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]].
+#redirect [[User:CompactStar/Lefts and rights notation]]
-== Explanation ==
-Regular interval names corresponds to [[Pythagorean]] intervals, e.g. [[32/27]] is a minor third. To name non-Pythagorean intervals, they are given the name of a nearby Pythagorean interval (see [[#Mapping non-Pythagorean intervals]]), then prefixed with a sequence of lefts and rights (abbreviated as < and > respectively). Left and right have the following meaning (where X is any left/right sequence, and Y is a regular interval category like "major third"):
-* Xleft Y = the simplest (with respect to [[Tenney height]]) Y whose left/right sequence starts with X and is flatter than X Y
-* Xright Y = the simplest (with respect to [[Tenney height]]) Y whose left/right sequence starts with X and is sharper than X Y
-More simply, left means to find the simplest flatter interval, and right means to find the simplest sharper interval, with each new left/right having less and less of an impact. For example, [[5/4]] is the leftmajor third, since it is the simplest major third flatter than [[81/64]], and [[9/7]] is the rightmajor third, since it is the simplest major third sharper than [[81/64]].
-=== Mapping non-Pythagorean intervals ===