No-twos subgroup temperaments: Difference between revisions

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 This is a collection of [[subgroup temperament]]s which omit the prime harmonic of 2. Because of the absence of octaves, these are all [[nonoctave]] scales using a period of a [[tritave]], or if harmonic 3 is also excluded, [[5/1]].
-== Izar ==
+== Arcturus ==
-[[Subgroup]]: 3.5.7
+''see [[Arcturus]], [[Arcturus clan]]''
+Subgroup: 3.5.7
+[[Comma list]]: 15625/15309
-[[Comma list]]: 13841287201/13839609375
+[[Sval]] [[mapping]]: [{{val| 1 0 -7 }}, {{val| 0 1 6 }}]
-{{Mapping|legend=2|1 7 5|0 -12 -7}}
+Sval mapping generators: ~3, ~5
-Sval mapping generators: ~3, ~16807/10125
+[[POTE generator]]: ~5/3 = 878.042
-[[Optimal tuning]] (CTE): ~3 = 1\1edt, ~16807/10125 = 877.280
+[[Optimal ET sequence]]: [[2edt|b2]], [[11edt|b11]], [[13edt|b13]]
-[[Support]]ing [[ET]]s: {{EDs|b13, b11cd, b193, b15cd, b180, b24c, b167, b37c, b154, 141, b50c, b28cd, b128, b63c|equave=t}}
+== Aldebaran ==
-==Canopus==
+''see [[Aldebaran]]''
-[[Subgroup]]: 3.5.7
-[[Comma list]]: 16875/16807
+[[Subgroup]]: 3.5.13
-{{Mapping|legend=2|1 3 3|0 -5 -4}}
+[[Comma list]]: 3159/3125
-Sval mapping generators: ~3, ~7/5
+[[Mapping]]: [{{val|1 0 5}}, {{val|0 1 -2}}]
-[[Optimal tuning]] (CTE): ~3 = 1\1edt, ~7/5 = 584.017
+[[Support]]ing [[ET]]s: 15, 17, 13, 32, 47, 28, 11[-13], 19[+13], 43, 9[-13], 7[-13], 49[+13], 21[+13], 41[-13]
-[[Support]]ing [[ET]]s: {{EDs|b13, b10, b75, b62, b23, b49, b36, b16, b7cd, 29, b42c, b19cd, b33cd, b55c|equave=t}}
+[[CTE tuning|CTE generator]]: ~[[5/3]] = 887.76
 == BPS ==
@@ Line 40: / Line 43: @@
 [[Optimal ET sequence]]: [[4edt|b4]], [[9edt|b9]], [[13edt|b13]], [[56edt|b56]], [[69edt|b69]], [[82edt|b82]], [[95edt|b95]]
+==Canopus==
+[[Subgroup]]: 3.5.7
-== Arcturus ==
+[[Comma list]]: 16875/16807
-''see [[Arcturus]], [[Arcturus clan]]''
-Subgroup: 3.5.7
+{{Mapping|legend=2|1 3 3|0 -5 -4}}
-[[Comma list]]: 15625/15309
+Sval mapping generators: ~3, ~7/5
-[[Sval]] [[mapping]]: [{{val| 1 0 -7 }}, {{val| 0 1 6 }}]
+[[Optimal tuning]] (CTE): ~3 = 1\1edt, ~7/5 = 584.017
-Sval mapping generators: ~3, ~5
+[[Support]]ing [[ET]]s: {{EDs|b13, b10, b75, b62, b23, b49, b36, b16, b7cd, 29, b42c, b19cd, b33cd, b55c|equave=t}}
-[[POTE generator]]: ~5/3 = 878.042
+== Izar ==
+[[Subgroup]]: 3.5.7
-[[Optimal ET sequence]]: [[2edt|b2]], [[11edt|b11]], [[13edt|b13]]
+[[Comma list]]: 13841287201/13839609375
-== Aldebaran ==
+{{Mapping|legend=2|1 7 5|0 -12 -7}}
-''see [[Aldebaran]]''
-[[Subgroup]]: 3.5.13
+Sval mapping generators: ~3, ~16807/10125
-[[Comma list]]: 3159/3125
+[[Optimal tuning]] (CTE): ~3 = 1\1edt, ~16807/10125 = 877.280
-[[Mapping]]: [{{val|1 0 5}}, {{val|0 1 -2}}]
-[[Support]]ing [[ET]]s: 15, 17, 13, 32, 47, 28, 11[-13], 19[+13], 43, 9[-13], 7[-13], 49[+13], 21[+13], 41[-13]
-[[CTE tuning|CTE generator]]: ~[[5/3]] = 887.76
+[[Support]]ing [[ET]]s: {{EDs|b13, b11cd, b193, b15cd, b180, b24c, b167, b37c, b154, 141, b50c, b28cd, b128, b63c|equave=t}}
 == No-twos-or-threes subgroup temperaments ==
 === Juggernaut ===