Superpartient ratio
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
where a is greater than 1 (a > 1) and is also coprime (reduced to its lowest terms) to n. Ratios of the form are also greater than one, but are called superparticular ratios and are not superpartient.
| Ratio | n+a/n | Related musical interval | Audio |
|---|---|---|---|
| 5:3 | 3+2/3 | Major sixth |  Play |
| 7:4 | 4+3/4 | Harmonic seventh | Play |
| 8:5 | 5+3/5 | Minor sixth | Play |
See also
Sources
Further reading
- Partch, Harry (1979). Genesis of a Music, p.68. ISBN 978-0-306-80106-8.
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