No-twos subgroup temperaments: Difference between revisions

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 [[EDT]]s: 99, 17, 82, 116, 181, 65, 14[-5], 280, 48, 215, 31, 133, 314, 263
+== Fomalhaut ==
+The 23-limit version of Fomalhaur was created first, as an attempt to approximate the no-2s, no-7s 23-limit as accurately as possible using 25 to 35 notes per equave. Then the lower limit versions were created by simply extrapolating the temperament downwards.
+Fomalhaut follows the convention of naming no-twos temperaments after stars.
+<pre>
+Reduced Mapping
+	5	11
+[ ⟨	1	5	1	]
+⟨	0	-9	3	] ⟩
+TE Generator Tunings (cents)
+⟨1903.7622, 748.1091]
+TE Step Tunings (cents)
+⟨61.30782, 5.67101]
+TE Tuning Map (cents)
+⟨1903.762, 2785.829, 4148.089]
+TE Mistunings (cents)
+⟨1.807, -0.485, -3.228]
+Complexity	1.299882
+Adjusted Error	2.972273 cents
+TE Error	0.859180 cents/octave
+Unison Vector
+[-8, 1, 3⟩ (6655:6561)
+Subsets
+b28, b5p, b33, b23f, b61, b56f, b38c, b10cf, b66c, b51ff
+</pre>
+=== 3.5.11.13 ===
+<pre>
+Reduced Mapping
+	5	11	13
+[ ⟨	1	5	1	-2	]
+⟨	0	-9	3	11	] ⟩
+TE Generator Tunings (cents)
+⟨1905.7904, 749.5240]
+TE Step Tunings (cents)
+⟨40.98455, 22.97646]
+TE Tuning Map (cents)
+⟨1905.790, 2783.236, 4154.362, 4433.183]
+TE Mistunings (cents)
+⟨3.835, -3.077, 3.044, -7.345]
+Complexity	1.561892
+Adjusted Error	6.495941 cents
+TE Error	1.755451 cents/octave
+Unison Vectors
+[-8, 1, 3, 0⟩ (6655:6561)
+[1, 2, -5, 3⟩ (164775:161051)
+[-7, 3, -2, 3⟩ (274625:264627)
+[-15, 4, 1, 3⟩ (15104375:14348907)
+Subsets
+b28, b5p, b33, b23f, b61, b56f, b38c, b10cf, b66c, b51ff
+</pre>
+=== 3.5.11.13.17 ===
+<pre>
+Reduced Mapping
+	5	11	13	17
+[ ⟨	1	5	1	-2	1	]
+⟨	0	-9	3	11	4	] ⟩
+TE Generator Tunings (cents)
+⟨1905.8711, 749.5638]
+TE Step Tunings (cents)
+⟨40.71768, 23.20533]
+TE Tuning Map (cents)
+⟨1905.871, 2783.281, 4154.563, 4433.460, 4904.126]
+TE Mistunings (cents)
+⟨3.916, -3.033, 3.245, -7.068, -0.829]
+Complexity	1.418914
+Adjusted Error	6.431616 cents
+TE Error	1.573498 cents/octave
+Unison Vectors
+[-2, 1, -2, 1, 1⟩ (1105:1089)
+[-5, 0, 1, -1, 2⟩ (3179:3159)
+[-5, 2, 0, 2, -1⟩ (4225:4131)
+[-8, 1, 3, 0, 0⟩ (6655:6561)
+[-3, 1, 2, 1, -2⟩ (7865:7803)
+[1, 0, -4, 0, 3⟩ (14739:14641)
+Subsets
+b28, b5p, b33, b23f, b61, b56f, b38c, b10cf, b66c, b51ffg
+</pre>
+=== 3.5.11.13.17.19 ===
+<pre>
+Reduced Mapping
+	5	11	13	17	19
+[ ⟨	1	5	1	-2	1	7	]
+⟨	0	-9	3	11	4	-11	] ⟩
+TE Generator Tunings (cents)
+⟨1905.9598, 749.5710]
+TE Step Tunings (cents)
+⟨41.63378, 22.43072]
+TE Tuning Map (cents)
+⟨1905.960, 2783.660, 4154.673, 4433.362, 4904.244, 5096.437]
+TE Mistunings (cents)
+⟨4.005, -2.654, 3.355, -7.166, -0.712, -1.076]
+Complexity	1.449992
+Adjusted Error	6.125446 cents
+TE Error	1.441985 cents/octave
+Unison Vectors
+[-5, 0, 0, 1, 0, 1⟩ (247:243)
+[0, 2, 0, 1, -1, -1⟩ (325:323)
+[-2, 1, -2, 1, 1, 0⟩ (1105:1089)
+[-3, -1, 2, 0, -1, 1⟩ (2299:2295)
+[-5, 0, 1, -1, 2, 0⟩ (3179:3159)
+[0, 0, -1, 2, -2, 1⟩ (3211:3179)
+[-5, 2, 0, 2, -1, 0⟩ (4225:4131)
+[-5, 2, 1, 0, 1, -1⟩ (4675:4617)
+Subsets
+b28, b33, b5p, b61, b56f, b23f, b38ch, b66ch, b89fgh, b10cfh
+</pre>
+=== 3.5.11.13.17.19.23 ===
+<pre>
+Reduced Mapping
+	5	11	13	17	19	23
+[ ⟨	1	5	1	-2	1	7	6	]
+⟨	0	-9	3	11	4	-11	-8	] ⟩
+TE Generator Tunings (cents)
+⟨1905.4824, 749.4748]
+TE Step Tunings (cents)
+⟨38.60323, 24.98764]
+TE Tuning Map (cents)
+⟨1905.482, 2782.139, 4153.907, 4433.258, 4903.382, 5094.154, 5437.096]
+TE Mistunings (cents)
+⟨3.527, -4.175, 2.589, -7.270, -1.574, -3.359, 8.822]
+Complexity	1.382541
+Adjusted Error	7.087107 cents
+TE Error	1.566709 cents/octave
+Unison Vectors
+[-2, 0, 1, 0, 0, 1, -1⟩ (209:207)
+[1, 1, -1, 0, 1, 0, -1⟩ (255:253)
+[-3, 0, -1, 1, 0, 0, 1⟩ (299:297)
+[0, 2, 0, 1, -1, -1, 0⟩ (325:323)
+[-5, 2, 1, 0, 1, -1, 0⟩ (4675:4617)
+[0, -2, -1, 1, -1, 2, 0⟩ (4693:4675)
+Subsets
+b28, b5p, b33, b23f, b61, b56f, b38ch, b10cfhi, b66ch, b51ffg
+</pre>
 = 3.7.11 subgroup temperaments =