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 is not a multimos. This is how to determine the handedness of the scale:

Assume a scale is [[MV3]] and is of the form ax by bz. Additionally assume that the mos ax 2bY 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 is how to determine the handedness of the scale:

# 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 ''right-handed''. Otherwise, it is ''left-handed''~~. We know that the two chiral variants are not equivalent because there are no rotations that will make the two equivalent (each mode of the mos ax 2bY corresponding to two chiral variants)~~.

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

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

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.

[[Category:EDO theory pages]]

@@ Line 118: / Line 118: @@
 == Chirality in MV3 scales ==
-Assume a scale is [[MV3]] and is of the form ax by bz. Additionally assume that the mos ax 2bY is not a multimos. This is how to determine the handedness of the scale:
+Assume a scale is [[MV3]] and is of the form ax by bz. Additionally assume that the mos ax 2bY 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 is how to determine the handedness of the scale:
 # 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 ''right-handed''. Otherwise, it is ''left-handed''. We know that the two chiral variants are not equivalent because there are no rotations that will make the two equivalent (each mode of the mos ax 2bY corresponding to two chiral variants).
+# If y is bigger than z then the chiral variant beginning with y is ''right-handed''. Otherwise, it is ''left-handed''.
-Such chiral mv3's could be named in the format [handedness] [mv3 name] [the corresponding mode of ax 2bY]. For example, 331323132 can be named "Left-Handed Diasem 8|0", where 8|0 is the [[UDP]] notation for the [[5L 4s]] mode LLSLSLSLS.
+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.
 [[Category:EDO theory pages]]