@@ Line 407: / Line 407: @@
 Comma list: 273/272, 441/440, 561/560
-Mapping: {{mapping| 1 0 0 0 -3 11 7 | 0 1 0 0 2 -4 -3 | 0 0 1 0 -1 2 2 | 0 0 0 1 2 -2 -1 }}
+{{Mapping|legend=0| 1 0 0 0 -3 11 7 | 0 1 0 0 2 -4 -3 | 0 0 1 0 -1 2 2 | 0 0 0 1 2 -2 -1 }}
 Optimal tunings:
@@ Line 578: / Line 578: @@
 [[Badness]] (Sintel): 1.04
+== Moctdelismic (1375/1372) ==
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 1375/1372
+{{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 0 0 | 0 0 1 0 -3 | 0 0 0 1 3 }}
+: mapping generators: ~2, ~3, ~5, ~7
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0558{{c}}, ~3/2 = 701.8991{{c}}, ~5/4 = 385.7504{{c}}, ~7/4 = 969.3743{{c}}
+: [[error map]]: {{val| +0.056 -0.000 -0.452 +0.660 -0.334 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9100{{c}}, ~5/4 = 385.7894{{c}}, ~7/4 = 969.4163{{c}}
+: error map: {{val| 0.000 -0.045 -0.524 +0.590 -0.437 }}
+{{Optimal ET sequence|legend=1| 12, 19e, 27, 29, 31, 41, 60e, 68, 72, 140, 152, 224, 364, 436, 547, 588, 619, 843, 1055ce }}
+[[Badness]] (Sintel): 0.723
 == Lehmerismic (3025/3024) ==
@@ Line 613: / Line 631: @@
 [[Badness]] (Sintel): 0.272
+== Vishdelismic (5632/5625) ==
+Vishdelismic tempers out 5632/5625, the [[vishdelisma]], and adds to [[vishdelic]] an independent generator for prime 7. From 5632/5625 = ([[176/175]])/([[225/224]]), vishdelismic has the feature of making [[14/9]], [[25/16]], and [[11/7]] equidistant.
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 5632/5625
+{{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 0 0 | 0 0 1 0 -3 | 0 0 0 1 3 }}
+: mapping generators: ~2, ~3, ~5, ~7
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.8976{{c}}, ~3/2 = 702.1145{{c}}, ~5/4 = 386.7638{{c}}, ~7/4 = 969.0306{{c}}
+: [[error map]]: {{val| -0.102 +0.057 +0.245 -0.000 -0.136 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.1309{{c}}, ~5/4 = 386.7770{{c}}, ~7/4 = 969.0087{{c}}
+: error map: {{val| 0.000 +0.176 +0.463 +0.183 +0.052 }}
+{{Optimal ET sequence|legend=1| 12, 19e, 22, 31, 53, 84e, 87, 99e, 118, 130, 152, 239, 270, 670, 822, 940, 1092, 1362c, 2032c, 2302c }}
+[[Badness]] (Sintel): 0.804
 == Trimitone (8019/8000) ==
@@ Line 729: / Line 767: @@
 [[Badness]] (Sintel): 0.164
-==== 17-limit ====
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 9801/9800, 10648/10647, 194481/194480
-Mapping: {{mapping| 2 0 1 0 4 9 -22 | 0 1 0 0 -2 -4 10 | 0 0 2 0 2 3 -7 | 0 0 0 1 1 1 2 }}
-Optimal tuning:
-* WE: ~99/70 = 600.0011{{c}}, ~3/2 = 701.9430{{c}}, ~1053/560 = 1093.1625{{c}}, ~7/4 = 968.8308{{c}}
-: error map: {{val| +0.002 -0.010 +0.012 +0.009 -0.044 +0.024 +0.006 }}
-* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9426{{c}}, ~1053/560 = 1093.1618{{c}}, ~7/4 = 968.8316{{c}}
-: error map: {{val| 0.000 -0.012 +0.010 +0.006 -0.048 +0.019 +0.001 }}
-{{Optimal ET sequence|legend=0| 46, 58, 104c, 166, 178, 212, 224, 270, 494g, 552g, 684g, 896ef, 908, 954, 1178, 1236, 1506, 2414, 2460, 3638, 3920, 4874, 5144, 6380, 10018e, 11524, 16398e }}
-Badness (Sintel): 0.655
 == Unisquary (12005/11979) ==
@@ Line 892: / Line 913: @@
 Comma list: 1216/1215, 1540/1539, 2080/2079
-Mapping: {{mapping| 1 0 0 0 -8 -13 -6 | 0 1 0 0 9 12 5 | 0 0 1 0 0 -1 1 | 0 0 0 1 -1 0 0 }}
+{{Mapping|legend=0| 1 0 0 0 -8 -13 -6 | 0 1 0 0 9 12 5 | 0 0 1 0 0 -1 1 | 0 0 0 1 -1 0 0 }}
 Optimal tunings:
@@ Line 1,003: / Line 1,024: @@
 Comma list: 2080/2079, 3510/3509, 4096/4095
-Mapping: {{mapping| 1 0 0 0 17 12 -21 | 0 1 0 0 -5 -2 11 | 0 0 1 0 0 -1 0 | 0 0 0 1 -2 -1 3 }}
+{{Mapping|legend=0| 1 0 0 0 17 12 -21 | 0 1 0 0 -5 -2 11 | 0 0 1 0 0 -1 0 | 0 0 0 1 -2 -1 3 }}
 Optimal tunings:
@@ Line 1,014: / Line 1,035: @@
 Badness (Sintel): 0.505
+==== Commas 2080/2079, 3250/3249, 4096/4095 ====
+This is a [[weak extension]] of olympic, requiring the split of the prime 7 in half; or alternatively, the septimal comma or the garischisma.
+Subgroup: 2.3.5.7.11.13.19
+Comma list: 2080/2079, 3250/3249, 4096/4095
+{{Mapping|legend=0| 1 0 0 1 15 11 -13 6 | 0 1 0 0 -5 -2 5 -2 | 0 0 1 0 0 -1 2 1 | 0 0 0 2 -4 -2 5 -1 }}
+Optimal tunings:
+* WE: ~2 = 1199.9639{{c}}, ~3/2 = 702.0643{{c}}, ~5/4 = 386.3218{{c}}, ~247/132 = 1084.4676{{c}}
+: error map: {{val| -0.036 +0.073 -0.064 +0.073 +0.129 -0.166 -0.004 }}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0887{{c}}, ~5/4 = 386.3257{{c}}, ~247/132 = 1084.5006{{c}}
+: error map: {{val| 0.000 +0.134 +0.012 +0.175 +0.236 -0.032 +0.135 }}
+{{Optimal ET sequence|legend=0| 41, 53, 84, 94, 137, 176, 217, 270, 581, 851, 935, 1205, 2193, 2463, 2774e }}
+Badness (Sintel): 0.618
+===== 2.3.5.7.11.13.19.29 subgroup =====
+Subgroup: 2.3.5.7.11.13.19.29
+Comma list: 2080/2079, 3250/3249, 3510/3509, 4096/4095
+{{Mapping|legend=0| 1 0 0 1 15 11 -13 6 -18 | 0 1 0 0 -5 -2 5 -2 -11 | 0 0 1 0 0 -1 2 1 0 | 0 0 0 2 -4 -2 5 -1 6 }}
+Optimal tunings:
+* WE: ~2 = 1199.9594{{c}}, ~3/2 = 702.0487{{c}}, ~5/4 = 386.3262{{c}}, ~247/132 = 1084.4677{{c}}
+: error map: {{val| -0.041 +0.053 -0.069 +0.069 +0.163 -0.170 +0.005 +0.048 }}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0709{{c}}, ~5/4 = 386.3327{{c}}, ~247/132 = 1084.5064{{c}}
+: error map: {{val| -0.000 +0.116 +0.019 +0.187 +0.302 -0.015 +0.171 +0.241 }}
+{{Optimal ET sequence|legend=0| 41, 53j, 94, 137j, 176, 217, 270, 487, 581j, 718, 894, 935, 988, 1205, 2193, 3398dehj}}
+Badness (Sintel): 1.10
 ==== Metaolympic ====
-Metaolympic is a [[weak extension]] of olympic, requiring the split of the prime 7 in half; or alternatively, the septimal comma or the garischisma. It is better without prime 17, but prime 17 can be added easily into the temperament by also tempering out 4200/4199, which also takes advantage of the split prime 7 at the cost of higher complexity.
+Metaolympic is the above extension with prime 17 added. It is better without prime 17, but prime 17 can be added easily into the temperament by also tempering out 4200/4199, which also takes advantage of the split prime 7 at the cost of higher complexity.
 Subgroup: 2.3.5.7.11.13.17
@@ Line 1,022: / Line 1,079: @@
 Comma list: 2080/2079, 4096/4095, 35000/34969
-Mapping: {{mapping| 1 0 0 1 15 11 -13 | 0 1 0 0 -5 -2 5 | 0 0 1 0 0 -1 2 | 0 0 0 2 -4 -2 5 }}
+{{Mapping|legend=0| 1 0 0 1 15 11 -13 | 0 1 0 0 -5 -2 5 | 0 0 1 0 0 -1 2 | 0 0 0 2 -4 -2 5 }}
 : mapping generators: ~2, ~3, ~5, ~187/100
@@ Line 1,040: / Line 1,097: @@
 Comma list: 2080/2079, 3250/3249, 4096/4095, 4200/4199
-Mapping: {{mapping| 1 0 0 1 15 11 -13 6 | 0 1 0 0 -5 -2 5 -2 | 0 0 1 0 0 -1 2 1 | 0 0 0 2 -4 -2 5 -1 }}
+{{Mapping|legend=0| 1 0 0 1 15 11 -13 6 | 0 1 0 0 -5 -2 5 -2 | 0 0 1 0 0 -1 2 1 | 0 0 0 2 -4 -2 5 -1 }}
 Optimal tunings:
@@ Line 1,057: / Line 1,114: @@
 Comma list: 2080/2079, 3250/3249, 3510/3509, 4096/4095, 4200/4199
-Mapping: {{mapping| 1 0 0 1 15 11 -13 6 -18 | 0 1 0 0 -5 -2 5 -2 -11 | 0 0 1 0 0 -1 2 1 0 | 0 0 0 2 -4 -2 5 -1 6 }}
+{{Mapping|legend=0| 1 0 0 1 15 11 -13 6 -18 | 0 1 0 0 -5 -2 5 -2 -11 | 0 0 1 0 0 -1 2 1 0 | 0 0 0 2 -4 -2 5 -1 6 }}
 Optimal tunings:
@@ Line 1,068: / Line 1,125: @@
 Badness (Sintel): 1.27
-==== Commas 2080/2079, 3250/3249, 4096/4095 ====
-Subgroup: 2.3.5.7.11.13.19
-Comma list: 2080/2079, 3250/3249, 4096/4095
-Mapping: {{mapping| 1 0 0 1 15 11 -13 6 | 0 1 0 0 -5 -2 5 -2 | 0 0 1 0 0 -1 2 1 | 0 0 0 2 -4 -2 5 -1 }}
-Optimal tunings:
-* WE: ~2 = 1199.9639{{c}}, ~3/2 = 702.0643{{c}}, ~5/4 = 386.3218{{c}}, ~187/100 = 1084.4676{{c}}
-: error map: {{val| -0.036 +0.073 -0.064 +0.073 +0.129 -0.166 -0.004 }}
-* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0887{{c}}, ~5/4 = 386.3257{{c}}, ~187/100 = 1084.5006{{c}}
-: error map: {{val| 0.000 +0.134 +0.012 +0.175 +0.236 -0.032 +0.135 }}
-{{Optimal ET sequence|legend=0| 41, 53, 84, 94, 137, 176, 217, 270, 581, 851, 935, 1205, 2193, 2463, 2774e }}
-Badness (Sintel): 0.618
-===== 2.3.5.7.11.13.19.29 subgroup =====
-Subgroup: 2.3.5.7.11.13.19.29
-Comma list: 2080/2079, 3250/3249, 3510/3509, 4096/4095
-Mapping: {{mapping| 1 0 0 1 15 11 -13 6 -18 | 0 1 0 0 -5 -2 5 -2 -11 | 0 0 1 0 0 -1 2 1 0 | 0 0 0 2 -4 -2 5 -1 6 }}
-Optimal tunings:
-* WE: ~2 = 1199.9594{{c}}, ~3/2 = 702.0487{{c}}, ~5/4 = 386.3262{{c}}, ~187/100 = 1084.4677{{c}}
-: error map: {{val| -0.041 +0.053 -0.069 +0.069 +0.163 -0.170 +0.005 +0.048 }}
-* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0709{{c}}, ~5/4 = 386.3327{{c}}, ~187/100 = 1084.5064{{c}}
-: error map: {{val| -0.000 +0.116 +0.019 +0.187 +0.302 -0.015 +0.171 +0.241 }}
-{{Optimal ET sequence|legend=0| 41, 53j, 94, 137j, 176, 217, 270, 487, 581j, 718, 894, 935, 988, 1205, 2193, 3398dehj}}
-Badness (Sintel): 1.10
 == Alphaxenic (131769/131072) ==
@@ Line 1,181: / Line 1,204: @@
 Comma list: 352/351, 715/714, 155771/155520
-Mapping: {{mapping| 1 0 -6 0 1 6 0 | 0 1 3 0 2 -1 3 | 0 0 5 0 -1 -1 3 | 0 0 0 1 0 0 -1 }}
+{{Mapping|legend=0| 1 0 -6 0 1 6 0 | 0 1 3 0 2 -1 3 | 0 0 5 0 -1 -1 3 | 0 0 0 1 0 0 -1 }}
 Optimal tunings:
@@ Line 1,196: / Line 1,219: @@
 Comma list: 352/351, 715/714, 1463/1458, 2057/2052
-Mapping: {{mapping| 1 0 -6 0 1 6 0 0 | 0 1 3 0 2 -1 3 4 | 0 0 5 0 -1 -1 3 1 | 0 0 0 1 0 0 -1 -1 }}
+{{Mapping|legend=0| 1 0 -6 0 1 6 0 0 | 0 1 3 0 2 -1 3 4 | 0 0 5 0 -1 -1 3 1 | 0 0 0 1 0 0 -1 -1 }}
 Optimal tunings:
@@ Line 1,205: / Line 1,228: @@
 Badness (Sintel): 2.63
+== Nexus (1771561/1769472) ==
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 1771561/1769472
+{{Mapping|legend=1| 3 0 0 0 8 | 0 2 0 0 1 | 0 0 1 0 0 | 0 0 0 1 0 }}
+: mapping generators: ~121/96, ~1331/768, ~5, ~7
+[[Optimal tuning]]s:
+* [[WE]]: ~121/96 = 400.0154{{c}}, ~1331/768 = 950.9883{{c}}, ~5/4 = 386.2216{{c}}, ~7/4 = 968.7338{{c}}
+: [[error map]]: {{val| +0.046 +0.022 -0.000 -0.000 -0.207 }}
+* [[CWE]]: ~121/96 = 400.0000{{c}}, ~1331/768 = 950.9685{{c}}, ~5/4 = 386.2485{{c}}, ~7/4 = 968.7470{{c}}
+: error map: {{val| 0.000 -0.018 -0.065 -0.079 -0.349 }}
+{{Optimal ET sequence|legend=1| 9, 15, 24, 33cd, 39(d), 48, 57, 63, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566, 2091e, 2361e, 2433e, 2703e, 3045e, 3315ee, 3657ee }}
+[[Badness]] (Sintel): 10.7
+=== Commas 676/675, 6656/6655 ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 676/675, 6656/6655
+{{Mapping|legend=0| 3 0 0 0 8 -3 | 0 2 0 0 1 3 | 0 0 1 0 0 1 | 0 0 0 1 0 0 }}
+Optimal tunings:
+* WE: ~121/96 = 400.0003{{c}}, ~1331/768 = 951.0845{{c}}, ~5/4 = 386.5832{{c}}, ~7/4 = 968.8238{{c}}
+* CWE: ~121/96 = 400.0000{{c}}, ~1331/768 = 951.0840{{c}}, ~5/4 = 386.5837{{c}}, ~7/4 = 968.8241{{c}}
+{{Optimal ET sequence|legend=0| 9, 15, 24, 39c/df, 48c, 57f, 63, 72, 87, 111, 159, 183, 198, 270 }}
+Badness (Sintel): 1.69
 == Quartismic (117440512/117406179) ==

Catalog of rank-4 temperaments: Difference between revisions