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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 ==
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| 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"):
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| * Xleft Y = the simplest (with respect to [[Tenney height]]) Y whose left/right sequence starts with X and is flatter than X Y
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| * Xright Y = the simplest (with respect to [[Tenney height]]) Y whose left/right sequence starts with X and is sharper than X Y
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| 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,.
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| === Mapping non-Pythagorean intervals ===
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