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. | ||