In mathematics, a superpartient ratio, also called superpartient number or epimeric ratio, is a rational number that is greater than one and is not superparticular. The term has fallen out of use in modern pure mathematics, but continues to be used in music theory and in the historical study of mathematics.

Superpartient ratios were written about by Nicomachus in his treatise Introduction to Arithmetic.

Overview

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Mathematically, a superpartient number is a ratio of the form

 

where a is greater than 1 (a > 1) and is also coprime to n. Ratios of the form   are also greater than one and fully reduced, but are called superparticular ratios and are not superpartient.

Examples
Ratio   Related musical interval Audio
5:3   Major sixth Play
7:4   Harmonic seventh Play
8:5   Minor sixth Play

Etymology

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"Superpartient" comes from Greek ἐπιμερής epimeres "containing a whole and a fraction," literally "superpartient".

See also

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Further reading

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  • Partch, Harry (1979). Genesis of a Music, p.68. ISBN 978-0-306-80106-8.