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Began describing a general notion of warping a scale; used 5L 2s as an example
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Proposed terms: mega-edo explicitly refers to divisions in the millions; deka-, hecto-, and kilo-edo for divisions in the tens, hundreds, and thousands
 
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== Warped scales ==
== Warped scales ==
A somewhat generalized notion of warping, but applied to the mos 5L 2s, the equal-tempered whole-tone scale (effectively 6edo), and the equal-tempered chromatic scale (effectively 12edo).
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).
 
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.  


=== Warped 5L 2s ===
{| class="wikitable"
{| 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" |Replacement
!-1L
!+0L
!+1L
|-
|-
!Step size
!-1s
!New mos
|
!Step size
|5L 1s
!New mos
|6L 1s
!Step size
!New mos
|-
|-
| rowspan="2" |5L 2s
!+0s
|1 L
|5L 1s
|'''5L 2s'''
|6L 2s
|6L 2s
|1 L
|-
|4L 2s
!+1s
|1 L->s
|4L 3s
|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
|-
|-
|1 s
!+0s
|5L 3s
|
|1 s
|'''6edo'''
|1L 6s
|-
!+1s
|5L 1s
|5L 1s
|1 s->L
|6L 1s
|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
|
|}
== EDO/ED classifications ==
* Deka-edo (deka-division): an equal division of the octave (or equave) where the number of divisions is in the tens.
* Hecto-edo (hecto-division): an equal division of the octave (or equave) where the number of divisions is in the hundreds.
* Kilo-edo (kilo-division): an equal division of the octave (or equave) where the number of divisions is in the thousands.
* Mega-edo (mega-division): an equal division of the octave (or equave) where the number of divisions is in the millions.
** This term already exists to refer to a large edo, but how large is subjective. Since the terms deka-, hecto-, and kilo-edo (and deka-, hecto-, and kilo-division) explicitly refer to specific powers of 10 (specifically, tens, hundreds, and thousands), so should mega-edo and mega-division to refer to divisions in the millions.
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