All art constantly aspires to the condition of music.
[…] why do so many of us constantly try to explain the beauty of music, thus apparently depriving it of its mystery? The fact is that music is not only a mysterious and metaphorical art; it is also born of science. It is made of mathematically measurable elements […] And so any explication of music must combine mathematics with aesthetics […]
In 1893 Erik Satie composed Vexations, a musical piece consisting of a short theme – of about a minute and twenty seconds – which had to be played “840 times in succession” with the player(s) prepared beforehand “in the deepest silence, by serious immobilities”. A possible goal of this piece was, apparently, to bore his critics. In the trade-off between boredom and confusion Satie was structuring his piece to achieve the former.
Yet repetition is, in many forms and in smaller doses, an essential constituent of music, allowing themes to be re-expressed and patterns to be displayed. What is more, its many forms correspond to different geoemetric transformations whose use is neatly exemplified in the various kinds of canon, a form of imitative counterpoint common in the Baroque. They are also the building bricks which, via the notion of invariance, are used to obtain the different symmetries occurring in music.
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