Schismic–commatic equivalence continuum: Difference between revisions

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VisualWikitext

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 {{Mapping|legend=1| 1 0 -23 | 0 1 16 }}
 : Mapping generators: ~2, ~3
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 {{Mapping|legend=1| 1 0 34 | 0 1 -20 }}
 : Mapping generators: ~2, ~3
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 == Biscordial ==
-Biscordial has a period of half-octave, and tempers out the biscordial comma, {{Monzo| -49 28 2 }}. The ~5/4 is reached by 17 periods minus 14 fifths. It corresponds to {{nowrap| ''n'' {{=}} -2 }}.
+Named by [[Xenllium]] in 2026, biscordial has a period of half-octave, and tempers out the biscordial comma, {{monzo| -49 28 2 }}. The ~5/4 is reached by 17 periods minus 14 fifths. It corresponds to {{nowrap| ''n'' {{=}} -2 }}.
 [[Subgroup]]: 2.3.5
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 {{Mapping|legend=1| 2 0 49 | 0 1 -14 }}
 : Mapping generators: ~23914845/16777216, ~3
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 {{Optimal ET sequence|legend=1| 12, 166, 178, 190, 392, 582 }}
-[[Badness]] (Sintel): 15.714
+[[Badness]] (Sintel): 15.7
 == Triscordial ==
-Triscordial has a period of 1/3-octave, and tempers out the triscordial comma, {{Monzo| -64 36 3 }}. The ~5/4 is reached by 22 periods minus 12 fifths. It corresponds to {{nowrap| ''n'' {{=}} -3 }}.
+Named by [[Xenllium]] in 2026, triscordial has a period of 1/3-octave, and tempers out the triscordial comma, {{monzo| -64 36 3 }}. The ~5/4 is reached by 22 periods minus 12 fifths. It corresponds to {{nowrap| ''n'' {{=}} -3 }}.
 [[Subgroup]]: 2.3.5
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 {{Optimal ET sequence|legend=1| 12, 231, 243, 255, 498, 753 }}
-[[Badness]] (Sintel): 28.367
+[[Badness]] (Sintel): 28.4
-== Heptacot ==
-Heptacot tempers out the [[heptacot comma]] and divides the 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.
-[[Subgroup]]: 2.3.5
-[[Comma list]]: {{monzo| 86 -44 -7 }}
-{{Mapping|legend=1| 1 1 6 | 0 7 -44 }}
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1199.9328{{c}}, ~{{monzo| -37 19 3 }} = 100.3012{{c}}
-: [[error map]]: {{val| -0.067 +0.086 +0.029 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~{{monzo| -37 19 3 }} = 100.3076{{c}}
-: error map: {{val| 0.000 +0.198 +0.153 }}
-{{Optimal ET sequence|legend=1| 12, …, 287, 299, 311, 323, 981, 1304, 5539bc, 6843bbcc }}
-[[Badness]] (Sintel): 16.0
 == Sextile (5-limit) ==
 {{See also| Landscape microtemperaments #Sextile }}
-The 5-limit version of sextile reaches the interval class of 5 by −6 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.
 [[Subgroup]]: 2.3.5
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 {{Mapping|legend=1| 6 0 71 | 0 1 -6 }}]
 : Mapping generators: ~4096/3645, ~3
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 == Wronecki ==
-Wronecki equates a stack of six ~10/9's with the octave. It reaches the interval class of 5 by +2 perfect fifths (i.e. a major second) plus a period of 1/6-octave. It corresponds to {{nowrap| ''m'' {{=}} 6 }}, meaning the Pythagorean comma is equated with a stack of six syntonic commas.
+Wronecki equates a stack of six ~[[10/9]]'s with the octave. It reaches the interval class of 5 by +2 [[3/2|perfect fifths]] (i.e. a major second) plus a period of 1/6-octave. It corresponds to {{nowrap| ''m'' {{=}} 6 }}, meaning the Pythagorean comma is equated with a stack of six syntonic commas.
 [[Subgroup]]: 2.3.5
@@ Line 367: / Line 344: @@
 [[Badness]] (Sintel): 8.02
+== Heptacot ==
+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 [[Akselai]] in 2024, for it splits the perfect fifth into seven.
+[[Subgroup]]: 2.3.5
+[[Comma list]]: {{monzo| 86 -44 -7 }}
+{{Mapping|legend=1| 1 1 6 | 0 7 -44 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9328{{c}}, ~{{monzo| -37 19 3 }} = 100.3012{{c}}
+: [[error map]]: {{val| -0.067 +0.086 +0.029 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~{{monzo| -37 19 3 }} = 100.3076{{c}}
+: error map: {{val| 0.000 +0.198 +0.153 }}
+{{Optimal ET sequence|legend=1| 12, …, 287, 299, 311, 323, 981, 1304, 5539bc, 6843bbcc }}
+[[Badness]] (Sintel): 16.0
 [[Category:12edo]]
 [[Category:Equivalence continua]]