Superparticular number - Definition and Overview

Superparticular numbers, also called epimoric ratios, are improper rational fractions of the form

<math> {n + 1 \over n} = 1 + {1 \over n}. <math>

Superparticular numbers were written about by Nicomachus in his treatise "Introduction to Arithmetic". They are useful in the study of harmony: many musical intervals can be expressed as a superparticular ratio.

Examples:

See also

• mathematics of musical scales

External links

• The new Arithmonic Mean — Preliminaries (http://mipagina.cantv.net/arithmetic/roots.htm#I2) by D. Gómez.
• An Arithmetical Rubric (http://perso.club-internet.fr/daschour/micromegas/terpstra.html) by Siemen Terpstra, about the application of superparticular numbers to harmony.
• Superparticular numbers (http://www.redshift.com/~dcanright/super/) applied to construct pentatonic scales by David Canright.