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In mathematics, a superpartient ratio or superpartient number 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.

Mathematically, a superpartient number is a ratio of the form

$\frac{n+a}{n},$

where a is greater than 1 (a > 1) and is also coprime (reduced to its lowest terms) to n. Ratios of the form $\frac{n+1}{n}$ are also greater than one, but are called superparticular ratios and are not considered as superpartient.

Examples

Ratio	Related musical interval	Audio
5:3	Major sixth	My name: Lindsey Gavin My age: 28 Country: Sweden Home town: Vemdalen Postal code: 840 92 Address: Buanvagen 79 Look into my weblog :: http://www.hostgator1centcoupon.info/
7:4	Harmonic seventh	My name: Lindsey Gavin My age: 28 Country: Sweden Home town: Vemdalen Postal code: 840 92 Address: Buanvagen 79 Look into my weblog :: http://www.hostgator1centcoupon.info/
8:5	Minor sixth	My name: Lindsey Gavin My age: 28 Country: Sweden Home town: Vemdalen Postal code: 840 92 Address: Buanvagen 79 Look into my weblog :: http://www.hostgator1centcoupon.info/

See also

• Mathematics of musical scales
• Superparticular number

Sources

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Further reading

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