Chirality: Difference between revisions

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== Chirality in MV3 scales ==

Assume a scale is [[MV3]] and is of the form ax by bz. Additionally assume that the mos ax 2bY that results from equating y and z is not a multimos. Then the scale must be chiral because there are no rotations that will make the two equivalent (each mode of the mos ax 2bY corresponding to two chiral variants)~~. This defines a definition of handedness specifically for MV3 scales of this type:~~

Assume a scale is [[MV3]] and is of the form ax by bz. Additionally assume that the mos ax 2bY that results from equating y and z is not a multimos. Then the scale must be chiral because there are no rotations that will make the two equivalent (each mode of the mos ax 2bY corresponding to two chiral variants).

~~# Identify y and z to Y to get a mos. Take the mode that has the most x's at the beginning. When you undo the identification, the mv3 mode will start with either y or z first.~~

~~# If y is bigger than z then the chiral variant beginning with y is ''MV3-right-handed''. Otherwise, it is ''MV3-left-handed''.~~

~~Note that this definition of LH/RH won't agree with the lexicographical definition if x is not the biggest step. For example, LMMMSMM is lexicographically RH but MV3-LH.~~

Such chiral mv3's could be named in the format [handedness] [mv3 name] [the corresponding mode of ax 2bY]. For example, the chiral [[diasem]] mode 331323132 can be named "Left-Handed Diasem 8|0", where 8|0 is the [[UDP]] notation for the [[5L 4s]] mode LLSLSLSLS.

== External links ==

@@ Line 128: / Line 128: @@
 == Chirality in MV3 scales ==
-Assume a scale is [[MV3]] and is of the form ax by bz. Additionally assume that the mos ax 2bY that results from equating y and z is not a multimos. Then the scale must be chiral because there are no rotations that will make the two equivalent (each mode of the mos ax 2bY corresponding to two chiral variants). This defines a definition of handedness specifically for MV3 scales of this type:
+Assume a scale is [[MV3]] and is of the form ax by bz. Additionally assume that the mos ax 2bY that results from equating y and z is not a multimos. Then the scale must be chiral because there are no rotations that will make the two equivalent (each mode of the mos ax 2bY corresponding to two chiral variants).
-# Identify y and z to Y to get a mos. Take the mode that has the most x's at the beginning. When you undo the identification, the mv3 mode will start with either y or z first.
-# If y is bigger than z then the chiral variant beginning with y is ''MV3-right-handed''. Otherwise, it is ''MV3-left-handed''.
-Note that this definition of LH/RH won't agree with the lexicographical definition if x is not the biggest step. For example, LMMMSMM is lexicographically RH but MV3-LH.
-Such chiral mv3's could be named in the format [handedness] [mv3 name] [the corresponding mode of ax 2bY]. For example, the chiral [[diasem]] mode 331323132 can be named "Left-Handed Diasem 8|0", where 8|0 is the [[UDP]] notation for the [[5L 4s]] mode LLSLSLSLS.
 == External links ==