The relationship between ancient Greek music and proportion is also mentioned by the subject himself in the description of the problem, so I won't talk about it. In fact, composers and theorists in early ancient Greece, including the Middle Ages, were all regarded as scientists. Early music can be divided into two categories: "music as theory" and "music as practice". The former studies music from the perspective of pure theory, while the latter studies music from the perspective of playing methods. Many previous studies coincide with mathematics.

In addition, judging from many musical creation techniques and ideas, it is also closely related to mathematics. For example, in early music, the duration was divided into three parts at first, and then it was divided into two parts for display; And the determination of the proportion of each imitation part (morning music has no bar line in our music score today, so the time proportion between sounds was a more essential musical theory and creative element at that time); The early use of octave and fifth degree, the process of gradually adding third degree and sixth degree, and the idea of avoiding third degree all the time; The musical climax skill of golden section; In addition, an example of an actual musical work is Duffy's Nupper Rosalem Flores. This commissioned works is dedicated to Florence Cathedral. Its musical structure contains various mathematical proportions, which implies the architectural structure of the church. For example, the ratio of talea's 6: 4: 2: 3 is the ratio of nave, Auditorium, Back Hall and height of the church dome, and so on.

Various polyphonic techniques developed during the Baroque period are, to some extent, games of numbers. For example, reflection on the theme, retrograde and reflective retrograde.

Functional harmony, which existed in the whole Baroque period, classical period and The Romantic Period, was also closely related to mathematical models. For example, V-I(i) can establish a new tone, or the traditional tone sandhi is transferred between closely related tones, or the difference between "the first tone sandhi" and "the modular tone sandhi" (the scale is unchanged or the interval is unchanged) is essentially derived from a mathematical logic for a long time.

At the beginning of the 20th century, after Schoenberg broke the traditional tonality system, both free atonality and sequence music, and then octave music, were based on the theory of "set or set". This "sound set" is to digitize the material of a pitch combination and then develop it through various forms of deformation and variation. In addition, whether it is the complete matrix of twelve tones, the transposition of octaves, or the transposition mode defined by Mei Xian himself, as long as it involves the transposition of modes or scales, it is closely related to mathematics. Other music creation techniques, such as new complexity, are fundamentally conceived in more variable note proportions, and the scores are all like this:

Later, with the development of electronic music, many electronic music "creation" software or programs are themselves a programming behavior rather than the traditional "music creation" thinking, such as Max.

To sum up, as long as musical works are based on intervals and scales and their transpositions, they are closely related to mathematical thinking.