Chirality: Difference between revisions

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A scale is called '''chiral''' if reversing the order of the steps results in a different scale. The two scales form a '''chiral pair''' and are right/left-handed. Handedness is determined by writing both scales in their canonical mode and then comparing the size of both. The smallest example of a chiral pair in an EDO is 321/312, with the former being right-handed and the latter being left-handed.
A scale is called '''chiral''' if reversing the order of the steps results in a different scale. The two scales form a '''chiral pair''' and are right/left-handed. Handedness is determined by writing both scales in their canonical mode and then comparing the size of both. The smallest example of a chiral pair in an [[EDO]] is 321/312, with the former being right-handed and the latter being left-handed.


Scales for which this property does not hold are called '''achiral'''. For example, the diatonic scale is achiral because 2221221 reverses to 1221222, which is identical to the original scale up to cyclical permutation.
Scales for which this property does not hold are called '''achiral'''. For example, the diatonic scale is achiral because 2221221 reverses to 1221222, which is identical to the original scale up to cyclical permutation.


==Properties:==
== Properties ==
<ol><li>Chiral scales can only exist in EDO's larger than 5-EDO</li><li>Chiral scales are at least max-variety 3 (they cannot be MOS or DE)</li><li>Chiral scales have at least 3 notes</li><li>Chiral scales have a [http://en.wikipedia.org/wiki/Natural_density density] of 1 (see table below)</li></ol>


{| class="wikitable"
# Chiral scales can only exist in EDO's larger than [[5-EDO]]
|-
# Chiral scales are at least max-variety 3 (they cannot be [[MOS]] or [[DE]])
| | '''EDO'''
# Chiral scales have at least 3 notes
| | '''Number of'''
# Chiral scales have a [http://en.wikipedia.org/wiki/Natural_density density] of 1 (see table below)


'''Chiral Scales'''
{| class="wikitable" style="text-align:right"
| | '''Percentage of'''
! EDO
 
! Number of <br> Chiral Scales
'''Chiral Scales'''
! Percentage of <br> Chiral Scales
| | '''Corresponding Ratio'''
! Corresponding <br> Ratio
|-
|-
| | 1
| 1
| | 0
| 0
| | 0.0%
| 0.0%
| | 0/1
| style="text-align:center" | 0/1
|-
|-
| | 2
| 2
| | 0
| 0
| | 0.0%
| 0.0%
| | 0/1
| style="text-align:center" | 0/1
|-
|-
| | 3
| 3
| | 0
| 0
| | 0.0%
| 0.0%
| | 0/1
| style="text-align:center" | 0/1
|-
|-
| | 4
| 4
| | 0
| 0
| | 0.0%
| 0.0%
| | 0/1
| style="text-align:center" | 0/1
|-
|-
| | 5
| 5
| | 0
| 0
| | 0.0%
| 0.0%
| | 0/1
| style="text-align:center" | 0/1
|-
|-
| | 6
| 6
| | 2
| 2
| | 22.2%
| 22.2%
| | 2/9
| style="text-align:center" | 2/9
|-
|-
| | 7
| 7
| | 4
| 4
| | 22.2%
| 22.2%
| | 2/9
| style="text-align:center" | 2/9
|-
|-
| | 8
| 8
| | 12
| 12
| | 40.0%
| 40.0%
| | 2/5
| style="text-align:center" | 2/5
|-
|-
| | 9
| 9
| | 28
| 28
| | 50.0%
| 50.0%
| | 1/2
| style="text-align:center" | 1/2
|-
|-
| | 10
| 10
| | 60
| 60
| | 60.6%
| 60.6%
| | 20/33
| style="text-align:center" | 20/33
|-
|-
| | 11
| 11
| | 124
| 124
| | 66.7%
| 66.7%
| | 2/3
| style="text-align:center" | 2/3
|-
|-
| | 12
| 12
| | 254
| 254
| | 75.8%
| 75.8%
| | 254/335
| style="text-align:center" | 254/335
|-
|-
| | 13
| 13
| | 504
| 504
| | 80.0%
| 80.0%
| | 4/5
| style="text-align:center" | 4/5
|-
|-
| | 14
| 14
| | 986
| 986
| | 84.9%
| 84.9%
| | 986/1161
| style="text-align:center" | 986/1161
|-
|-
| | 15
| 15
| | 1936
| 1936
| | 88.7%
| 88.7%
| | 968/1091
| style="text-align:center" | 968/1091
|-
|-
| | 16
| 16
| | 3720
| 3720
| | 91.2%
| 91.2%
| | 31/34
| style="text-align:center" | 31/34
|-
|-
| | 17
| 17
| | 7200
| 7200
| | 93.4%
| 93.4%
| | 240/257
| style="text-align:center" | 240/257
|-
|-
| | 18
| 18
| | 13804
| 13804
| | 95.0%
| 95.0%
| | 493/519
| style="text-align:center" | 493/519
|-
|-
| | 19
| 19
| | 26572
| 26572
| | 96.3%
| 96.3%
| | 26/27
| style="text-align:center" | 26/27
|-
|-
| | 20
| 20
| | 50892
| 50892
| | 97.2%
| 97.2%
| | 16964/17459
| style="text-align:center" | 16964/17459
|}
|}
[[Category:edo]]
[[Category:edo]]
[[Category:scales]]
[[Category:scales]]
[[Category:term]]
[[Category:term]]
[[Category:theory]]
[[Category:theory]]

Revision as of 20:53, 28 May 2020

A scale is called chiral if reversing the order of the steps results in a different scale. The two scales form a chiral pair and are right/left-handed. Handedness is determined by writing both scales in their canonical mode and then comparing the size of both. The smallest example of a chiral pair in an EDO is 321/312, with the former being right-handed and the latter being left-handed.

Scales for which this property does not hold are called achiral. For example, the diatonic scale is achiral because 2221221 reverses to 1221222, which is identical to the original scale up to cyclical permutation.

Properties

  1. Chiral scales can only exist in EDO's larger than 5-EDO
  2. Chiral scales are at least max-variety 3 (they cannot be MOS or DE)
  3. Chiral scales have at least 3 notes
  4. Chiral scales have a density of 1 (see table below)
EDO Number of
Chiral Scales 		Percentage of
Chiral Scales 		Corresponding
Ratio
1 0 0.0% 0/1
2 0 0.0% 0/1
3 0 0.0% 0/1
4 0 0.0% 0/1
5 0 0.0% 0/1
6 2 22.2% 2/9
7 4 22.2% 2/9
8 12 40.0% 2/5
9 28 50.0% 1/2
10 60 60.6% 20/33
11 124 66.7% 2/3
12 254 75.8% 254/335
13 504 80.0% 4/5
14 986 84.9% 986/1161
15 1936 88.7% 968/1091
16 3720 91.2% 31/34
17 7200 93.4% 240/257
18 13804 95.0% 493/519
19 26572 96.3% 26/27
20 50892 97.2% 16964/17459
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