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Music and Mathematics: From Pythagoras to Fractals

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The invitation to write an introduction to this collection offered a welcome opportunity to reflect on some of the historical, scientific, and artistic approaches that have been developed in the linking of mathematics and music. The two have traditionally been so closely connected that it is their separation that elicits surprise. During the late sixteenth and early seventeenth centuries when music began to be recognized more as an art and to be treated pedagogically as language and analysed in expressive terms, it might have been expected to lose thereby some of its scientific connotations; yet in fact the science of music went on to develop with renewed impetus.

This introduction sets out to explore, via a variety of texts, some of the many historical and compositional manifestations of the links between mathematics and music. (This endeavour cannot be other than selective: the field is vast, ranging from ancient theory and early developments in structure such as those of the medieval motet, to the new ideas of post-tonal music and experimental musical techniques explored over the past century.) In what follows, the field is viewed particularly from the perspective of a music historian with a special interest in the history of music in its educational dimension.
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