@@ Line 1: / Line 1: @@
-{{interwiki
-| de = Magische Temperaturen
-| en = Magic family
-| es =
-| ja =
-}}
 {{Technical data page}}
 The '''magic family''' of temperaments tempers out [[3125/3072]], the small diesis or magic comma. The septimal version of magic is locally optimal, for some searches, in the [[9-odd-limit]]. Magic has a slightly higher complexity than [[meantone]] but it is closer to just intonation. It is the simplest rank-2 temperament that tunes every [[9-odd-limit]] interval better than is possible in [[12edo]]. The most prominent deficiency is that it lacks [[Rothenberg propriety|proper]] or nearly-proper [[mos scale]]s in the 5- to 10-note region. Properties may depend on tuning and extension.
@@ Line 92: / Line 86: @@
 Comma list: 100/99, 225/224, 245/243
-Mapping: {{mapping| 1 0 2 -1 6 | 0 5 1 12 -8 }}
+{{Mapping|legend=0| 1 0 2 -1 6 | 0 5 1 12 -8 }}
 Optimal tunings:
@@ Line 117: / Line 111: @@
 Comma list: 100/99, 105/104, 144/143, 196/195
-Mapping: {{mapping| 1 0 2 -1 6 -2 | 0 5 1 12 -8 18 }}
+{{Mapping|legend=0| 1 0 2 -1 6 -2 | 0 5 1 12 -8 18 }}
 Optimal tunings:
@@ Line 136: / Line 130: @@
 Comma list: 100/99, 105/104, 120/119, 144/143, 154/153
-Mapping: {{mapping| 1 0 2 -1 6 -2 6 | 0 5 1 12 -8 18 -6 }}
+{{Mapping|legend=0| 1 0 2 -1 6 -2 6 | 0 5 1 12 -8 18 -6 }}
 Optimal tunings:
@@ Line 146: / Line 140: @@
 Badness (Sintel): 1.05
-====== 19-limit ======
+====== Magicus ======
 Subgroup: 2.3.5.7.11.13.17.19
 Comma list: 100/99, 105/104, 120/119, 133/132, 144/143, 154/153
-Mapping: {{mapping| 1 0 2 -1 6 -2 6 9 | 0 5 1 12 -8 18 -6 -15 }}
+{{Mapping|legend=0| 1 0 2 -1 6 -2 6 9 | 0 5 1 12 -8 18 -6 -15 }}
 Optimal tunings:
@@ Line 166: / Line 160: @@
 Comma list: 100/99, 105/104, 120/119, 144/143, 154/153, 171/169
-Mapping: {{mapping| 1 0 2 -1 6 -2 6 -4 | 0 5 1 12 -8 18 -6 26 }}
+{{Mapping|legend=0| 1 0 2 -1 6 -2 6 -4 | 0 5 1 12 -8 18 -6 26 }}
 Optimal tunings:
@@ Line 181: / Line 175: @@
 Comma list: 100/99, 105/104, 144/143, 170/169, 196/195
-Mapping: {{mapping| 1 0 2 -1 6 -2 -7 | 0 5 1 12 -8 18 35 }}
+{{Mapping|legend=0| 1 0 2 -1 6 -2 -7 | 0 5 1 12 -8 18 35 }}
 Optimal tunings:
@@ Line 196: / Line 190: @@
 Comma list: 100/99, 105/104, 144/143, 170/169, 171/169, 196/195
-Mapping: {{mapping| 1 0 2 -1 6 -2 -7 -4 | 0 5 1 12 -8 18 35 26 }}
+{{Mapping|legend=0| 1 0 2 -1 6 -2 -7 -4 | 0 5 1 12 -8 18 35 26 }}
 Optimal tunings:
@@ Line 228: / Line 222: @@
 Comma list: 65/64, 78/77, 91/90, 100/99
-Mapping: {{mapping| 1 0 2 -1 6 4 | 0 5 1 12 -8 -1 }}
+{{Mapping|legend=0| 1 0 2 -1 6 4 | 0 5 1 12 -8 -1 }}
 Optimal tunings:
@@ Line 237: / Line 231: @@
 Badness (Sintel): 1.07
-===== 17-limit =====
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 52/51, 65/64, 78/77, 91/90, 100/99
-Mapping: {{mapping| 1 0 2 -1 6 4 6 | 0 5 1 12 -8 -1 -6 }}
-Optimal tunings:
-* WE: ~2 = 1200.4822{{c}}, ~5/4 = 380.8818{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.7356{{c}}
-{{Optimal ET sequence|legend=0| 19, 22 }}
-Badness (Sintel): 1.21
-===== 19-limit =====
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 52/51, 65/64, 78/77, 91/90, 100/99, 133/132
-Mapping: {{mapping| 1 0 2 -1 6 4 6 9 | 0 5 1 12 -8 -1 -6 -15 }}
-Optimal tunings:
-* WE: ~2 = 1200.6684{{c}}, ~5/4 = 380.8328{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.6212{{c}}
-{{Optimal ET sequence|legend=0| 19, 22 }}
-Badness (Sintel): 1.41
 ==== Necromancy ====
@@ Line 273: / Line 237: @@
 Comma list: 100/99, 225/224, 245/243, 275/273
-Mapping: {{mapping| 1 0 2 -1 6 11 | 0 5 1 12 -8 -23 }}
+{{Mapping|legend=0| 1 0 2 -1 6 11 | 0 5 1 12 -8 -23 }}
 Optimal tunings:
@@ Line 288: / Line 252: @@
 Comma list: 100/99, 120/119, 154/153, 225/224, 273/272
-Mapping: {{mapping| 1 0 2 -1 6 11 6 | 0 5 1 12 -8 -23 -6 }}
+{{Mapping|legend=0| 1 0 2 -1 6 11 6 | 0 5 1 12 -8 -23 -6 }}
 Optimal tunings:
@@ Line 297: / Line 261: @@
 Badness (Sintel): 1.12
-===== 19-limit =====
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 100/99, 120/119, 133/132, 154/153, 209/208, 225/224
-Mapping: {{mapping| 1 0 2 -1 6 11 6 9 | 0 5 1 12 -8 -23 -6 -15 }}
-Optimal tunings:
-* WE: ~2 = 1199.6176{{c}}, ~5/4 = 380.6981{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.7355{{c}}
-{{Optimal ET sequence|legend=0| 19f, 22, 41 }}
-Badness (Sintel): 1.28
 ==== Soothsaying ====
@@ Line 318: / Line 267: @@
 Comma list: 100/99, 225/224, 245/243, 1352/1331
-Mapping: {{mapping| 2 0 4 -2 12 15 | 0 5 1 12 -8 -12 }}
+{{Mapping|legend=0| 2 0 4 -2 12 15 | 0 5 1 12 -8 -12 }}
 Optimal tunings:
@@ Line 333: / Line 282: @@
 Comma list: 100/99, 221/220, 225/224, 245/243, 273/272
-Mapping: {{mapping| 2 0 4 -2 12 15 5 | 0 5 1 12 -8 -12 5 }}
+{{Mapping|legend=0| 2 0 4 -2 12 15 5 | 0 5 1 12 -8 -12 5 }}
 Optimal tunings:
@@ Line 348: / Line 297: @@
 Comma list: 100/99, 133/132, 221/220, 225/224, 245/243, 273/272
-Mapping: {{mapping| 2 0 4 -2 12 15 5 18 | 0 5 1 12 -8 -12 5 -15 }}
+{{Mapping|legend=0| 2 0 4 -2 12 15 5 18 | 0 5 1 12 -8 -12 5 -15 }}
 Optimal tunings:
@@ Line 363: / Line 312: @@
 Comma list: 55/54, 99/98, 176/175
-Mapping: {{mapping| 1 0 2 -1 -1 | 0 5 1 12 14 }}
+{{Mapping|legend=0| 1 0 2 -1 -1 | 0 5 1 12 14 }}
 Optimal tunings:
@@ Line 378: / Line 327: @@
 Comma list: 55/54, 65/64, 91/90, 99/98
-Mapping: {{mapping| 1 0 2 -1 -1 4 | 0 5 1 12 14 -1 }}
+{{Mapping|legend=0| 1 0 2 -1 -1 4 | 0 5 1 12 14 -1 }}
 Optimal tunings:
@@ Line 387: / Line 336: @@
 Badness (Sintel): 1.05
-===== 17-limit =====
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 55/54, 65/64, 85/84, 91/90, 99/98
-Mapping: {{mapping| 1 0 2 -1 -1 4 -1 | 0 5 1 12 14 -1 16 }}
-Optimal tunings:
-* WE: ~2 = 1202.5560{{c}}, ~5/4 = 381.4295{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.7843{{c}}
-{{Optimal ET sequence|legend=0| 19eg, 22, 41efg }}
-Badness (Sintel): 1.03
-===== 19-limit =====
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 55/54, 57/56, 65/64, 76/75, 85/84, 99/98
-Mapping: {{mapping| 1 0 2 -1 -1 4 -1 2 | 0 5 1 12 14 -1 16 7 }}
-Optimal tunings:
-* WE: ~2 = 1203.4043{{c}}, ~5/4 = 381.5989{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.7353{{c}}
-{{Optimal ET sequence|legend=0| 19egh, 22, 41efghh }}
-Badness (Sintel): 1.16
 ==== Intuition ====
@@ Line 423: / Line 342: @@
 Comma list: 55/54, 66/65, 99/98, 105/104
-Mapping: {{mapping| 1 0 2 -1 -1 -2 | 0 5 1 12 14 18 }}
+{{Mapping|legend=0| 1 0 2 -1 -1 -2 | 0 5 1 12 14 18 }}
 Optimal tunings:
@@ Line 432: / Line 351: @@
 Badness (Sintel): 1.08
-===== 17-limit =====
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 55/54, 66/65, 85/84, 99/98, 105/104
-Mapping: {{mapping| 1 0 2 -1 -1 -2 -1 | 0 5 1 12 14 18 16 }}
-Optimal tunings:
-* WE: ~2 = 1201.3593{{c}}, ~5/4 = 381.0356{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.7204{{c}}
-{{Optimal ET sequence|legend=0| 19eg, 22f }}
-Badness (Sintel): 1.03
-===== 19-limit =====
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 55/54, 66/65, 77/76, 85/84, 99/98, 105/104
-Mapping: {{mapping| 1 0 2 -1 -1 -2 -1 -4 | 0 5 1 12 14 18 16 26 }}
-Optimal tunings:
-* WE: ~2 = 1201.5266{{c}}, ~5/4 = 381.0019{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.6275{{c}}
-{{Optimal ET sequence|legend=0| 19egh, 22fh }}
-Badness (Sintel): 1.19
 === Horcrux ===
@@ Line 468: / Line 357: @@
 Comma list: 45/44, 56/55, 245/243
-Mapping: {{mapping| 1 0 2 -1 0 | 0 5 1 12 11 }}
+{{Mapping|legend=0| 1 0 2 -1 0 | 0 5 1 12 11 }}
 Optimal tunings:
@@ Line 483: / Line 372: @@
 Comma list: 45/44, 56/55, 78/77, 245/243
-Mapping: {{mapping| 1 0 2 -1 0 -2 | 0 5 1 12 11 18 }}
+{{Mapping|legend=0| 1 0 2 -1 0 -2 | 0 5 1 12 11 18 }}
 Optimal tunings:
@@ Line 498: / Line 387: @@
 Comma list: 45/44, 56/55, 78/77, 85/84, 245/243
-Mapping: {{mapping| 1 0 2 -1 0 -2 0 | 0 5 1 12 11 18 16 }}
+{{Mapping|legend=0| 1 0 2 -1 0 -2 0 | 0 5 1 12 11 18 16 }}
 Optimal tunings:
@@ Line 513: / Line 402: @@
 Comma list: 35/34, 45/44, 52/51, 56/55, 245/243
-Mapping: {{mapping| 1 0 2 -1 0 -2 0 | 0 5 1 12 11 18 13 }}
+{{Mapping|legend=0| 1 0 2 -1 0 -2 0 | 0 5 1 12 11 18 13 }}
 Optimal tunings:
@@ Line 528: / Line 417: @@
 Comma list: 45/44, 56/55, 65/64, 245/243
-Mapping: {{mapping| 1 0 2 -1 0 4 | 0 5 1 12 11 -1 }}
+{{Mapping|legend=0| 1 0 2 -1 0 4 | 0 5 1 12 11 -1 }}
 Optimal tunings:
@@ Line 543: / Line 432: @@
 Comma list: 225/224, 245/243, 441/440
-Mapping: {{mapping| 1 0 2 -1 -7 | 0 5 1 12 33 }}
+{{Mapping|legend=0| 1 0 2 -1 -7 | 0 5 1 12 33 }}
 Optimal tunings:
@@ Line 558: / Line 447: @@
 Comma list: 105/104, 196/195, 245/243, 275/273
-Mapping: {{mapping| 1 0 2 -1 -7 -2 | 0 5 1 12 33 18 }}
+{{Mapping|legend=0| 1 0 2 -1 -7 -2 | 0 5 1 12 33 18 }}
 Optimal tunings:
@@ Line 573: / Line 462: @@
 Comma list: 105/104, 154/153, 170/169, 196/195, 245/243
-Mapping: {{mapping| 1 0 2 -1 -7 -2 -7 | 0 5 1 12 33 18 35 }}
+{{Mapping|legend=0| 1 0 2 -1 -7 -2 -7 | 0 5 1 12 33 18 35 }}
 Optimal tunings:
@@ Line 582: / Line 471: @@
 Badness (Sintel): 1.06
-==== 19-limit ====
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 105/104, 133/132, 154/153, 170/169, 171/169, 196/195
-Mapping: {{mapping| 1 0 2 -1 -7 -2 -7 -4 | 0 5 1 12 33 18 35 26 }}
-Optimal tunings:
-* WE: ~2 = 1201.2528{{c}}, ~5/4 = 380.5518{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.2052{{c}}
-{{Optimal ET sequence|legend=0| 19egh, 41, 60eh }}
-Badness (Sintel): 1.13
 === Divination ===
@@ Line 603: / Line 477: @@
 Comma list: 121/120, 225/224, 245/243
-Mapping: {{mapping| 2 0 4 -2 5 | 0 5 1 12 3 }}
+{{Mapping|legend=0| 2 0 4 -2 5 | 0 5 1 12 3 }}
 Optimal tunings:
@@ Line 618: / Line 492: @@
 Comma list: 105/104, 121/120, 196/195, 245/243
-Mapping: {{mapping| 2 0 4 -2 5 -4 | 0 5 1 12 3 18 }}
+{{Mapping|legend=0| 2 0 4 -2 5 -4 | 0 5 1 12 3 18 }}
 Optimal tunings:
@@ Line 633: / Line 507: @@
 Comma list: 105/104, 121/120, 154/153, 196/195, 245/243
-Mapping: {{mapping| 2 0 4 -2 5 -4 5 | 0 5 1 12 3 18 5 }}
+{{Mapping|legend=0| 2 0 4 -2 5 -4 5 | 0 5 1 12 3 18 5 }}
 Optimal tunings:
@@ Line 648: / Line 522: @@
 Comma list: 225/224, 243/242, 245/242
-Mapping: {{mapping| 1 -5 1 -13 -13 | 0 10 2 24 25 }}
+{{Mapping|legend=0| 1 -5 1 -13 -13 | 0 10 2 24 25 }}
 Optimal tunings:
@@ Line 663: / Line 537: @@
 Comma list: 105/104, 196/195, 243/242, 245/242
-Mapping: {{mapping| 1 -5 1 -13 -13 -20 | 0 10 2 24 25 36 }}
+{{Mapping|legend=0| 1 -5 1 -13 -13 -20 | 0 10 2 24 25 36 }}
 Optimal tunings:
@@ Line 678: / Line 552: @@
 Comma list: 105/104, 154/153, 196/195, 243/242, 245/242
-Mapping: {{mapping| 1 -5 1 -13 -13 -20 -15 | 0 10 2 24 25 36 29 }}
+{{Mapping|legend=0| 1 -5 1 -13 -13 -20 -15 | 0 10 2 24 25 36 29 }}
 Optimal tunings:
@@ Line 693: / Line 567: @@
 Comma list: 105/104, 154/153, 196/195, 243/242, 245/242
-Mapping: {{mapping| 1 -5 1 -13 -13 -20 -3 | 0 10 2 24 25 36 29 11 }}
+{{Mapping|legend=0| 1 -5 1 -13 -13 -20 -3 | 0 10 2 24 25 36 29 11 }}
 Optimal tunings:
@@ Line 734: / Line 608: @@
 Comma list: 45/44, 126/125, 385/384
-Mapping: {{mapping| 1 0 2 5 0 | 0 5 1 -7 11 }}
+{{Mapping|legend=0| 1 0 2 5 0 | 0 5 1 -7 11 }}
 Optimal tunings:
@@ Line 753: / Line 627: @@
 Comma list: 45/44, 65/64, 78/77, 126/125
-Mapping: {{mapping| 1 0 2 5 0 4 | 0 5 1 -7 11 -1 }}
+{{Mapping|legend=0| 1 0 2 5 0 4 | 0 5 1 -7 11 -1 }}
 Optimal tunings:
@@ Line 768: / Line 642: @@
 Comma list: 33/32, 126/125, 176/175
-Mapping: {{mapping| 1 0 2 5 5 | 0 5 1 -7 -5 }}
+{{Mapping|legend=0| 1 0 2 5 5 | 0 5 1 -7 -5 }}
 Optimal tunings:
@@ Line 783: / Line 657: @@
 Comma list: 33/32, 65/64, 105/104, 126/125
-Mapping: {{mapping| 1 0 2 5 5 4 | 0 5 1 -7 -5 -1 }}
+{{Mapping|legend=0| 1 0 2 5 5 4 | 0 5 1 -7 -5 -1 }}
 Optimal tunings:
@@ Line 793: / Line 667: @@
 Badness (Sintel): 1.19
-== Darkstone ==
+== Brightstone ==
-Darkstone (16 & 19d) is a low-accuacy temperament which tempers out 36/35 and 1875/1792. It makes the major third and the fifth even flatter than those of muggles. In [http://www.tonalsoft.com/enc/m/magic.aspx ''Encyclopedia of Microtonal Music Theory'', Tonalsoft], this temperament is given a name ''witch''.
+Brightstone tempers out 64/63 and may be described as {{nowrap| 22 & 25 }}. 22edo itself is a good tuning, in which case it is identical to magic. Brightstone can be extended to the 11- and 13-limit in a similar way to muggles.
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 36/35, 1875/1792
+[[Comma list]]: 64/63, 3125/3024
-{{Mapping|legend=1| 1 0 2 0 | 0 5 1 9 }}
+{{Mapping|legend=1| 1 0 2 6 | 0 5 1 -10 }}
 [[Optimal tuning]]s:
-* [[WE]]: ~2 = 1201.7458{{c}}, ~5/4 = 377.2996{{c}}
+* [[WE]]: ~2 = 1198.1701{{c}}, ~5/4 = 381.3741{{c}}
-: [[error map]]: {{val| +1.746 -15.457 -5.523 +26.870 }}
+: error map: {{val| -1.830 +4.915 -8.599 +6.454 }}
-* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 376.9630{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 381.9562{{c}}
-: error map: {{val| 0.000 -17.140 -9.351 +23.841 }}
+: error map: {{val| 0.000 +7.826 -4.358 +11.613 }}
-{{Optimal ET sequence|legend=1| 3d, …, 13b, 16 }}
+{{Optimal ET sequence|legend=1| 3, 19d, 22 }}
-[[Badness]] (Sintel): 2.13
+[[Badness]] (Sintel): 2.23
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 36/35, 45/44, 363/343
+Comma list: 55/54, 64/63, 625/616
-Mapping: {{mapping| 1 0 2 0 0 | 0 5 1 9 11 }}
+{{Mapping|legend=0| 1 0 2 6 -1 | 0 5 1 -10 14 }}
 Optimal tunings:
-* WE: ~2 = 1201.7428{{c}}, ~5/4 = 377.3134{{c}}
+* WE: ~2 = 1198.5372{{c}}, ~5/4 = 381.7556{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 376.9735{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 382.1943{{c}}
-{{Optimal ET sequence|legend=0| 3de, 13be, 16 }}
+{{Optimal ET sequence|legend=0| 22, 69b }}
-Badness (Sintel): 1.55
+Badness (Sintel): 1.85
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 27/26, 36/35, 45/44, 363/343
+Comma list: 40/39, 55/54, 64/63, 625/616
-Mapping: {{mapping| 1 0 2 0 0 -1 | 0 5 1 9 11 15 }}
+{{Mapping|legend=0| 1 0 2 6 6 4 | 0 5 1 -10 14 -4 }}
 Optimal tunings:
-* WE: ~2 = 1201.7428{{c}}, ~5/4 = 377.3134{{c}}
+* WE: ~2 = 1197.2300{{c}}, ~5/4 = 381.6164{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 376.4221{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 382.4690{{c}}
+{{Optimal ET sequence|legend=0| 22f, 47bff }}
+Badness (Sintel): 1.99
-{{Optimal ET sequence|legend=0| 3def, 13beff, 16 }}
+== Darkstone ==
+Darkstone (16 & 19d) is a low-accuracy temperament which tempers out 36/35 and 1875/1792. It makes the major third and the fifth even flatter than those of muggles.
-Badness (Sintel): 1.58
+This temperament is known as ''witch'' in [http://www.tonalsoft.com/enc/m/magic.aspx Tonalsoft Encyclopedia].
-== Brightstone ==
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 64/63, 3125/3024
+[[Comma list]]: 36/35, 1875/1792
-{{Mapping|legend=1| 1 0 2 6 | 0 5 1 -10 }}
+{{Mapping|legend=1| 1 0 2 0 | 0 5 1 9 }}
 [[Optimal tuning]]s:
-* [[WE]]: ~2 = 1198.1701{{c}}, ~5/4 = 381.3741{{c}}
+* [[WE]]: ~2 = 1201.7458{{c}}, ~5/4 = 377.2996{{c}}
-: error map: {{val| -1.830 +4.915 -8.599 +6.454 }}
+: [[error map]]: {{val| +1.746 -15.457 -5.523 +26.870 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 381.9562{{c}}
+* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 376.9630{{c}}
-: error map: {{val| 0.000 +7.826 -4.358 +11.613 }}
+: error map: {{val| 0.000 -17.140 -9.351 +23.841 }}
-{{Optimal ET sequence|legend=1| 3, 19d, 22 }}
+{{Optimal ET sequence|legend=1| 3d, …, 13b, 16 }}
-[[Badness]] (Sintel): 2.23
+[[Badness]] (Sintel): 2.13
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 64/63, 100/99, 605/588
+Comma list: 36/35, 45/44, 363/343
-Mapping: {{mapping| 1 0 2 6 6 | 0 5 1 -10 -8 }}
+{{Mapping|legend=0| 1 0 2 0 0 | 0 5 1 9 11 }}
 Optimal tunings:
-* WE: ~2 = 1198.8032{{c}}, ~5/4 = 381.3145{{c}}
+* WE: ~2 = 1201.7428{{c}}, ~5/4 = 377.3134{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 381.7119{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 376.9735{{c}}
-{{Optimal ET sequence|legend=0| 3, 19d, 22 }}
+{{Optimal ET sequence|legend=0| 3de, 13be, 16 }}
-Badness (Sintel): 1.57
+Badness (Sintel): 1.55
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 64/63, 65/63, 100/99, 169/165
+Comma list: 27/26, 36/35, 45/44, 363/343
-Mapping: {{mapping| 1 0 2 6 6 4 | 0 5 1 -10 -8 -1 }}
+{{Mapping|legend=0| 1 0 2 0 0 -1 | 0 5 1 9 11 15 }}
 Optimal tunings:
-* WE: ~2 = 1199.9726{{c}}, ~5/4 = 381.7271{{c}}
+* WE: ~2 = 1201.7428{{c}}, ~5/4 = 377.3134{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 381.7362{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 376.4221{{c}}
+{{Optimal ET sequence|legend=0| 3def, 13beff, 16 }}
+Badness (Sintel): 1.58
-{{Optimal ET sequence|legend=0| 3, 22 }}
+Scales: [[User:BudjarnLambeth/Volcanic glass]]
-Badness (Sintel): 1.64
+Music: [https://www.youtube.com/watch?v=oXy_RXrBVWA ''Rain in the crystal mirror caves''] - [[Budjarn Lambeth]] (2026)
 == Hocum ==
@@ Line 935: / Line 817: @@
 Comma list: 385/384, 441/440, 625/616
-Mapping: {{mapping| 1 -5 1 5 -4 | 0 15 3 -5 17 }}
+{{Mapping|legend=0| 1 -5 1 5 -4 | 0 15 3 -5 17 }}
 Optimal tunings:
@@ Line 950: / Line 832: @@
 Comma list: 105/104, 144/143, 275/273, 625/616
-Mapping: {{mapping| 1 -5 1 5 -4 -2 | 0 15 3 -5 17 13 }}
+{{Mapping|legend=0| 1 -5 1 5 -4 -2 | 0 15 3 -5 17 13 }}
 Optimal tunings:
@@ Line 999: / Line 881: @@
 Comma list: 245/242, 385/384, 625/616
-Mapping: {{mapping| 1 -15 -1 -3 -4 | 0 20 4 7 9 }}
+{{Mapping|legend=0| 1 -15 -1 -3 -4 | 0 20 4 7 9 }}
 Optimal tunings:
@@ Line 1,014: / Line 896: @@
 Comma list: 105/104, 144/143, 245/242, 625/616
-Mapping: {{mapping| 1 5 3 4 5 9 | 0 -20 -4 -7 -9 -31 }}
+{{Mapping|legend=0| 1 -15 -1 -3 -22 | 0 20 4 7 9 31 }}
 Optimal tunings:
@@ Line 1,048: / Line 930: @@
 Comma list: 385/384, 625/616, 2401/2376
-Mapping: {{mapping| 1 -10 0 -6 3 | 0 25 5 19 1 }}
+{{Mapping|legend=0| 1 -10 0 -6 3 | 0 25 5 19 1 }}
 Optimal tunings:
@@ Line 1,063: / Line 945: @@
 Comma list: 196/195, 364/363, 385/384, 625/616
-Mapping: {{mapping| 1 -10 0 -6 3 0 | 0 25 5 19 1 8 }}
+{{Mapping|legend=0| 1 -10 0 -6 3 0 | 0 25 5 19 1 8 }}
 Optimal tunings:
@@ Line 1,092: / Line 974: @@
 [[Badness]] (Sintel): 7.27
-[[Category:Temperament families]]
-[[Category:Pages with mostly numerical content]]
 [[Category:Magic family| ]] <!-- main article -->
 [[Category:Magic| ]] <!-- key article -->
-[[Category:Rank 2]]
+[[Category:Temperament families]]
+[[Category:Catalogs of rank-2 temperaments]]
 [[Category:Listen]]

Magic family: Difference between revisions