Chirality: Difference between revisions

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

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.

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 lexicographically comparing all modes of each scale (i.e. treat scale step size sequences as words in "alphabetical order", where this alphabetical order is from biggest to smallest) and then lexicographically comparing the respective lexicographically brightest modes. 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.

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 '''Chirality''' is a property of asymmetry which can be applied to [[periodic scale]]s.
-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.
+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 lexicographically comparing all modes of each scale (i.e. treat scale step size sequences as words in "alphabetical order", where this alphabetical order is from biggest to smallest) and then lexicographically comparing the respective lexicographically brightest modes. 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.