User:CompactStar/Ordinal interval notation

Lefts and rights notation is a notation for just intonation primarily developed by CompactStar. It represents every just interval as a sequence of lefts/rights and a diatonic degree.

Explanation

All intervals are given a diatonic degree, calculated from their 7edo patent val mapping. If k is a degree, the central k-th is the simplest (according to Tenney height) just ratio which is a k-th. For example, the central 3rd is 5/4, since it is the simplest 3rd, and the central 7th is 7/4, since it is the simplest 7th. The left k-th is the simplest k-th which is flatter than central, and the right k-th is the simplest k-th which is sharper than central. Central, left and right are abbreviated as c, l, and r respectively.

Left and right can be used multiple times to produce more complex qualities. For example, leftleft is flatter than left, leftright is between left and central, rightleft is between central and right, and rightright is sharper than right. In general, adding a left always means to go flatter, and adding a right always means to go sharper. Each added left/right has an increasingly minute impact, so for example rightleft does not cancel out but is "slightly right".