User:CompactStar/Lefts and rights notation
WIP (the reason this is in userspace)
Lefts and rights notation is a notation for just intonation developed by CompactStar. It is a combination of Pythagorean notation and a sequence of lefts and rights which is based on a binary search.
Definition
In order to map all intervals into Pythagorean intervals, each prime harmonic is mapped to the lowest-complexity Pythagorean interval that is within √(2187/2048) of it (this is similar to the algorithm used by the Functional Just System). Here are some examples for smaller primes:
| Prime harmonic | Notation | ||
|---|---|---|---|
| 2/1 | P8 | perfect octave | C |
| 3/2 | P5 | perfect fifth | G |
| 5/4 | M3 | major third | E |
| 7/4 | m7 | minor seventh | Bb |
| 11/8 | P4 | perfect fourth | F |
| 13/8 | m6 | minor sixth | Ab |
| 17/16 | m2 | minor second | Db |
| 19/16 | m3 | minor third | Eb |
| 23/16 | A4 | augmented fourth | F# |
| 29/16 | m7 | minor seventh | Bb |
| 31/16 | P8 | perfect octave | C |
| 37/32 | M2 | major second | D |
| 41/32 | M3 | major third | E |
| 43/32 | P4 | perfect fourth | F |
| 47/32 | P5 | perfect fifth | G |
| 53/32 | M6 | major sixth | A |
| 59/32 | M7 | major seventh | B |
| 61/32 | M7 | major seventh | B |