Language is Music is Math

Quoting from The Art of Music (Cannon, Johnson & Waite 1960)

What is Music? In every age a different answer has been found. Today music may be the art of organizing tones so that an aesthetic experience may result. It was once held to be sound related to number, and at another time the union of word and tone. Two thousand years after Plato, Johannes Kepler still adhered to Plato's idea that music was a force regulating the universe through the mathematical relationships inherent in musical intervals. For a man of the Enlightenment music was matter in motion, while a man of the nineteenth century would have described it as the language of the emotions, an irrational form of speech capable of expressing the inexpressible.

* * * *

There is another reason why music has been such an important aspect of human thought. For millenia music was held to be not only an art, but a science. Tradition ascribes to Pythagoras, a Greek thinker of the sixth century B.C., the discovery that the relationships of musical tones are measurable by specific mathematical proportions. Although the earliest makers of musical instruments, such as the person who bored holes in a wooden pipe to produce different tones, must have had some knowledge of these numerical relationships, it was not until the fifth or sixth century B.C. that they were formulated mathematically.

This discovery, that sound is subject to the rational laws of number, was one of the first intimations the Greeks had that nature is an orderly process. If the harmony which exists between tones is the product of mathematical proportions, could it be possible that other aspects of the world are regulated by the same numbers? May not the succession of the seasons, the ebb and flow of the tides, the balance and discords of the human spirit all be related through the same proportions? May not music be the foundation of the universe? As a result of such speculations music became the companion of arithmetic, geometry, and astronomy as a science that measures and explains the causes and relationships of the universe. In subsequent centuries the evolution of music as an art was continually to be influenced by the premises of music as a science. Even today the mathematical aspect of music is an important element in the theories of many composers. (see also math rock).

* * * *

[E]ven in the prehistory of Greece music was pre-eminent among the arts. In the earliest Hellenic times before the establishment of laws, it was the poet-musician who preserved and guided the traditions of his people through a recitation of the deeds of the heroes of his race. For the early Greeks music was not simply tone as such. It was a composite art: word and music united in the utterances of the bards. The poet, composer, and singer were one, the lawgiver who guided his primitive political society through the examples of proper action recited in his songs. Through the force of his thought, ennobled by musical expression, the musician could move his audience to emotions and actions. This power of music was felt to be of divine origin, and it was said to have come into the possession of mortals as a gift of the gods who had invented musical instruments.

Poetry and music were the transmitters and the mainstay of culture. The first form of education was "musical," by which the Greeks meant an indoctrination into the arts of music and poetry as well as the assimilation of the examples and laws furnished by poetry. Music was considered to be necessary for the preservation of the community and it was inextricably interwoven with the life of the state. All public occasions were graced by music, often performed by the populace. Contests were established in which both singers and instrumentalists participated to win public acclaim. ...