Chirality: Difference between revisions
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Scales for which this property does not hold are called ''achiral''. For example, the [[5L 2s|diatonic scale]] of 12edo is achiral because 2221221 reverses to 1221222, which is identical to the original scale up to cyclical permutation. | Scales for which this property does not hold are called ''achiral''. For example, the [[5L 2s|diatonic scale]] of 12edo is achiral because 2221221 reverses to 1221222, which is identical to the original scale up to cyclical permutation. | ||
== Examples == | |||
* Odd-sized [[GO]] scales, such as [[diasem]], are chiral; even-sized GO scales, such as [[blackdye]], are not. | |||
* A [[CPS]] made by choosing n/2 out of n elements (for n even) is achiral. Otherwise it may be chiral (for example, the 1 3 5 7 9 11 [[pentadekany]] is chiral). | |||
== Properties == | == Properties == | ||
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* Chiral scales have a [http://en.wikipedia.org/wiki/Natural_density density] of 1 (see table below) | * Chiral scales have a [http://en.wikipedia.org/wiki/Natural_density density] of 1 (see table below) | ||
* Chiral scales with rational step ratios can only exist in edos larger than [[5edo]] | * Chiral scales with rational step ratios can only exist in edos larger than [[5edo]] | ||
== Chiral scales in edos up to 20edo == | == Chiral scales in edos up to 20edo == | ||