User:CompactStar/Ordinal interval notation: Difference between revisions

Latest revision as of 03:31, 2 January 2024

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-'''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. 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.
+#redirect [[User:CompactStar/Lefts and rights notation]]
-== 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.
-== Examples ==
-=== Simple directions ===