Schismic–commatic equivalence continuum: Difference between revisions

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[[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

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[[Badness]] (Sintel): 16.0

== World calendar restriction ==

: ''For extensions, see [[Septischismic clan #World calendar]].''

[[Subgroup]]: 2.3.5

[[Comma list]]: {{monzo| 101 -52 -8 }}

: mapping generators: ~39858075/33554432, ~{{monzo| -37 19 3 }}

[[Optimal tuning]]s:

* [[WE]]: ~39858075/33554432 = 299.9886{{c}}, ~{{monzo| -37 19 3 }} = 801.0127{{c}}

: [[error map]]: {{val| -0.046 +0.059 +0.019 }}

* [[CWE]]: ~39858075/33554432 = 300.0000{{c}}, ~{{monzo| -37 19 3 }} = 801.0449{{c}}

: error map: {{val| 0.000 +0.135 +0.103 }}

{{Optimal ET sequence|legend=1| 12, …, 340, 352, 364, 376, 388, 764, 1152, 1916, 3068, 8052bc, 11120bbcc }}

[[Badness]] (Sintel): 17.7

[[Category:12edo]]

[[Category:Equivalence continua]]

@@ Line 325: / Line 325: @@
 [[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
@@ Line 343: / Line 345: @@
 [[Badness]] (Sintel): 16.0
+== World calendar restriction ==
+: ''For extensions, see [[Septischismic clan #World calendar]].''
+[[Subgroup]]: 2.3.5
+[[Comma list]]: {{monzo| 101 -52 -8 }}
+{{Mapping|legend=1| 4 1 44 | 0 2 -13 }}
+: mapping generators: ~39858075/33554432, ~{{monzo| -37 19 3 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~39858075/33554432 = 299.9886{{c}}, ~{{monzo| -37 19 3 }} = 801.0127{{c}}
+: [[error map]]: {{val| -0.046 +0.059 +0.019 }}
+* [[CWE]]: ~39858075/33554432 = 300.0000{{c}}, ~{{monzo| -37 19 3 }} = 801.0449{{c}}
+: error map: {{val| 0.000 +0.135 +0.103 }}
+{{Optimal ET sequence|legend=1| 12, …, 340, 352, 364, 376, 388, 764, 1152, 1916, 3068, 8052bc, 11120bbcc }}
+[[Badness]] (Sintel): 17.7
 [[Category:12edo]]
 [[Category:Equivalence continua]]