Schismic–commatic equivalence continuum: Difference between revisions
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== Sextile (5-limit) == | == Sextile (5-limit) == | ||
: ''For extensions, see [[Septischismic clan #Sextile]].'' | |||
The 5-limit version of sextile reaches the [[interval class]] of [[5/1|5]] by −6 [[3/2|perfect fifths]] (i.e. a diminished fifth) minus a period of 1/6-octave. It corresponds to {{nowrap| ''n'' {{=}} 6 }}, meaning the Pythagorean comma is equated with a stack of six schismas. | The 5-limit version of sextile reaches the [[interval class]] of [[5/1|5]] by −6 [[3/2|perfect fifths]] (i.e. a diminished fifth) minus a period of 1/6-octave. It corresponds to {{nowrap| ''n'' {{=}} 6 }}, meaning the Pythagorean comma is equated with a stack of six schismas. | ||
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* [[WE]]: ~10/9 = 200.1488{{c}}, ~3/2 = 695.5574{{c}} | * [[WE]]: ~10/9 = 200.1488{{c}}, ~3/2 = 695.5574{{c}} | ||
: [[error map]]: {{val| +0.893 -5.505 +5.843 }} | : [[error map]]: {{val| +0.893 -5.505 +5.843 }} | ||
* [[CWE]]: ~10/9 = | * [[CWE]]: ~10/9 = 200.0000{{c}}, ~3/2 = 695.6109{{c}} | ||
: error map: {{val| 0.000 -6.344 +4.908 }} | : error map: {{val| 0.000 -6.344 +4.908 }} | ||
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== Heptacot (5-limit) == | == Heptacot (5-limit) == | ||
: ''For extensions, see [[ | : ''For extensions, see [[Septischismic clan #Heptacot]].'' | ||
The 5-limit version of heptacot tempers out the [[heptacot comma]] and divides the [[3/2|perfect fifth]] into seven equal parts, the most notable example being [[12edo]] (7\12). It corresponds to {{nowrap| ''n'' {{=}} 7 }}, meaning the Pythagorean comma is equated with a stack of seven schismas. It was named by [[Tristan Bay]] in 2024, for it splits the perfect fifth into seven. | The 5-limit version of heptacot tempers out the [[heptacot comma]] and divides the [[3/2|perfect fifth]] into seven equal parts, the most notable example being [[12edo]] (7\12). It corresponds to {{nowrap| ''n'' {{=}} 7 }}, meaning the Pythagorean comma is equated with a stack of seven schismas. It was named by [[Tristan Bay]] in 2024, for it splits the perfect fifth into seven. | ||