Schismic–commatic equivalence continuum: Difference between revisions

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@@ Line 23: / Line 23: @@
 ! Ratio
 ! Monzo
+|-
+| -3
+| 9/4
+| [[Triscordial]]
+| (40 digits)
+| {{Monzo| -64 36 3 }}
+|-
+| -2
+| 7/3
+| [[Biscordial]]
+| (30 digits)
+| {{Monzo| -49 28 2 }}
 |-
 | -1
@@ Line 220: / Line 232: @@
 {{Mapping|legend=1| 1 0 -23 | 0 1 16 }}
-: mapping generators: ~2, ~3
+: Mapping generators: ~2, ~3
 [[Optimal tuning]]s:
@@ Line 243: / Line 255: @@
 {{Mapping|legend=1| 1 0 34 | 0 1 -20 }}
-: mapping generators: ~2, ~3
+: Mapping generators: ~2, ~3
 [[Optimal tuning]]s:
@@ Line 254: / Line 266: @@
 [[Badness]] (Sintel): 7.20
+== 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 }}.
+[[Subgroup]]: 2.3.5
+[[Comma list]]: 571919811374025/562949953421312
+{{Mapping|legend=1| 2 0 49 | 0 1 -14 }}
+: Mapping generators: ~23914845/16777216, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~23914845/16777216 = 600.153{{c}}, ~3/2 = 701.211{{c}}
+* [[CWE]]: ~23914845/16777216 = 600.000{{c}}, ~3/2 = 701.019{{c}}
+{{Optimal ET sequence|legend=1| 12, 166, 178, 190, 392, 582 }}
+[[Badness]] (Sintel): 15.714
+== 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 }}.
+[[Subgroup]]: 2.3.5
+[[Comma list]]: {{Monzo| -64 36 3 }}
+{{Mapping|legend=1| 3 0 64 | 0 1 -12 }}
+: Mapping generators: ~2657205/2097152, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~2657205/2097152 = 400.084{{c}}, ~3/2 = 701.343{{c}}
+* [[CWE]]: ~2657205/2097152 = 400.000{{c}}, ~3/2 = 701.182{{c}}
+{{Optimal ET sequence|legend=1| 12, 231, 243, 255, 498, 753 }}
+[[Badness]] (Sintel): 28.367
+== 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) ==
@@ Line 266: / Line 335: @@
 {{Mapping|legend=1| 6 0 71 | 0 1 -6 }}]
-: mapping generators: ~4096/3645, ~3
+: Mapping generators: ~4096/3645, ~3
 [[Optimal tuning]]s:
@@ Line 287: / Line 356: @@
 {{Mapping|legend=1| 6 0 -5 | 0 1 2 }}
-: mapping generators: ~10/9, ~3
+: Mapping generators: ~10/9, ~3
 [[Optimal tuning]]s:
@@ Line 298: / Line 367: @@
 [[Badness]] (Sintel): 8.02
-== 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
 [[Category:12edo]]
 [[Category:Equivalence continua]]