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 |