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 (e.g. 3/2 is a fifth), derived from their 7edo patent val mapping. A basic (b) n-th is the simplest (via Tenney height) just n-th (the term basic is used rather than perfect, since these intervals can be perfect, major or, in the case of 7/4, minor). A left (<) n-th is the simplest n-th that is flatter than the basic n-th, and similarly a right (>) n-th is the simplest n-th that is sharper than the basic n-th. More complex qualities are obtained as combinations of lefts and rights. For exampe, leftleft is flatter than left, leftright is between left and basic, rightleft is between basic snd right, and rightright is sharper than right. Here is an example of every third with less than 4 lefts or rights:

Basic third (b3) = 5/4

Left third (<3) = 6/5

Right third (>3) = 9/7

Leftleft third (<<3) = 7/6

Leftright third (<>3) = 11/9

Rightleft third (><3) = 14/11

Rightright third (>>3) = 22/17

Leftleftleft third (<<<3) = 22/19