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 (which is not a mode of the original scale). The two scales form a ''chiral pair'' and are right/left-handed. Handedness is determined by:

A scale is called ''chiral'' if reversing the order of the steps results in a different scale (which is not a mode of the original scale). The two scales form a ''chiral pair'' and are right/left-handed. Handedness is determined as follows:

# ~~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). ~~Record~~ the ~~lexicographically~~ first modes M and M'.

# Lexicographically compare 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). For each chirality, record the mode that comes first according to this alphabetical order; you should end up with two modes M and M'.

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

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

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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 (which is not a mode of the original scale). The two scales form a ''chiral pair'' and are right/left-handed. Handedness is determined by:
+A scale is called ''chiral'' if reversing the order of the steps results in a different scale (which is not a mode of the original scale). The two scales form a ''chiral pair'' and are right/left-handed. Handedness is determined as follows:
-# 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). Record the lexicographically first modes M and M'.
+# Lexicographically compare 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). For each chirality, record the mode that comes first according to this alphabetical order; you should end up with two modes M and M'.
-# lexicographically compare M and M'. We choose the convention that if M lexicographically comes before M', then it and all its modes are ''right-handed''. Otherwise it is ''left-handed''.
+# Lexicographically compare M and M'. We choose the convention that if M lexicographically comes before M', then it and all its modes are ''right-handed''. Otherwise it is ''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.