User:Ganaram inukshuk/Notes: Difference between revisions

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 A somewhat generalized notion of warping, described by the addition, removal, or substitution of a single step. The most common scales of 12edo are used as examples: 5L 2s, the whole-tone scale (effectively 6edo), the chromatic scale (effectively 12edo), and the diminished scale (4L 4s, hardness of 2).
-=== Warped 5L 2s ===
+The simplest ways to warp a scale are through the addition of a step and the removal of a step. Substitution of a step, where one step is changed for a step of a different size, can be thought of removing a step of one size and adding a step of a different size.
 {| class="wikitable"
-|+
+|+Warped 5L 2s
-! rowspan="2" |Original scale
+! rowspan="2" |Small step changes
-! colspan="2" |Addition
+! colspan="3" |Large step changes
-! colspan="2" |Removal
-! colspan="2" |Substitution
 |-
-!Step size
+!-1L
-!New scale
+!+0L
-!Step size
+!+1L
-!New scale
-!Step size
-!New scale
 |-
-| rowspan="2" |5L 2s
+!-1s
-|1 L
+|
+|5L 1s
+|6L 1s
+|-
+!+0s
+|5L 1s
+|'''5L 2s'''
 |6L 2s
-|1 L
+|-
-|4L 2s
+!+1s
-|1 L->s
 |4L 3s
+|5L 3s
+|
+|}
+{| class="wikitable"
+|+Warped 6edo
+(equal-tempered whole-tone scale)
+! rowspan="2" |Small step changes
+! colspan="3" |Large step changes
+|-
+!-1L
+!+0L
+!+1L
+|-
+!-1s
+|
+|
+|1L 5s
+|-
+!+0s
+|
+|'''6edo'''
+|1L 6s
 |-
-|1 s
+!+1s
-|5L 3s
-|1 s
 |5L 1s
-|1 s->L
 |6L 1s
+|
+|}
+{| class="wikitable"
+|+Warped 12edo
+(equal-tempered chromatic scale)
+! rowspan="2" |Small step changes
+! colspan="3" |Large step changes
+|-
+!-1L
+!+0L
+!+1L
+|-
+!-1s
+|
+|
+|1L 11s
+|-
+!+0s
+|
+|'''12edo'''
+|1L 12s
+|-
+!+1s
+|1L 11s
+|12L 1s
+|
+|}
+{| class="wikitable"
+|+Warped 4L 4s
+! rowspan="2" |Small step changes
+! colspan="3" |Large step changes
+|-
+!-1L
+!+0L
+!+1L
+|-
+!-1s
+|
+|4L 3s
+|5L 3s
+|-
+!+0s
+|3L 4s
+|'''4L 4s'''
+|5L 4s
+|-
+!+1s
+|3L 5s
+|4L 5s
+|
 |}