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