Quote: Motion appears in many aspects-but there are two obvious kinds, one which appears in astronomy and another which is the echo of that. As the eyes are made for astronomy so are the ears made for the motion which produces harmony: and thus we have two sister sciences, as the Pythagoreans teach, and we assent. Plato
The mathematical study of musical sounds did not start with the application of trigonometric functions. Indeed, it goes back to the very first emergence of any real mathematics and science, namely the beginning of the classical Greek period.
Sounds given off by almost all musical instruments and by the human voice are not simple sounds: that is, they are not represent able by functions of the form. Yet these sounds are intelligible, which means that they must be periodic or that the pattern of displacement versus time must repeat itself.
When we hear a poet recite his or her own poem, the inflection, cantor and so forth adds to our understanding of the sincerity the author expressed with fresh original expression.
If an aspiring poet takes the technical skill mastery and becomes familiar with all the conventions, an ear for word-music can improvise flawless heroic blank verse or any other form of blank verse, improvise elaborately rhymed sonnets, but poetry from the heart will only come in rare hours when the poet has a concentrated word that must be said.
Why a connection between music, poetry and math? There is a truth in Wordsworth's dictum, "The wish is father to the thought." There must be, also, an obstacle to the immediate fulfillment of the wish; otherwise the poet would proceed to achieve his wish and have no need for the poem to express it. Because of obstacles to creating music and poetry and mastery of math, a tremendous inner compulsion comes upon the sensitive poet to seek relief by creating his wish-fulfillment in words: and so it is that poems are born; we become adept at math; and our poems are arranged as music.
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