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 lexicographically comparing all modes of each chirality (i.e. treat scale step size sequences as words to be arranged in "alphabetical order", where this alphabetical order is from bigger step to smaller step) and then lexicographically comparing the respective lexicographically first modes. ~~The~~ chirality that comes lexicographically first at the end is called the ''right-handed'' chirality ~~by convention~~.

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 chirality (i.e. treat scale step size sequences as words to be arranged in "alphabetical order", where this alphabetical order is from bigger step to smaller step) and then lexicographically comparing the respective lexicographically first modes. We choose the convention that the chirality that comes lexicographically first at the end is called the ''right-handed'' chirality.

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.

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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 lexicographically comparing all modes of each chirality (i.e. treat scale step size sequences as words to be arranged in "alphabetical order", where this alphabetical order is from bigger step to smaller step) and then lexicographically comparing the respective lexicographically first modes. The chirality that comes lexicographically first at the end is called the ''right-handed'' chirality by convention.
+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 chirality (i.e. treat scale step size sequences as words to be arranged in "alphabetical order", where this alphabetical order is from bigger step to smaller step) and then lexicographically comparing the respective lexicographically first modes. We choose the convention that the chirality that comes lexicographically first at the end is called the ''right-handed'' chirality.
 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.