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.
Contents
Superpartient ratios were written about by Nicomachus in his treatise Introduction to Arithmetic.
Overview
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
Etymology
"Superpartient" comes from Greek ἐπιμερής epimeres "containing a whole and a fraction," literally "superpartient".