User:CompactStar/Ordinal interval notation

Lefts and rights notation is a notation for just intonation devised by CompactStar.

Intervals are represented by a conventional interval category with a stack of lefts and rights (abbreviated as L and R) added before. To get the category of an interval, multiply the categories of the prime harmonics which it factors into, which are predefined as follows:

Prime harmonic	Notation
2/1	P8	perfect octave	C
3/2	P5	perfect 5th	G
5/4	M3	major 3rd	E
7/4	m7	minor 7th	Bb
11/8	P4	perfect 4th	F
13/8	m6	minor 6th	Ab
17/16	m2	minor 2nd	Db
19/16	m3	minor 3rd	Eb
23/16	A4	augmented 4th	F#
29/16	m7	minor 7th	Bb
31/16	P8	perfect octave	C
37/32	M2	major 2nd	D
41/32	M3	major 3rd	E
43/32	P4	perfect 4th	F
47/32	P5	perfect 5th	G
53/32	M6	major 6th	A
61/32	M7	major 7th	B
67/64	m2	minor 2nd	Db
71/64	M2	major 2nd	D
73/64	M2	major 2nd	D
79/64	M3	major 3rd	E
83/64	P4	perfect 4th	F
89/64	d5	diminished 5th	Gb
97/64	P5	perfect 5th	G

The simplest (with respect to Tenney height) interval inside a category does not use any lefts or rights (or is "central"), for example 6/5 for minor 3rd. The simplest interval which is flatter than the central interval is left (7/6 for minor 3rd), and the simplest interval which is sharper is right (11/9 for minor 3rd). Then the simplest interval which is flatter than the left is leftleft, the simplest interval between left and central is leftright, the simplest interval which is between central and right is rightleft, and the simplest interval which is sharper than right is rightright. This process of bisection with lefts/rights can be continued infinitely to name all just intervals that are in a category. Some general associations about qualities can be made like leftminor = subminor, rightminor = lesser neutral, leftmajor = greater neutral and rightmajor = supermajor.