User:CompactStar/Ordinal interval notation

Lefts and rights notation is a notation for just intonation primarily developed by CompactStar. It represents all intervals by a direction, which is a sequence of lefts and rights, and a degree. The direction with no lefts and rights is called "central". Left and right always mean flatter and sharper. Each new left/right has less and less of an impact, so for example "rightleft" does not cancel out but means "slightly right". Central, left, and right are abbreviated as C, L, and R respectively.

Formal defintion

In the following definition, k is a degree and X is any (possibly empty) sequence of lefts and rights.

• The central k-th is the just interval with the smallest Tenney height that is mapped to k-1 steps in 7edo's patent val and is within 20 cents of (k-1)\7edo.
• The Xleft k-th is the just interval with the smallest Tenney height whose direction starts with X and is flatter than the X k-th.
• The Xright k-th is the just interval with the smallest Tenney height whose direction starts with X and is sharper than the X k-th.