User:CompactStar/Ordinal interval notation

Indexed interval notation is a notation for just intonation in which all intervals are represented by a normal interval classification combined with a ordinal number or index. An index of 1 is used for the simplest interval in an interval class (such as 6/5 for minor thirds), an index of 2 is used for the second-simplest, an index of 3 is used for the third-simplest, and so on.

Definition

To get the classification for an interval, multiply the interval classes of the prime harmonics which it factors into, which are predefined as follows:

Prime harmonic	Interval classification
2/1	P8	perfect octave
3/2	P5	perfect fifth
5/4	M3	major third
7/4	m7	minor seventh
11/8	P4	perfect fourth
13/8	m6	minor sixth
17/16	m2	minor second
19/16	m3	minor third
23/16	A4	augmented fourth
29/16	m7	minor seventh
31/16	P8	perfect octave