Chirality: Difference between revisions

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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 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 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 of that comes first (among all the modes of the chirality) 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''.

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 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 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 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 of that comes first (among all the modes of the chirality) 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''.