@@ Line 513: / Line 513: @@
 <nowiki>*</nowiki> wart for 4
+=== Fourwar ===
+The 23-limit version of Fourwar was created first, as an attempt to approximate subgroup 4.6.5.7.11.13.17.19.23 as accurately as possible using 25 to 35 notes per equave. Then the lower limit versions were created by simply extrapolating the temperament downwards.
+Fourwar is named after the closely related [[hemiwar]] temperament.
+<pre>
+Reduced Mapping
+	6	5
+[ ⟨	1	0	1	]
+⟨	0	16	2	] ⟩
+TE Generator Tunings (cents)
+⟨2399.3973, 193.8643]
+TE Step Tunings (cents)
+⟨25.21211, 47.81337]
+TE Tuning Map (cents)
+⟨2399.397, 3101.829, 2787.126]
+TE Mistunings (cents)
+⟨-0.603, -0.126, 0.812]
+Complexity	1.369085
+Adjusted Error	0.692892 cents
+TE Error	0.268047 cents/octave
+Unison Vector
+[8, 1, -8⟩ (393216:390625)
+Subsets
+q99, q62, q37, q161, q136, q198, q25, q124, q74, q235
+</pre>
+==== 4.6.5.7 ====
+<pre>
+Reduced Mapping
+	6	5	7
+[ ⟨	1	0	1	1	]
+⟨	0	16	2	5	] ⟩
+TE Generator Tunings (cents)
+⟨2399.4195, 193.8654]
+TE Step Tunings (cents)
+⟨25.23883, 47.79592]
+TE Tuning Map (cents)
+⟨2399.420, 3101.846, 2787.150, 3368.747]
+TE Mistunings (cents)
+⟨-0.580, -0.109, 0.837, -0.079]
+Complexity	1.192044
+Adjusted Error	0.653313 cents
+TE Error	0.232715 cents/octave
+Unison Vectors
+[-2, -1, -2, 4⟩ (2401:2400)
+[3, 0, -5, 2⟩ (3136:3125)
+[5, 1, -3, -2⟩ (6144:6125)
+[8, 1, -8, 0⟩ (393216:390625)
+Subsets
+q99, q62, q37, q161, q136, q198, q25, q124, q74, q235
+</pre>
+==== 4.6.5.7.11 ====
+<pre>
+Reduced Mapping
+	6	5	7	11
+[ ⟨	1	0	1	1	1	]
+⟨	0	16	2	5	9	] ⟩
+TE Generator Tunings (cents)
+⟨2400.1097, 193.9498]
+TE Step Tunings (cents)
+⟨24.18752, 48.52491]
+TE Tuning Map (cents)
+⟨2400.110, 3103.196, 2788.009, 3369.859, 4145.658]
+TE Mistunings (cents)
+⟨0.110, 1.241, 1.696, 1.033, -5.660]
+Complexity	1.068792
+Adjusted Error	2.926965 cents
+TE Error	0.846083 cents/octave
+Unison Vectors
+[-1, -1, -1, 0, 2⟩ (121:120)
+[2, 0, -2, -1, 1⟩ (176:175)
+[-3, -1, 1, 1, 1⟩ (385:384)
+[-1, 0, 3, -3, 1⟩ (1375:1372)
+[-2, -1, -2, 4, 0⟩ (2401:2400)
+[1, 0, 1, -4, 2⟩ (2420:2401)
+Subsets
+q37, q25, q62, q12, q74, q99, q87, q49r, q50r, q124
+</pre>
+==== 4.6.5.7.11.13 ====
+<pre>
+Reduced Mapping
+	6	5	7	11	13
+[ ⟨	1	0	1	1	1	0	]
+⟨	0	16	2	5	9	23	] ⟩
+TE Generator Tunings (cents)
+⟨2401.2305, 193.5378]
+TE Step Tunings (cents)
+⟨42.79107, 35.98524]
+TE Tuning Map (cents)
+⟨2401.230, 3096.606, 2788.306, 3368.920, 4143.071, 4451.371]
+TE Mistunings (cents)
+⟨1.230, -5.349, 1.992, 0.094, -8.247, 10.843]
+Complexity	1.219191
+Adjusted Error	6.699599 cents
+TE Error	1.810487 cents/octave
+Unison Vectors
+[0, 1, -1, 0, 1, -1⟩ (66:65)
+[-1, -1, -1, 0, 2, 0⟩ (121:120)
+[1, 2, 0, 0, -1, -1⟩ (144:143)
+[2, 0, -2, -1, 1, 0⟩ (176:175)
+[-2, 1, 1, 1, 0, -1⟩ (105:104)
+[-3, -1, 1, 1, 1, 0⟩ (385:384)
+[-3, 0, 0, 1, 2, -1⟩ (847:832)
+[1, 3, -1, 0, 0, -2⟩ (864:845)
+[-1, 0, 3, -3, 1, 0⟩ (1375:1372)
+Subsets
+q25, q37f, q12f, q62, q50rf, q13rff, q49rff, q87, q74ff, q24rfff
+</pre>
+==== 4.6.5.7.11.13.17 ====
+<pre>
+Reduced Mapping
+	6	5	7	11	13	17
+[ ⟨	1	0	1	1	1	0	1	]
+⟨	0	16	2	5	9	23	13	] ⟩
+TE Generator Tunings (cents)
+⟨2400.4701, 193.4599]
+TE Step Tunings (cents)
+⟨43.39350, 35.55764]
+TE Tuning Map (cents)
+⟨2400.470, 3095.359, 2787.390, 3367.770, 4141.609, 4449.578, 4915.449]
+TE Mistunings (cents)
+⟨0.470, -6.596, 1.076, -1.056, -9.709, 9.050, 10.494]
+Complexity	1.129881
+Adjusted Error	8.082725 cents
+TE Error	1.977443 cents/octave
+Unison Vectors
+[0, 1, -1, 0, 1, -1, 0⟩ (66:65)
+[1, 1, 1, -1, 0, 0, -1⟩ (120:119)
+[1, 2, 0, 0, -1, -1, 0⟩ (144:143)
+[-2, 1, 1, 1, 0, -1, 0⟩ (105:104)
+[-1, 2, 2, 0, 0, -1, -1⟩ (225:221)
+[-1, 1, 2, -2, 0, -1, 1⟩ (1275:1274)
+Subsets
+q25, q12f, q37f, q13rffg, q50rf, q62, q49rffg, q24rfffg, q38rreffg, q74ffg
+</pre>
+==== 4.6.5.7.11.13.17.19 ====
+<pre>
+Reduced Mapping
+	6	5	7	11	13	17	19
+[ ⟨	1	0	1	1	1	0	1	1	]
+⟨	0	16	2	5	9	23	13	14	] ⟩
+TE Generator Tunings (cents)
+⟨2399.9219, 193.3952]
+TE Step Tunings (cents)
+⟨44.14256, 35.03670]
+TE Tuning Map (cents)
+⟨2399.922, 3094.324, 2786.712, 3366.898, 4140.479, 4448.090, 4914.060, 5107.455]
+TE Mistunings (cents)
+⟨-0.078, -7.631, 0.399, -1.928, -10.839, 7.562, 9.104, 9.942]
+Complexity	1.058472
+Adjusted Error	8.712222 cents
+TE Error	2.050935 cents/octave
+Unison Vectors
+[0, 1, -1, 0, 1, -1, 0, 0⟩ (66:65)
+[-1, 0, 0, 1, 1, 0, 0, -1⟩ (77:76)
+[2, 1, -1, 0, 0, 0, 0, -1⟩ (96:95)
+[1, 1, 1, -1, 0, 0, -1, 0⟩ (120:119)
+[0, 1, 1, 1, -1, 0, 0, -1⟩ (210:209)
+[0, 0, 1, -2, 1, 0, 1, -1⟩ (935:931)
+[2, 0, -3, 1, 0, 0, -1, 1⟩ (2128:2125)
+Subsets
+q25, q12fh, q37f, q13rffgh, q50rf, q62, q49rffgh, q24rfffghh, q38rreffgh, q74ffgh
+</pre>
+==== 4.6.5.7.11.13.17.19.23 ====
+<pre>
+Reduced Mapping
+	6	5	7	11	13	17	19	23
+[ ⟨	1	0	1	1	1	0	1	1	0	]
+⟨	0	16	2	5	9	23	13	14	28	] ⟩
+TE Generator Tunings (cents)
+⟨2399.3286, 193.5316]
+TE Step Tunings (cents)
+⟨37.31613, 39.63311]
+TE Tuning Map (cents)
+⟨2399.329, 3096.506, 2786.392, 3366.987, 4141.113, 4451.227, 4915.240, 5108.771, 5418.885]
+TE Mistunings (cents)
+⟨-0.671, -5.449, 0.078, -1.839, -10.205, 10.699, 10.284, 11.258, -9.389]
+Complexity	1.115920
+Adjusted Error	9.502017 cents
+TE Error	2.100561 cents/octave
+Unison Vectors
+[0, 1, -1, 0, 1, -1, 0, 0, 0⟩ (66:65)
+[1, 0, 0, -1, 0, -1, 0, 0, 1⟩ (92:91)
+[0, -1, 1, 0, 0, 0, 0, -1, 1⟩ (115:114)
+[1, 1, 1, -1, 0, 0, -1, 0, 0⟩ (120:119)
+[2, 0, -2, -1, 1, 0, 0, 0, 0⟩ (176:175)
+[-3, -1, 1, 1, 1, 0, 0, 0, 0⟩ (385:384)
+[1, 0, -2, 1, 0, 0, 1, -1, 0⟩ (476:475)
+[1, 0, 0, -2, 1, 0, -1, 1, 0⟩ (836:833)
+[0, 0, 1, -2, 1, 0, 1, -1, 0⟩ (935:931)
+[1, -1, 0, 0, 0, 0, -2, 1, 1⟩ (874:867)
+Subsets
+q25i, q12fhi, q37f, q13rffghii, q62, q50rfii, q49rffghii, q24rfffghhiii, q74ffghi, q38rreffghiii
+</pre>
 == 4.9.25 subgroup ==

Subgroup temperaments: Difference between revisions