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Roots of the ClassicalThe Popular Origins of Western Music$
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Peter Van der Merwe

Print publication date: 2004

Print ISBN-13: 9780198166474

Published to Oxford Scholarship Online: May 2008

DOI: 10.1093/acprof:oso/9780198166474.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 22 October 2021

The Subtle Mathematics of Music

The Subtle Mathematics of Music

(p.7) 1 The Subtle Mathematics of Music
Roots of the Classical

Peter van der Merwe

Oxford University Press

What distinguishes music from other sounds is symmetry. Only in music are sounds related to one another by precise, quasi-mathematical ratios, and even there only in melodic pitch and rhythmic duration. The mind groups these ratios into subjective patterns (as opposed to objective shapes). These are hierarchically grouped, often according to the principle of self-similarity, i.e., the similarity of the whole to the part, or of the larger part to the smaller part. Over time, these patterns grow more and more complex in an almost organic way, but there is always a tendency to revert to their simple original forms.

Keywords:   symmetry, pattern, hierarchy, self-similarity, melodic pitch, rhythmic duration

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