User:CompactStar/Ordinal interval notation: Difference between revisions
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'''Lefts and rights notation''' is a notation for [[just intonation]] primarily developed by [[User:CompactStar|CompactStar]]. | '''Lefts and rights notation''' is a notation for [[just intonation]] primarily developed by [[User:CompactStar|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, with each new left/right having less and less of an impact. 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 a 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 leftX k-th is the just interval with the smallest [[Tenney height]] whose direction ends with X and is flatter than the X k-th | |||
* The rightX k-th is the just interval with the smallest [[Tenney height]] whose direction ends with X and is sharper than the X k-th | |||
== Examples | == Examples == | ||
=== Simple directions === | |||
Revision as of 08:43, 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, with each new left/right having less and less of an impact. 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 a 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 leftX k-th is the just interval with the smallest Tenney height whose direction ends with X and is flatter than the X k-th
- The rightX k-th is the just interval with the smallest Tenney height whose direction ends with X and is sharper than the X k-th