Schismic–commatic equivalence continuum: Difference between revisions

Move discussion on the *k*-continuum below *m*-continuum as they are more closely related.
Heptacot: update
 
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== Sextile (5-limit) ==
== Sextile (5-limit) ==
{{See also| Landscape microtemperaments #Sextile }}
{{See also| Garischismic 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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[[Badness]] (Sintel): 8.02
[[Badness]] (Sintel): 8.02


== Heptacot ==
== Heptacot (5-limit) ==
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.  
: ''For extensions, see [[Garischismic 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.  


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5