User:CompactStar/Ordinal interval notation: Difference between revisions

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'''Lefts and rights notation''' is a notation for [[just intonation]] devised by [[User:CompactStar|CompactStar]].

'''Lefts and rights notation''' is a relatively simple notation for [[just intonation]] devised by [[User:CompactStar|CompactStar]].

Intervals are represented by a conventional interval category with a stack of lefts and rights (abbreviated as L and R) added before. To get the category of an interval, multiply the categories of the prime harmonics which it factors into, which are predefined as follows:

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|perfect 5th

|G

|-

|}

The simplest (with respect to [[Tenney height]]) interval inside a category does not use any lefts or rights (or is "central"), for example [[6/5]] for minor 3rd. The simplest interval which is flatter than the central interval is left ([[7/6]] for minor 3rd), and the simplest interval which is sharper is right ([[11/9]] for minor 3rd). Then the simplest interval which is flatter than the left is leftleft, the simplest interval between left and central is leftright, the simplest interval which is between central and right is rightleft, and the simplest interval which is sharper than right is rightright. This process of bisection with lefts/rights can be continued infinitely to name all just intervals that are in a category. ~~Some general associations about qualities can be made like leftminor = subminor, rightminor~~ = ~~lesser neutral~~, ~~leftmajor = greater neutral~~ and ~~rightmajor = supermajor~~.

The simplest (with respect to [[Tenney height]]) interval inside a category does not use any lefts or rights (or is "central"), for example [[6/5]] for minor 3rd. The simplest interval which is flatter than the central interval is left ([[7/6]] for minor 3rd), and the simplest interval which is sharper is right ([[11/9]] for minor 3rd). Then the simplest interval which is flatter than the left is leftleft, the simplest interval between left and central is leftright , the simplest interval which is between central and right is rightleft, and the simplest interval which is sharper than right is rightright. This process of bisection with lefts/rights can be continued infinitely to name all just intervals that are in a category. Interval arithmetic is preserved (e.g. M2 + M2 = M3), however the lefts and rights do not combine like accidentals do.

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-'''Lefts and rights notation''' is a notation for [[just intonation]] devised by [[User:CompactStar|CompactStar]].
+'''Lefts and rights notation''' is a relatively simple notation for [[just intonation]] devised by [[User:CompactStar|CompactStar]].
 Intervals are represented by a conventional interval category with a stack of lefts and rights (abbreviated as L and R) added before. To get the category of an interval, multiply the categories of the prime harmonics which it factors into, which are predefined as follows:
@@ Line 126: / Line 126: @@
 |perfect 5th
 |G
-|-
 |}
-The simplest (with respect to [[Tenney height]]) interval inside a category does not use any lefts or rights (or is "central"), for example [[6/5]] for minor 3rd. The simplest interval which is flatter than the central interval is left ([[7/6]] for minor 3rd), and the simplest interval which is sharper is right ([[11/9]] for minor 3rd). Then the simplest interval which is flatter than the left is leftleft, the simplest interval between left and central is leftright, the simplest interval which is between central and right is rightleft, and the simplest interval which is sharper than right is rightright. This process of bisection with lefts/rights can be continued infinitely to name all just intervals that are in a category. Some general associations about qualities can be made like leftminor = subminor, rightminor = lesser neutral, leftmajor = greater neutral and rightmajor = supermajor.
+The simplest (with respect to [[Tenney height]]) interval inside a category does not use any lefts or rights (or is "central"), for example [[6/5]] for minor 3rd. The simplest interval which is flatter than the central interval is left ([[7/6]] for minor 3rd), and the simplest interval which is sharper is right ([[11/9]] for minor 3rd). Then the simplest interval which is flatter than the left is leftleft, the simplest interval between left and central is leftright , the simplest interval which is between central and right is rightleft, and the simplest interval which is sharper than right is rightright. This process of bisection with lefts/rights can be continued infinitely to name all just intervals that are in a category. Interval arithmetic is preserved (e.g. M2 + M2 = M3), however the lefts and rights do not combine like accidentals do.