Superparticular ratio: Difference between revisions

Superparticular ratios appear frequently in [[just intonation]] and [[harmonic series]] music. Consecutive [[harmonic]]s are separated by superparticular [[interval]]s: for instance, the 20th and 21st by the superparticular ratio [[21/20]]. As the harmonics get closer together, the superparticular intervals get smaller and smaller. Thus, an examination of the superparticular intervals is an examination of some of the simplest small intervals in rational tuning systems. Indeed, many but not all common [[comma]]s are superparticular ratios.

[[Kite Giedraitis]] has proposed a [[delta-N]] terminology (where [[delta]] means difference, here the difference between the numerator and the denominator). Thus delta-1 is an alternative term for superparticular, delta-2 is for ratios of the form <math>\frac{n+2}{n}</math>, likewise delta-3, delta-4, etc.