Chirality: Difference between revisions

Line 1:

~~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{{clarify}} 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~~.

'''Chirality''' is a property of asymmetry which can be applied to [[periodic scale]]s.

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.

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{{clarify}} 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. Similarly, the simplest chiral pair for abstract patterns is Lms/Lsm.

Scales for which this property does not hold are called ''achiral''. For example, the [[5L 2s|diatonic scale]] of 12edo is achiral because 2221221 reverses to 1221222, which is identical to the original scale up to cyclical permutation.

== Properties ==

* Chiral scales have at least 3 notes;

* Chiral scales are at least max-variety 3 (they cannot be [[MOS]] or [[DE]])

* Chiral scales have a [http://en.wikipedia.org/wiki/Natural_density density] of 1 (see table below)

* Chiral scales with rational step ratios can only exist in edos larger than [[5edo]]

# Chiral scales ~~can only exist~~ in ~~EDO's larger than [[5-EDO]]~~

== Chiral scales in edos up to 20edo ==

~~# Chiral scales are at least max-variety 3 (they cannot be [[MOS]] or [[DE]])~~

~~# Chiral scales have at least 3 notes~~

~~# Chiral scales have a [http://en.wikipedia.org/wiki/Natural_density density] of 1 (see table below)~~

{| class="wikitable" style="text-align:right"

! EDO

Line 124:

Line 126:

Such chiral mv3's could be named in the format [handedness] [mv3 name] [the corresponding mode of ax 2bY]. For example, the chiral [[diasem]] mode 331323132 can be named "Left-Handed Diasem 8|0", where 8|0 is the [[UDP]] notation for the [[5L 4s]] mode LLSLSLSLS.

[[~~Category~~:~~EDO theory pages~~]]

== External links ==

[[Category:~~scales~~]]

* [[Wikipedia: Chirality]]

[[Category:Scale]]

[[Category:Terms]]

~~[[Category:theory]]~~

@@ Line 1: / Line 1: @@
-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{{clarify}} 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.
+'''Chirality''' is a property of asymmetry which can be applied to [[periodic scale]]s.
-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.
+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{{clarify}} 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. Similarly, the simplest chiral pair for abstract patterns is Lms/Lsm.
+Scales for which this property does not hold are called ''achiral''. For example, the [[5L 2s|diatonic scale]] of 12edo is achiral because 2221221 reverses to 1221222, which is identical to the original scale up to cyclical permutation.
 == Properties ==
+* Chiral scales have at least 3 notes;
+* Chiral scales are at least max-variety 3 (they cannot be [[MOS]] or [[DE]])
+* Chiral scales have a [http://en.wikipedia.org/wiki/Natural_density density] of 1 (see table below)
+* Chiral scales with rational step ratios can only exist in edos larger than [[5edo]]
-# Chiral scales can only exist in EDO's larger than [[5-EDO]]
+== Chiral scales in edos up to 20edo ==
-# Chiral scales are at least max-variety 3 (they cannot be [[MOS]] or [[DE]])
-# Chiral scales have at least 3 notes
-# Chiral scales have a [http://en.wikipedia.org/wiki/Natural_density density] of 1 (see table below)
 {| class="wikitable" style="text-align:right"
 ! EDO
@@ Line 124: / Line 126: @@
 Such chiral mv3's could be named in the format [handedness] [mv3 name] [the corresponding mode of ax 2bY]. For example, the chiral [[diasem]] mode 331323132 can be named "Left-Handed Diasem 8|0", where 8|0 is the [[UDP]] notation for the [[5L 4s]] mode LLSLSLSLS.
-[[Category:EDO theory pages]]
+== External links ==
-[[Category:scales]]
+* [[Wikipedia: Chirality]]
+[[Category:Scale]]
 [[Category:Terms]]
-[[Category:theory]]