User:CompactStar/Ordinal interval notation: Difference between revisions

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CompactStar (talk | contribs)
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Wait, intevval arithmetic does make sense if iit's pythagorean-based, just tha you can't predict how many lefts/rights will be in something.
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(Probably will never finish this, because interval arithmetic makes no sense.)
Lefts and rights notation is a notation for just intonation in which all intervals are represented by a normal interval category combined with a sequence of lefts and rights. Left and right always mean flatter and sharper respectively. Each new left/right has less and less of an impact, so for example "rightleft" does not cancel out but means "slightly sharp".
 
'''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.
 
== 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 ===

Revision as of 02:26, 2 November 2023

Lefts and rights notation is a notation for just intonation in which all intervals are represented by a normal interval category combined with a sequence of lefts and rights. Left and right always mean flatter and sharper respectively. Each new left/right has less and less of an impact, so for example "rightleft" does not cancel out but means "slightly sharp".

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