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