音，时长为这两个音的时值总和，音符的音高选择按照如下概率进行：第一行表示音高，第二行表示音高的编码，第三行为出现的概率，仍然采用音程变异的方法进行随机选取。C. Merge of notes: Merge two notes into one note. The duration of the merged note is the same as the duration of the original two notes. The steps are as follows: replace the two notes with a random note, and the duration is the sum of the duration of the two notes. , the pitch of the note is selected according to the following probability: the first line represents the pitch, the second line represents the encoding of the pitch, and the third line represents the probability of occurrence, and the method of interval variation is still used for random selection.

表9音符合并分配方案Table 9 phonetic combination allocation scheme

4、设定适应度函数：适应度函数分两步进行，首先对生成的每个小节进行评判，当所有12小节全部生成后，然后对整个旋律进行适应度函数的评判，小节的适应度函数如下所示：4. Set the fitness function: the fitness function is carried out in two steps. First, judge each generated measure. After all 12 measures are generated, then judge the fitness function of the entire melody. The fitness function of the measure As follows:

$\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span><span><span>=</span>=</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>N</span>N</span>}}\mathrm{<span><span>P</span>P</span>}\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>c</span>c</span>}\mathrm{<span><span>h</span>h</span>}<span><span>(</span>(</span>\mathrm{<span><span>j</span>j</span>}<span><span>)</span>)</span><span><span>/</span>/</span>\mathrm{<span><span>N</span>N</span>}<span><span>+</span>+</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>N</span>N</span>}}\mathrm{<span><span>D</span>D.</span>}\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>a</span>a</span>}\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>o</span>o</span>}\mathrm{<span><span>n</span>no</span>}<span><span>(</span>(</span>\mathrm{<span><span>j</span>j</span>}<span><span>)</span>)</span><span><span>/</span>/</span>\mathrm{<span><span>N</span>N</span>}<span><span>+</span>+</span>\frac{\mathrm{<span><span>I</span>I</span>}\mathrm{<span><span>n</span>no</span>}\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>e</span>e</span>}\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>v</span>v</span>}\mathrm{<span><span>a</span>a</span>}\mathrm{<span><span>l</span>l</span>}\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>\mathrm{<span><span>m</span>m</span>}}<span><span>+</span>+</span>\mathrm{<span><span>M</span>m</span>}\mathrm{<span><span>e</span>e</span>}\mathrm{<span><span>l</span>l</span>}\mathrm{<span><span>o</span>o</span>}\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>y</span>the\; y</span>}\mathrm{<span><span>3</span>3</span>}<span><span>+</span>+</span>\mathrm{<span><span>M</span>m</span>}\mathrm{<span><span>e</span>e</span>}\mathrm{<span><span>l</span>l</span>}\mathrm{<span><span>o</span>o</span>}\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>y</span>the\; y</span>}\mathrm{<span><span>4</span>4</span>}<span><span>+</span>+</span>\mathrm{<span><span>R</span>R</span>}\mathrm{<span><span>h</span>h</span>}\mathrm{<span><span>y</span>the\; y</span>}\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>h</span>h</span>}\mathrm{<span><span>m</span>m</span>}$

(公式2)，(Formula 2),

其中i表示第i个小节，j表示第i个小节中的第j个音符，N表示小节中音符的个数，m表示该小节中音程量≥48的旋律音程个数；Wherein i represents the i-th bar, j represents the j-th note in the i-th bar, N represents the number of notes in the bar, and m represents the number of melody intervals with an interval amount ≥ 48 in the bar;

A、Pitch：用于检测出现的每一个音符：根据作曲规则中得出的不同音高音符出现的概率，可以用Pitch(i)来表示不同音高的适应度函数，如表10所示：A. Pitch: used to detect each note that appears: according to the probability of occurrence of different pitch notes obtained in the composition rules, Pitch(i) can be used to represent the fitness function of different pitches, as shown in Table 10:

表10音符音高函数表Table 10 note pitch function table

条件conditionPitch(i)Pitch(i)条件conditionPitch(i)Pitch(i)i＝-48i=-480.0490.049i＝16i=160.7950.795i＝0，2，33i=0, 2, 3300i＝19i=191.0001.000i＝4i=40.010.01i＝21i=210.6140.614i＝7i=70.1320.132i＝24i=240.4560.456i＝9i=90.2720.272i＝26i=260.1840.184i＝12i=120.5250.525i＝28i=280.0890.089i＝14i=140.6530.653i＝31i=310.0130.013

B、Duration：用于检测每个音符出现的时值：根据作曲规则中得出的不同时值的音符出现的概率，可以用Pitch(i)来表示不同时值的适应度函数，如表11所示：B. Duration: used to detect the time value of each note: according to the probability of occurrence of notes of different time values obtained in the composition rules, Pitch(i) can be used to represent the fitness function of different time values, as shown in Table 11 Shown:

表11音符时值函数表Table 11 note duration function table

条件conditionDuration(i)Duration(i)条件conditionDuration(i)Duration(i)i＝0.5i=0.511i＝1i=10.2270.227i＝0.25i=0.250.9240.924i＝1.5i=1.50.0460.046i＝0.75i=0.750.0860.086i＝0.125i=0.1250.010.01i＝2i=20.0920.092i＝0.375i=0.3750.0050.005

C、Interval1：表示小节内旋律音程的评估：江南小调的旋律音程间隔大部分都是小于7的，所以如果相邻两个音之间的音程间隔大于7，就认为间隔太大，不符合江南小调旋律部分特征。江南小调以0，2，3的音程间隔行进方式占据了整体的88％左右，加上偶有的音程间隔为5的纯四度和音程间隔为7的纯五度跳进，这些音程间隔一共占据了约93％。因此Interval1的适应度函数如(公式3)所示：C. Interval1: Indicates the evaluation of the melody interval in the measure: most of the melody intervals in Jiangnan minor are less than 7, so if the interval between two adjacent tones is greater than 7, it is considered that the interval is too large and does not conform to Jiangnan Minor melodic part features. Jiangnan minor’s progression of intervals of 0, 2, and 3 accounts for about 88% of the overall scale, plus occasional pure fourths with an interval of 5 and pure fifths with an interval of 7. These intervals total Takes about 93%. Therefore, the fitness function of Interval1 is shown in (Formula 3):

(公式3) (Formula 3)

其中a表示某一小节中音程间隔小于4的值，b表示音程间隔等于4或者5的值，c表示其他音程间隔。那么当音程间隔小于4的值越多时，则此函数值越大。Among them, a represents the value of interval less than 4 in a measure, b represents the value of interval equal to 4 or 5, and c represents other intervals. Then when there are more values with intervals smaller than 4, the value of this function is larger.

D、Melody3：三个音构成的特色音程向量的评价函数，Melody3是要把小节中特殊的3个音的音程向量找出来，因此计算Melody3之前，先做判定：把3个音构成时长为2拍或1拍的特殊音程向量挑选出来，如果不存在音程向量，则直接不计算Melody3，三个音构成的特色音程向量的评价函数如表12所示：D. Melody3: The evaluation function of the characteristic interval vector composed of three tones. Melody3 is to find out the interval vector of the special three tones in the measure. Therefore, before calculating Melody3, first make a judgment: the duration of the three tones is 2 The special interval vector of beat or 1 beat is selected. If there is no interval vector, Melody3 will not be calculated directly. The evaluation function of the characteristic interval vector composed of three tones is shown in Table 12:

表12三个音构成的音程向量评价函数The interval vector evaluation function that three tones of table 12 form

条件conditionMelody3Melody3P_i+2＞P_i+1＞P_iP_i+2 >P_i+1 >P_i0.60.6P_i+2＜P_i+1＜P_iP_i+2 <P_i+1 <P_i0.920.92P_i+2＝P_i+1≠P_iP_i+2 ＝P_i+1 ≠P_i0.080.08P_i+1＝P_i≠P_i+2P_i+1 ＝P_i ≠P_i+20.860.86P_i＝P_i+1＝P_i+2P_i =P_i+1 =P_i+20.170.17

(P_i+2-P_i+1)(P_i+1-P_i)＜0且|P_i+2-P_i+1|＝|(P_i+1-P_i)|≠0(P_i+2 -P_i+1 )(P_i+1 -P_i )<0 and |P_i+2 -P_i+1 |=|(P_i+1 -P_i )|≠011

E、Melody4：四个音构成的特色音程向量的评价函数：与Melody3一样，在计算该函数之前先做判定，将时长为2拍或1拍的特殊音程向量找出来，四个音构成的特色音程向量的评价函数如表13所示：E. Melody4: The evaluation function of the characteristic interval vector composed of four tones: the same as Melody3, make a judgment before calculating the function, find out the special interval vector with a duration of 2 beats or 1 beat, and the characteristics of the four tones The evaluation function of the interval vector is shown in Table 13:

表13四个音构成的音程向量评价函数The interval vector evaluation function formed by four tones of table 13

条件conditionMelody4Melody4P_i+3＞P_i+2＞P_i+1＞P_iP_i+3 >P_i+2 >P_i+1 >P_i0.300.30P_i+3＜P_i+2＜P_i+1＜P_iP_i+3 <P_i+2 <P_i+1 <P_i0.210.21(P_i+2-P_i+1)(P_i+1-P_i)＜0且|P_i+2-P_i+1|＝|(P_i+1-P_i)|≠|P_i+3-P_i+2|≠0(P_i+2 -P_i+1 )(P_i+1 -P_i )<0 and |P_i+2 -P_i+1 |=|(P_i+1 -P_i )|≠|P_{i +3} -P_i+2 |≠011(P_i+2-P_i+1)(P_i+1-P_i)＜0且|P_i+2-P_i+1|＝|(P_i+1-P_i)|＝|P_i+3-P_i+2|≠0(P_i+2 -P_i+1 )(P_i+1 -P_i )<0 and |P_i+2 -P_i+1 |=|(P_i+1 -P_i )|=|P_{i +3} -P_i+2 |≠00.150.15P_i+3＝P_i+2或P_i+2＝P_i+1或P_i+1＝P_iP_i+3 =P_i+2 or P_i+2 =P_i+1 or P_i+1 =P_i0.500.50(P_i+2-P_i+1)(P_i+3-P_i+2)＜0且|P_i+2-P_i+1|＝|(P_i+3-P_i+2)|≠|P_i+1-P_i|≠0(P_i+2 -P_i+1 )(P_i+3 -P_i+2 )<0 and |P_i+2 -P_i+1 |=|(P_i+3 -P_i+2 )| ≠|P_i+1 -P_i |≠00.210.21

F、Rhythm：特色节奏型的评价函数：从所含有的节奏型来看，主要包含两大类，一类是节奏型的时长为2拍的，另一类是节奏型为1拍的。因此节奏型函数将分成两个部分进行计算，一个是Rhythm1(计算时长为1拍的节奏型)函数，另一个是Rhythm2(计算时长为2拍的节奏型)函数，节奏型Rhythm2评价函数如表14所示：F. Rhythm: The evaluation function of the characteristic rhythm type: from the perspective of the included rhythm types, it mainly includes two categories, one is the rhythm type whose duration is 2 beats, and the other is the rhythm type whose duration is 1 beat. Therefore, the rhythm function will be divided into two parts for calculation, one is the Rhythm1 (rhythm type whose calculation time is 1 beat) function, and the other is the Rhythm2 (rhythm type whose calculation time is 2 beats) function, and the rhythm type Rhythm2 evaluation function is shown in the table 14 shows:

表14节奏型Rhythm2评价函数Table 14 Rhythm type Rhythm2 evaluation function

条件conditionRhythm2Rhythm2N＝3N=30.160.16N＝2且D₁＞D₂N=2 and D₁ >D₂0.260.26N＝2且D₁＜D₂N=2 and D₁ <D₂0.040.04N＝1N=10.560.56其他other00

在此表中，D₁表示某一小节中第一个音级的时值编码，D₂表示此小节第二个音级时值编码，N表示此节奏型的音符数量，节奏型Rhythm1评价函数如表15所示：In this table, D₁ represents the time value code of the first sound level in a certain measure, D₂ represents the time value code of the second sound level in this measure, N represents the number of notes of this rhythm pattern, and the rhythm pattern Rhythm1 evaluation function As shown in Table 15:

表15节奏型Rhythm1评价函数Table 15 Rhythm type Rhythm1 evaluation function

条件conditionRhythm1Rhythm1条件conditionRhythm1Rhythm1

N＝1N=10.630.63N＝3且D₁＝D₂N=3 and D₁ =D₂0.140.14N＝2且D₁＝D₂N=2 and D₁ =D₂11N＝3且D₁＞D₂N=3 and D₁ >D₂0.380.38N＝2且D₁＜D₂N=2 and D₁ <D₂0.010.01N＝3且D₁＜D₂N=3 and D₁ <D₂0.030.03N＝2且D₁＞D₂N=2 and D₁ >D₂0.280.28N＝4N=40.440.44

在此表中，D₁表示某一小节中第一个音级的时值编码，D₂表示此小节第二个音级时值编码，N表示此节奏型中的音符数量。In this table, D₁ represents the time value code of the first sound level in a certain measure, D₂ represents the time value code of the second sound level in this measure, and N represents the number of notes in this rhythm pattern.

整体旋律的适应度函数：The fitness function of the overall melody:

$\mathrm{<span><span>F</span>f</span>}<span><span>=</span>=</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>12</span>12</span>}}\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span><span><span>+</span>+</span>\mathrm{<span><span>I</span>I</span>}\mathrm{<span><span>n</span>no</span>}\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>e</span>e</span>}\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>v</span>v</span>}\mathrm{<span><span>a</span>a</span>}\mathrm{<span><span>l</span>l</span>}\mathrm{<span><span>2</span>2</span>}$

(公式4)(Formula 4)

G、Interval2表示小节间旋律音程的评判G, Interval2 means the judgment of melody interval between bars

根据之前的作曲规则，小节间旋律音程的评判如表16所示：According to the previous composition rules, the evaluation of melody intervals between bars is shown in Table 16:

表16Interval2评价函数Table 16 Interval2 evaluation function

音程差pitch differenceInterval2Interval2音程差pitch differenceInterval2Interval2000.3290.32910100.0120.012221.0001.00012120.0170.017330.9900.99014140.0010.001440.1340.13415150.0030.003550.2010.20117170.0010.001770.0340.03419190.0010.001880.0140.014休止符pause0.0090.009990.0120.012其他other00

采用遗传算法生成江南小调的旋律时，初始种群为10个，以小节为迭代单元，设定适应度函数得分小于4分的小节下一轮迭代舍弃，生成12个小节的江南小调旋律，采用整个旋律的适应度函数进行评判，将得分最高的旋律视为生成的旋律。When the genetic algorithm is used to generate the melody of Jiangnan Minor, the initial population is 10, and the measure is used as the iterative unit, and the measure whose fitness function score is less than 4 is set to be discarded in the next round of iteration, and the melody of Jiangnan Minor with 12 measures is generated. The fitness function of the melody is judged, and the melody with the highest score is regarded as the generated melody.

实施例1Example 1

请参阅图3，一种基于混合算法的江南小调计算机辅助作曲的方法，具体步骤如下：Please refer to Figure 3, a method for computer-aided composition of Jiangnan minor based on a hybrid algorithm, the specific steps are as follows:

(1)初始音乐种群的生成：首先用户选择调式和速度，例如选择G徵调式和中慢速。系统接收到用户的需求后，在音乐素材库随机挑选符合该条件的10首音乐素材，并将每首音乐素材的第一小节作为初始种群；(1) Generation of the initial music population: first, the user selects a mode and a speed, for example, selects a G mode and a medium-slow speed. After the system receives the user's needs, it will randomly select 10 music materials that meet the conditions in the music material library, and use the first bar of each music material as the initial population;

(2)生成江南小调知识规则库：提取江南小调的特征参数，生成知识规则库。特征参数包括通过计算获取的11个声学特征以及基于统计的7个旋律特征，为遗传算法的编码规则、适应度函数和遗传算子提供算法依据；(2) Generating the knowledge rule base of Jiangnan Minor: extracting the characteristic parameters of Jiangnan Minor to generate a knowledge rule base. The feature parameters include 11 acoustic features obtained through calculation and 7 melodic features based on statistics, which provide the algorithm basis for the coding rules, fitness functions and genetic operators of the genetic algorithm;

(3)制定音乐的编码规则：编码规则是对每个音符进行编码，包括时值、音高和强弱。所有编码规则都参照MIDI格式的编码规则。音符时值是按照4分音符为1拍进行时值编码；江南小调的音高共包含三个八度，分别是小字组、小字一组和小字二组，以小字组c的音高设为0，其余音的编码值以一个半音为分辨率依次递增1或递减1；音符强度包括强拍和弱拍，设定强拍的力度为127，弱拍的力度为100，休止符的力度为0。(3) Formulate the encoding rules of music: the encoding rules are to encode each note, including duration, pitch and intensity. All encoding rules refer to the encoding rules of MIDI format. The time value of the note is coded according to the quarter note as 1 beat; the pitch of the Jiangnan minor contains three octaves, which are the small character group, the small character group and the small character group two, and the pitch of the small character group c is set to 0, the encoding value of the rest of the tone is incremented by 1 or decreased by 1 with a resolution of one semitone; the strength of the note includes strong beat and weak beat, set the strength of the strong beat to 127, the strength of the weak beat to 100, and the strength of the rest to 0 .

(4)适应度函数的设定：适应度函数的生成主要基于江南小调的作曲知识规则库提出的。适应度函数的评判分两步，首先迭代每个小节的时候仅计算每个小节的适应度函数，由于旋律的倒数第二小节要有特殊的结束旋法，因此针对该小节的适应度函数与评判其他小节的函数略有差别；当所有12小节全部生成后，计算整个旋律的适应度函数。相关的适应函数函数计算如下：(4) The setting of the fitness function: The generation of the fitness function is mainly based on the composition knowledge rule base of Jiangnan Minor. The evaluation of the fitness function is divided into two steps. First, only the fitness function of each subsection is calculated when iterating each subsection. Since the second-to-last subsection of the melody has a special ending rotation method, the fitness function and judgment of the subsection The functions of other bars are slightly different; when all 12 bars are generated, the fitness function of the entire melody is calculated. The relevant fitness function function is calculated as follows:

1)的适应度函数1) The fitness function

$\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span><span><span>=</span>=</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>N</span>N</span>}}\mathrm{<span><span>P</span>P</span>}\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>c</span>c</span>}\mathrm{<span><span>h</span>h</span>}<span><span>(</span>(</span>\mathrm{<span><span>j</span>j</span>}<span><span>)</span>)</span><span><span>/</span>/</span>\mathrm{<span><span>N</span>N</span>}<span><span>+</span>+</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>N</span>N</span>}}\mathrm{<span><span>D</span>D.</span>}\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>a</span>a</span>}\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>o</span>o</span>}\mathrm{<span><span>n</span>no</span>}<span><span>(</span>(</span>\mathrm{<span><span>j</span>j</span>}<span><span>)</span>)</span><span><span>/</span>/</span>\mathrm{<span><span>N</span>N</span>}<span><span>+</span>+</span>\frac{\mathrm{<span><span>I</span>I</span>}\mathrm{<span><span>n</span>no</span>}\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>e</span>e</span>}\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>v</span>v</span>}\mathrm{<span><span>a</span>a</span>}\mathrm{<span><span>l</span>l</span>}\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>\mathrm{<span><span>m</span>m</span>}}<span><span>+</span>+</span>\mathrm{<span><span>M</span>m</span>}\mathrm{<span><span>e</span>e</span>}\mathrm{<span><span>l</span>l</span>}\mathrm{<span><span>o</span>o</span>}\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>y</span>the\; y</span>}\mathrm{<span><span>3</span>3</span>}<span><span>+</span>+</span>\mathrm{<span><span>M</span>m</span>}\mathrm{<span><span>e</span>e</span>}\mathrm{<span><span>l</span>l</span>}\mathrm{<span><span>o</span>o</span>}\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>y</span>the\; y</span>}\mathrm{<span><span>4</span>4</span>}<span><span>+</span>+</span>\mathrm{<span><span>R</span>R</span>}\mathrm{<span><span>h</span>h</span>}\mathrm{<span><span>y</span>the\; y</span>}\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>h</span>h</span>}\mathrm{<span><span>m</span>m</span>}$

(公式1)(Formula 1)

其中i表示第i个小节，j表示第i个小节中的第j个音符，N表示小节中音符的个数，m表示该小节中音程量≥48的旋律音程个数。Among them, i represents the i-th measure, j represents the j-th note in the i-th measure, N represents the number of notes in the measure, and m represents the number of melody intervals in the measure with the interval amount ≥ 48.

适应度函数中评判的音乐特征有音符的音高、时长、音程关系、3个音的特色旋法、4个音的特色旋法和特色节奏型。The musical features judged in the fitness function include pitch, duration, interval relationship of notes, characteristic rotation of three tones, characteristic rotation of four tones and characteristic rhythm pattern.

2)倒数第二小节的适应度函数2) The fitness function of the penultimate section

$\begin{array}{c}\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>\mathrm{<span><span>i</span>i</span>}<span><span>)</span>)</span><span><span>=</span>=</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>N</span>N</span>}}\mathrm{<span><span>P</span>P</span>}\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>c</span>c</span>}\mathrm{<span><span>h</span>h</span>}<span><span>(</span>(</span>\mathrm{<span><span>j</span>j</span>}<span><span>)</span>)</span><span><span>/</span>/</span>\mathrm{<span><span>N</span>N</span>}<span><span>+</span>+</span>{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}_{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>N</span>N</span>}}\mathrm{<span><span>D</span>D.</span>}\mathrm{<span><span>u</span>u</span>}\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>a</span>a</span>}\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>o</span>o</span>}\mathrm{<span><span>n</span>no</span>}<span><span>(</span>(</span>\mathrm{<span><span>j</span>j</span>}<span><span>)</span>)</span><span><span>/</span>/</span>\mathrm{<span><span>N</span>N</span>}<span><span>+</span>+</span>\frac{\mathrm{<span><span>I</span>I</span>}\mathrm{<span><span>n</span>no</span>}\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>e</span>e</span>}\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>v</span>v</span>}\mathrm{<span><span>a</span>a</span>}\mathrm{<span><span>l</span>l</span>}\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>\mathrm{<span><span>m</span>m</span>}}<span><span>+</span>+</span>\mathrm{<span><span>M</span>m</span>}\mathrm{<span><span>e</span>e</span>}\mathrm{<span><span>l</span>l</span>}\mathrm{<span><span>o</span>o</span>}\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>y</span>the\; y</span>}\mathrm{<span><span>3</span>3</span>}<span><span>+</span>+</span>\mathrm{<span><span>M</span>m</span>}\mathrm{<span><span>e</span>e</span>}\mathrm{<span><span>l</span>l</span>}\mathrm{<span><span>o</span>o</span>}\mathrm{<span><span>d</span>d</span>}\mathrm{<span><span>y</span>the\; y</span>}\mathrm{<span><span>4</span>4</span>}\\ <span><span>+</span>+</span>\mathrm{<span><span>R</span>R</span>}\mathrm{<span><span>h</span>h</span>}\mathrm{<span><span>y</span>the\; y</span>}\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>h</span>h</span>}\mathrm{<span><span>m</span>m</span>}<span><span>+</span>+</span>\mathrm{<span><span>I</span>I</span>}\mathrm{<span><span>n</span>no</span>}\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>e</span>e</span>}\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>v</span>v</span>}\mathrm{<span><span>a</span>a</span>}\mathrm{<span><span>13</span>13</span>}\end{array}$

(公式5)，(Formula 5),

适应度函数增加了对结束旋法的要求，要求该小节最后两个音与调式主音的音程间隔小于5；The fitness function increases the requirements for the ending rotation, requiring that the interval between the last two tones of the measure and the tonic of the mode is less than 5;

3)旋律的适应度函数：3) The fitness function of the melody:

$F=\underset{i=1}{\overset{12}{\&Sigma;}}f\left(i\right)+Interval2$(公式4)$f=\underset{i=1}{\overset{12}{\&Sigma;}}f\left(i\right)+I\mathrm{no}terval2$ (Formula 4)

整个旋律的适应度函数增加了小节之间的音程关系评判；The fitness function of the whole melody increases the judgment of the interval relationship between the bars;

(5)遗传算子的设定：遗传算子包括选择、交叉和变异。选择算子采用锦标赛选择算法；交叉算子的算法是针对小节内时长为一拍的旋律段进行交叉，交叉概率为0.6；变异算子包括音程变异，音符分裂和音符合并三种，变异概率为0.3。(5) Setting of genetic operators: Genetic operators include selection, crossover and mutation. The selection operator adopts the tournament selection algorithm; the algorithm of the crossover operator is to crossover the melody segment with a duration of one beat in a measure, and the crossover probability is 0.6; the mutation operator includes interval variation, note splitting and note merging, and the mutation probability is 0.3.

(6)基于遗传算法生成音乐旋律：遗传迭代是按照小节进行，对初始种群进行选择、交叉和变异的操作，然后用适应度函数对新生成的小节进行评判，设定适应度函数得分小于4分的小节下一轮迭代舍弃，最终生成12个小节的江南小调旋律，采用整个旋律的适应度函数进行评判，将得分最高的旋律视为生成的旋律。(6) Generate music melody based on genetic algorithm: Genetic iteration is carried out according to the subsections, and the initial population is selected, crossed and mutated, and then the fitness function is used to judge the newly generated subsections, and the fitness function score is set to be less than 4 The sub-sections are discarded in the next round of iterations, and finally a 12-section Jiangnan minor melody is generated. The fitness function of the entire melody is used for evaluation, and the melody with the highest score is regarded as the generated melody.

(7)按照以上的方案完成江南小调计算机辅助作曲系统，首先对江南小调素材库进行特征参数的提取和计算，特征主要包括音高、时长、音程、特色旋法和特色节奏型，并由此生成江南小调的作曲知识规则库。其次根据知识规则库，设定遗传算法的编码规则，遗传算子和适应度函数。然后根据用户对生成旋律的需求，从素材库中调用相应的旋律，并生成初始种群。最后经过遗传算法多次迭代，生成12小节的江南小调的旋律。(7) Complete the Jiangnan Minor computer-aided composition system according to the above scheme. First, extract and calculate the characteristic parameters of the Jiangnan Minor material library. The features mainly include pitch, duration, interval, characteristic rotation and characteristic rhythm, and generate The composition knowledge rule base of Jiangnan Minor. Secondly, according to the knowledge rule base, the encoding rules, genetic operators and fitness functions of the genetic algorithm are set. Then according to the user's demand for melody generation, the corresponding melody is called from the material library, and the initial population is generated. Finally, after multiple iterations of the genetic algorithm, a 12-bar Jiangnan minor melody is generated.

利用本实施例中的方法，假设用户希望生成G徵调、中慢速的江南小调旋律，经过计算机计算，生成的旋律如图3所示。Using the method in this embodiment, assume that the user wishes to generate a Jiangnan minor melody in G key and medium-slow speed. After computer calculation, the generated melody is shown in FIG. 3 .

实验结果表明，基于江南小调知识规则库去设定遗传算法的适应度函数，可以较好的保证生成旋律符合江南小调的特点，例如生成的旋律为五声音阶，大二度和小三度的旋律级进为主，包含了音阶式、环绕式、定点式和迂回式四种特色旋法，形成以规整节奏型为主的旋律。The experimental results show that setting the fitness function of the genetic algorithm based on the Jiangnan minor knowledge rule base can better ensure that the generated melody conforms to the characteristics of the Jiangnan minor, for example, the generated melody is a pentatonic scale, a major second and a minor third. Gradation-based, including four characteristic melodies: scale, surround, fixed-point and roundabout, forming a melody dominated by regular rhythms.

本发明将遗传算法和知识规则库两种算法混合，首先根据江南小调的音乐特征及旋律特征，采用特征参数计算和统计分析的方法，提取了音色、音高、音程、特色旋法和特色节奏型等特征归纳出江南小调的作曲知识规则库，并由此建立遗传算法的适应度函数，编码规则和遗传算子，大大提高适应度函数的准确性，较好的生成江南小调的旋律。The present invention mixes the two algorithms of genetic algorithm and knowledge rule base. Firstly, according to the music characteristics and melody characteristics of Jiangnan Minor, it adopts the method of characteristic parameter calculation and statistical analysis to extract timbre, pitch, interval, characteristic melody and characteristic rhythm pattern. The composition knowledge rule base of Jiangnan Minor is summarized based on such characteristics, and the fitness function, coding rules and genetic operators of the genetic algorithm are established, which greatly improves the accuracy of the fitness function and better generates the melody of Jiangnan Minor.

本发明通过知识规则库来定义编码规则、遗传算子及适应度函数，利用适应度函数评判机制，从而实现江南小调计算机自动作曲功能，将江南小调的知识规则库用于建立遗传算法中的适应度函数，既可以避免交互式遗传算法的复杂性，还大大提高了适应度函数的准确性，从而提高了整个计算机辅助作曲系统的准确性。The invention defines coding rules, genetic operators and fitness functions through the knowledge rule base, utilizes the fitness function evaluation mechanism, thereby realizing the computer automatic composing function of Jiangnan Minor, and uses the knowledge rule base of Jiangnan Minor to establish the adaptation in the genetic algorithm. The degree function can not only avoid the complexity of the interactive genetic algorithm, but also greatly improve the accuracy of the fitness function, thereby improving the accuracy of the entire computer-aided composition system.

上面对本专利的较佳实施方式作了详细说明，但是本专利并不限于上述实施方式，在本领域的普通技术人员所具备的知识范围内，还可以在不脱离本专利宗旨的前提下作出各种变化。The preferred implementation of this patent has been described in detail above, but this patent is not limited to the above-mentioned implementation. Within the scope of knowledge possessed by those of ordinary skill in the art, various modifications can be made without departing from the purpose of this patent. kind of change.

Claims (5)

Translated fromChinese

1.一种基于混合算法的江南小调计算机辅助作曲的方法，其特征在于，具体步骤如下：1. A method for computer-aided composition of Jiangnan minor tune based on hybrid algorithm, is characterized in that, concrete steps are as follows:(1)建立江南小调音乐素材库：建立94首的江南小调音乐素材库，用于特征参数提取：(1) Establish Jiangnan Minor music material library: Establish a Jiangnan Minor music material library of 94 songs for feature parameter extraction:(2)建立江南小调作曲知识规则库：提取声学特征和旋律特征，建立知识规则库，用于遗传算法关键技术的制定；(2) Establish a knowledge rule base for Jiangnan minor composition: extract acoustic features and melody features, establish a knowledge rule base, and use it to formulate key technologies of genetic algorithms;(3)制定遗传算法的关键规则：对江南小调素材库进行特征参数计算及旋律特征的统计分析，根据提取的特征制定遗传算法的编码规则、遗传算子和适应度函数；(3) Formulate the key rules of the genetic algorithm: calculate the characteristic parameters and statistical analysis of the melody characteristics of the Jiangnan minor tune material database, and formulate the coding rules, genetic operators and fitness functions of the genetic algorithm according to the extracted features;(4)提取遗传算法的初始种群：根据用户选择的调式和速度，从素材库挑选对应的旋律，并提取旋律的第一小节作为遗传算法的初始种群；(4) Extract the initial population of the genetic algorithm: select the corresponding melody from the material library according to the mode and speed selected by the user, and extract the first bar of the melody as the initial population of the genetic algorithm;(5)生成江南小调旋律：通过计算适应度函数，开始进行选择、交叉和变异的遗传计算，经过多次迭代直到达到终止的条件，再进行下一小节的遗传计算，最终生成12小节的江南小调的旋律。(5) Generating the melody of Jiangnan Minor: By calculating the fitness function, the genetic calculation of selection, crossover and mutation is started. After multiple iterations until the termination condition is reached, the genetic calculation of the next section is performed, and finally 12 sections of Jiangnan are generated. melody in minor key.2.根据权利要求1所述的基于混合算法的江南小调计算机辅助作曲的方法，其特征在于，所述步骤(4)中的调式分别是G徵调、A羽调和C宫调，速度分别为中慢速和中快速。2. the method for the Jiangnan minor computer-aided composition based on hybrid algorithm according to claim 1, is characterized in that, the mode in the described step (4) is respectively G sign tune, A Yu tune and C palace tune, and speed is respectively middle Slow and medium fast.3.根据权利要求1所述的基于混合算法的江南小调计算机辅助作曲的方法，其特征在于，所述步骤(2)中建立江南小调作曲知识规则库时，分别提取江南小调的声学特征参数和旋律特征参数建，提取声学特征参数采用时频计算的方法，提取与音色、音高和调性相关的11个特征参数，计算频谱时所使用的傅立叶变换长度为8192个采样点，频率分辨率为5.38Hz，75％的重叠，得到的频谱为线性幅度谱，使用TrueEnvelope的方法来计算信号波形包络，所有声学特征参数均为帧平均值，帧时窗为0.05s，半重叠；旋律特征参数通过统计分析的方法获得，旋律特征参数共7个，包括特殊的旋律行进、节奏型和音程，旋律特征参数的统计概率计算公式如下：3. the method for the Jiangnan minor computer-aided composition based on hybrid algorithm according to claim 1, it is characterized in that, when setting up the Jiangnan minor composition knowledge rule base in the described step (2), extract respectively the acoustic feature parameter and the Jiangnan minor The construction of melody characteristic parameters and the extraction of acoustic characteristic parameters adopt the method of time-frequency calculation to extract 11 characteristic parameters related to timbre, pitch and tonality. 5.38Hz, 75% overlap, the obtained spectrum is a linear amplitude spectrum, using the method of TrueEnvelope to calculate the signal waveform envelope, all acoustic characteristic parameters are the frame average value, the frame time window is 0.05s, half overlap; melody feature The parameters are obtained through statistical analysis. There are 7 melody characteristic parameters in total, including special melody progression, rhythm pattern and interval. The statistical probability calculation formula of melody characteristic parameters is as follows:4.根据权利要求1所述的基于混合算法的江南小调计算机辅助作曲的方法，其特征在于，所述步骤(3)中的适应度函数分两步进行，首先对生成的每个小节进行评判，然后对整个旋律进行适应度函数的评判，小节的适应度函数如下所示：4. the method for the Jiangnan minor computer-aided composition based on hybrid algorithm according to claim 1, is characterized in that, the fitness function in the described step (3) is carried out in two steps, at first each bar of generation is judged , and then judge the fitness function of the whole melody, the fitness function of the subsection is as follows:$f\left(i\right)={\&Sigma;}_{j=1}^{N}Pitch\left(j\right)/N+{\&Sigma;}_{j=1}^{N}Duration\left(j\right)/N+\frac{Interval1}{N-1-m}+Melody3+Melody4+Rhythm$(公式2)，$f\left(i\right)={\&Sigma;}_{j=1}^{N}Pitch\left(j\right)/N+{\&Sigma;}_{j=1}^N\mathrm{D.}uratio\mathrm{no}\left(j\right)/N+\frac{I\mathrm{no}terval1}{N-1-m}+melod\mathrm{the\; y}3+melod\mathrm{the\; y}4+Rh\mathrm{the\; y}thm$ (Formula 2),其中i表示第i个小节，j表示第i个小节中的第j个音符，N表示小节中音符的个数，m表示该小节中音程量≥48的旋律音程个数；Wherein i represents the i-th bar, j represents the j-th note in the i-th bar, N represents the number of notes in the bar, and m represents the number of melody intervals with an interval amount ≥ 48 in the bar;整个旋律的适应度函数如下所示：The fitness function of the whole melody is as follows:$F=\underset{i=1}{\overset{12}{\&Sigma;}}f\left(i\right)+Interval2$(公式3)。$f=\underset{i=1}{\overset{12}{\&Sigma;}}f\left(i\right)+I\mathrm{no}terval2$ (Formula 3).5.根据权利要求1所述的基于混合算法的江南小调计算机辅助作曲的方法，其特征在于，所述步骤(5)中采用遗传算法生成江南小调的旋律时，初始种群为10个，以小节为迭代单元，设定适应度函数得分小于4分的小节下一轮迭代舍弃，生成12个小节的江南小调旋律，采用整个旋律的适应度函数进行评判，将得分最高的旋律视为生成的旋律。5. the method for the Jiangnan minor computer-aided composition based on hybrid algorithm according to claim 1, it is characterized in that, when adopting genetic algorithm to generate the melody of Jiangnan minor in the described step (5), initial population is 10, with bar As an iterative unit, set the measure whose fitness function score is less than 4 points to be discarded in the next round of iteration, generate 12 measures of Jiangnan minor melody, use the fitness function of the entire melody to judge, and regard the melody with the highest score as the generated melody .