User:CompactStar/Ordinal interval notation: Difference between revisions
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In the following definition, k is a degree and X is any (possibly empty) sequence of lefts and rights. | 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 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 | * 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 | * 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. | ||
== Examples == | == Examples == | ||
=== Simple directions === | === Simple directions === | ||
Revision as of 08:45, 23 July 2023
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.