Chirality: Difference between revisions

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# Lexicographically compare M and M'. We choose the convention that if M lexicographically comes before M', then M and all its modes are ''lexicographically right-handed''. Otherwise M and all its modes are ''lexicographically left-handed''.
# Lexicographically compare M and M'. We choose the convention that if M lexicographically comes before M', then M and all its modes are ''lexicographically right-handed''. Otherwise M and all its modes are ''lexicographically left-handed''.


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.
The smallest example of a chiral pair in an [[edo]] is 321/312, with the former being lexicographically right-handed and the latter being lexicographically 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.
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.