User:CompactStar/Ordinal interval notation: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ Line 1: / Line 1: @@
-'''Lefts and rights notation''' is a notation for [[just intonation]] devised by [[User:CompactStar|CompactStar]]. Intervals are represented by a conventional interval notation with lefts and rights added.
+'''Lefts and rights notation''' is a notation for [[just intonation]] devised by [[User:CompactStar|CompactStar]].
-== Definition ==
+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:
-To get the normal classification for an interval, multiply the interval classes of the prime harmonics which it factors into, which are predefined as follows:
 {|class="wikitable"
 |-
 !Prime harmonic
-!colspan="3"|Interval
+!colspan="3"|Notation
 |-
 |[[2/1]]
@@ Line 92: / Line 91: @@
 |major 7th
 |B
+|-
+|[[67/64]]
+|m2
+|minor 2nd
+|Db
+|-
+|[[71/64]]
+|M2
+|major 2nd
+|D
+|-
+|[[73/64]]
+|M2
+|major 2nd
+|D
+|-
+|[[79/64]]
+|M3
+|major 3rd
+|E
+|-
+|[[83/64]]
+|P4
+|perfect 4th
+|F
+|-
+|[[89/64]]
+|d5
+|diminished 5th
+|Gb
+|-
+|[[97/64]]
+|P5
+|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 indefinitely.