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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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The Subtle Mathematics of Music

The Subtle Mathematics of Music

Chapter:
(p.7) 1 The Subtle Mathematics of Music
Source:
Roots of the Classical
Author(s):

Peter van der Merwe

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198166474.003.0002

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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