@@ Line 5: / Line 5: @@
 === Archy ===
 See [[Archytas clan #Archy]].
-==== Supra ====
-See [[Archytas clan #Supra]].
-===== Supraphon =====
-See [[Archytas clan #Supraphon]].
 ==== Suhajira ====
@@ Line 22: / Line 16: @@
 Comma list: 64/63, 364/363, 1078/1053
-Mapping: {{mapping| 1 0 6 21 34 | 0 1 -2 -11 -19 }}
+{{Mapping|legend=0| 1 0 6 21 34 | 0 1 -2 -11 -19 }}
 Optimal tunings:
@@ Line 37: / Line 31: @@
 Comma list: 64/63, 209/208, 343/342, 364/363
-Mapping: {{mapping| 1 0 6 21 34 17 | 0 1 -2 -11 -19 -8 }}
+{{Mapping|legend=0| 1 0 6 21 34 17 | 0 1 -2 -11 -19 -8 }}
 Optimal tunings:
@@ Line 55: / Line 49: @@
 === Slendroschismic ===
 See [[5th-octave temperaments #Slendroschismic]].
-==== Pentadecoid ====
-See [[15th-octave temperaments #Pentadecoid]].
 === Navy ===
@@ Line 66: / Line 57: @@
 [[Comma list]]: 282429536481/281974669312
-{{Mapping|legend=2| 1 1 0| 0 5 24 }}
+{{Mapping|legend=3| 1 1 0| 0 5 24 }}
 : mapping generators: ~2, ~243/224
@@ Line 84: / Line 75: @@
 Comma list: 1331/1323, 19712/19683
-Subgroup-val mapping: {{mapping| 1 1 0 1 | 0 5 24 21 }}
+{{Mapping|legend=2| 1 1 0 1 | 0 5 24 21 }}
 Optimal tunings:
@@ Line 99: / Line 90: @@
 Comma list: 352/351, 729/728, 1331/1323
-Subgroup-val mapping: {{mapping| 1 1 0 1 3 | 0 5 24 21 6 }}
+{{Mapping|legend=2| 1 1 0 1 3 | 0 5 24 21 6 }}
 Optimal tunings:
@@ Line 114: / Line 105: @@
 [[Comma list]]: 177147/175616
-{{Mapping|legend=2| 1 0 -3 | 0 3 11 }}
+{{Mapping|legend=3| 1 0 -3 | 0 3 11 }}
-{{Mapping|legend=3| 1 0 0 -3 | 0 3 0 11 }}
+{{Mapping|legend=5| 1 0 0 -3 | 0 3 0 11 }}
 : mapping generators: ~2, ~81/56
@@ Line 133: / Line 124: @@
 === Hemif ===
-Hemif is the no-5 [[restriction]] of [[hemififths]], and the add-7 [[extension]] of [[namo]].
+Hemif tempers out the [[parahemif comma]], equating a [[Pythagorean apotome]] with a stack of two septimal third-tones of [[28/27]], and splits the fifth in two. In this temperament, the interval class of [[7/1|7]] is found at +13 steps, as a semi-augmented sixth (C–A{{demisharp2}}). It also equates the large septimal diesis of [[49/48]] with the [[Pythagorean comma]]. This means the fifth should be tuned sharp and the septimal third-tone should be flattened to a somewhat large quartertone which can be used as the undecimal quartertone of [[33/32]], leading to a natural 11-limit extension where [[243/242]] and [[896/891]] are tempered out.
+Hemif is the common [[restriction]] of [[hemififths]] (41 & 58) and [[salsa]] (24 & 41), and the add-7 [[extension]] of [[namo]]. A [[weak extension]] of it is [[sruti]] (24 & 34d).
 [[Subgroup]]: 2.3.7
@@ Line 139: / Line 132: @@
 [[Comma list]]: 1605632/1594323
-{{Mapping|legend=2| 1 1 -1 | 0 2 13 }}
+{{Mapping|legend=3| 1 1 -1 | 0 2 13 }}
-{{Mapping|legend=3| 1 1 0 -1 | 0 2 0 13 }}
+{{Mapping|legend=5| 1 1 0 -1 | 0 2 0 13 }}
 : mapping generators: ~2, ~2187/1792
@@ Line 159: / Line 152: @@
 Comma list: 243/242, 896/891
-Subgroup-val mapping: {{mapping| 1 1 -1 2 | 0 2 13 5 }}
+{{Mapping|legend=2| 1 1 -1 2 | 0 2 13 5 }}
-Gencom mapping: {{mapping| 1 1 0 -1 2 | 0 2 0 13 5 }}
+{{Mapping|legend=4| 1 1 0 -1 2 | 0 2 0 13 5 }}
 Optimal tunings:
@@ Line 178: / Line 171: @@
 Sval mapping: {{mapping| 1 1 -1 2 4 | 0 2 13 5 -1 }}
-Gencom mapping: {{mapping| 1 1 0 -1 2 4 | 0 2 0 13 5 -1 }}
+{{Mapping|legend=4| 1 1 0 -1 2 4 | 0 2 0 13 5 -1 }}
 Optimal tunings:
@@ Line 197: / Line 190: @@
 Comma list: 243/242, 896/891, 1083/1078
-Subgroup-val mapping: {{mapping| 1 1 -1 2 0 | 0 4 26 10 29 }}
+{{Mapping|legend=2| 1 1 -1 2 0 | 0 4 26 10 29 }}
 : mapping generators: ~2, ~21/19
@@ Line 217: / Line 210: @@
 [[Comma list]]: 34451725707/34359738368
-{{Mapping|legend=2| 1 1 5 | 0 4 -15 }}
+{{Mapping|legend=3| 1 1 5 | 0 4 -15 }}
 : mapping generators: ~2, ~567/512
@@ Line 235: / Line 228: @@
 Comma list: 243/242, 65536/65219
-Subgroup-val mapping: {{mapping| 1 1 5 2 | 0 4 -15 10 }}
+{{Mapping|legend=2| 1 1 5 2 | 0 4 -15 10 }}
 Optimal tunings:
@@ Line 250: / Line 243: @@
 Comma list: 243/242, 513/512, 1083/1078
-Subgroup-val mapping: {{mapping| 1 1 5 2 6 | 0 4 -15 10 -12 }}
+{{Mapping|legend=2| 1 1 5 2 6 | 0 4 -15 10 -12 }}
 Optimal tunings:
@@ Line 267: / Line 260: @@
 [[Comma list]]: 537824/531441
-{{Mapping|legend=2| 1 0 -1 | 0 5 12 }}
+{{Mapping|legend=3| 1 0 -1 | 0 5 12 }}
 : mapping generators: ~2, ~243/196
@@ Line 285: / Line 278: @@
 Comma list: 896/891, 26411/26244
-Subgroup-val mapping: {{mapping| 1 0 -1 6 | 0 5 12 -8 }}
+{{Mapping|legend=2| 1 0 -1 6 | 0 5 12 -8 }}
 Optimal tunings:
@@ Line 300: / Line 293: @@
 Comma list: 144/143, 343/338, 729/728
-Subgroup-val mapping: {{mapping| 1 0 -1 6 -2 | 0 5 12 -8 18 }}
+{{Mapping|legend=2| 1 0 -1 6 -2 | 0 5 12 -8 18 }}
 Optimal tunings:
@@ Line 315: / Line 308: @@
 Comma list: 144/143, 232/231, 343/338, 729/728
-Subgroup-val mapping: {{mapping| 1 0 -1 6 -2 2 | 0 5 12 -8 18 9 }}
+{{Mapping|legend=2| 1 0 -1 6 -2 2 | 0 5 12 -8 18 9 }}
 Optimal tunings:
@@ Line 330: / Line 323: @@
 Comma list: 352/351, 364/363, 26411/26244
-Subgroup-val mapping: {{mapping| 1 0 -1 6 11 | 0 5 12 -8 -23 }}
+{{Mapping|legend=2| 1 0 -1 6 11 | 0 5 12 -8 -23 }}
 Optimal tunings:
@@ Line 345: / Line 338: @@
 Comma list: 169/168, 896/891, 26411/26244
-Subgroup-val mapping: {{mapping| 1 0 -1 6 1 | 0 10 24 -16 17 }}
+{{Mapping|legend=2| 1 0 -1 6 1 | 0 10 24 -16 17 }}
 : mapping generators: ~2, ~143/128
@@ Line 361: / Line 354: @@
 Comma list: 784/783, 5887/5832
-Subgroup-val mapping: {{mapping| 1 0 -1 2 | 0 5 12 9 }}
+{{Mapping|legend=2| 1 0 -1 2 | 0 5 12 9 }}
 Optimal tunings:
@@ Line 380: / Line 373: @@
 [[Comma list]]: 19683/19208
-{{Mapping|legend=2| 1 -1 -3 | 0 4 9 }}
+{{Mapping|legend=3| 1 -1 -3 | 0 4 9 }}
-{{Mapping|legend=3| 1 -1 0 -3 | 0 4 0 9 }}
+{{Mapping|legend=5| 1 -1 0 -3 | 0 4 0 9 }}
 : mapping generators: ~2, ~14/9
@@ Line 400: / Line 393: @@
 Comma list: 99/98, 243/242
-Subgroup-val mapping: {{mapping| 1 -1 -3 -3 | 0 4 9 10 }}
+{{Mapping|legend=2| 1 -1 -3 -3 | 0 4 9 10 }}
-Gencom mapping: {{mapping| 1 -1 0 -3 -3 | 0 4 0 9 10 }}
+{{Mapping|legend=4| 1 -1 0 -3 -3 | 0 4 0 9 10 }}
 Optimal tunings:
@@ Line 417: / Line 410: @@
 Comma list: 78/77, 99/98, 243/242
-Subgroup-val mapping: {{mapping| 1 -1 -3 -3 -6 | 0 4 9 10 15 }}
+{{Mapping|legend=2| 1 -1 -3 -3 -6 | 0 4 9 10 15 }}
-Gencom mapping: {{mapping| 1 -1 0 -3 -3 -6 | 0 4 0 9 10 15}}
+{{Mapping|legend=4| 1 -1 0 -3 -3 -6 | 0 4 0 9 10 15}}
 Optimal tunings:
@@ Line 434: / Line 427: @@
 Comma list: 99/98, 144/143, 243/242
-Subgroup-val mapping: {{mapping| 1 -1 -3 -3 5 | 0 4 9 10 -2 }}
+{{Mapping|legend=2| 1 -1 -3 -3 5 | 0 4 9 10 -2 }}
-Gencom mapping: {{mapping| 1 -1 0 -3 -3 5 | 0 4 0 9 10 -2 }}
+{{Mapping|legend=4| 1 -1 0 -3 -3 5 | 0 4 0 9 10 -2 }}
 Optimal tunings:
@@ Line 453: / Line 446: @@
 Comma list: 99/98, 243/242, 363/361
-Subgroup-val mapping: {{mapping| 2 2 3 4 5 | 0 4 9 10 12 }}
+{{Mapping|legend=2| 2 2 3 4 5 | 0 4 9 10 12 }}
 : mapping generators: ~209/147, ~21/19
@@ Line 471: / Line 464: @@
 [[Comma list]]: [[59049/57344]]
-{{Mapping|legend=2| 1 0 -13 | 0 1 10 }}
+{{Mapping|legend=3| 1 0 -13 | 0 1 10 }}
-{{Mapping|legend=3| 1 0 0 -13 | 0 1 0 10 }}
+{{Mapping|legend=5| 1 0 0 -13 | 0 1 0 10 }}
 : mapping generators: ~2, ~3
@@ Line 487: / Line 480: @@
 === Bleu ===
-Bleu can be described as the {{nowrap| 8d & 9 }} temperament in the no-5 13-limit, and is the common [[restriction]] of [[progression]] and [[jerome]].
+Bleu can be described as the {{nowrap| 8d & 9 }} temperament in the no-5 13-limit, and is the common [[restriction]] of [[progression]], [[secund]] and [[jerome]].
 [[Subgroup]]: 2.3.7
@@ Line 493: / Line 486: @@
 [[Comma list]]: 17496/16807
-{{Mapping|legend=2| 1 1 2 | 0 5 7 }}
+{{Mapping|legend=3| 1 1 2 | 0 5 7 }}
-{{Mapping|legend=3| 1 1 0 2 | 0 5 0 7 }}
+{{Mapping|legend=5| 1 1 0 2 | 0 5 0 7 }}
 : mapping generators: ~2, ~54/49
@@ Line 513: / Line 506: @@
 Comma list: 99/98, 864/847
-Subgroup-val mapping: {{mapping| 1 1 2 3 | 0 5 7 4 }}
+{{Mapping|legend=2| 1 1 2 3 | 0 5 7 4 }}
-Gencom mapping: {{mapping| 1 1 0 2 3 | 0 5 0 7 4 }}
+{{Mapping|legend=4| 1 1 0 2 3 | 0 5 0 7 4 }}
 Optimal tunings:
@@ Line 530: / Line 523: @@
 Comma list: 78/77, 99/98, 144/143
-Subgroup-val mapping: {{mapping| 1 1 2 3 3 | 0 5 7 4 6 }}
+{{Mapping|legend=2| 1 1 2 3 3 | 0 5 7 4 6 }}
-Gencom mapping: {{mapping| 1 1 0 2 3 3 | 0 5 0 7 4 6 }}
+{{Mapping|legend=4| 1 1 0 2 3 3 | 0 5 0 7 4 6 }}
 Optimal tunings:
@@ Line 554: / Line 547: @@
 [[Comma list]]: 5764801/5668704
-{{Mapping|legend=2| 1 1 2 | 0 8 11 }}
+{{Mapping|legend=3| 1 1 2 | 0 8 11 }}
 : mapping generators: ~2, ~343/342
@@ Line 572: / Line 565: @@
 Comma list: 243/242, 2401/2376
-Subgroup-val mapping: {{mapping| 1 1 2 2 | 0 8 11 20 }}
+{{Mapping|legend=2| 1 1 2 2 | 0 8 11 20 }}
 Optimal tunings:
@@ Line 587: / Line 580: @@
 Comma list: 133/132, 243/242, 343/342
-Subgroup-val mapping: {{mapping| 1 1 2 2 3 | 0 8 11 20 17 }}
+{{Mapping|legend=2| 1 1 2 2 3 | 0 8 11 20 17 }}
 Optimal tunings:
@@ Line 598: / Line 591: @@
 === Purpleheart ===
-{{See also| Whitewood }}
+{{Main| Whitewood }}
 [[Subgroup]]: 2.3.7
@@ Line 604: / Line 597: @@
 [[Comma list]]: 2187/2048
-{{Mapping|legend=2| 7 11 0 | 0 0 1 }}
+{{Mapping|legend=3| 7 11 0 | 0 0 1 }}
 : mapping generators: ~9/8, ~7
@@ Line 624: / Line 617: @@
 [[Comma list]]: {{monzo| 83 -1 -29 }}
-{{Mapping|legend=2| 1 -4 3 | 0 29 -1 }}
+{{Mapping|legend=3| 1 -4 3 | 0 29 -1 }}
 : mapping generators: ~2, ~8/7
@@ Line 642: / Line 635: @@
 Comma list: 43923/43904, 5767168/5764801
-Subgroup-val mapping: {{mapping| 1 -4 3 5 | 0 29 -1 -8 }}
+{{Mapping|legend=2| 1 -4 3 5 | 0 29 -1 -8 }}
 Optimal tunings:
@@ Line 665: / Line 658: @@
 [[Comma list]]: 14680064/14348907
-{{Mapping|legend=2| 1 0 -21 | 0 1 15 }}
+{{Mapping|legend=3| 1 0 -21 | 0 1 15 }}
-{{Mapping|legend=3| 1 0 0 -21 | 0 1 0 15 }}
+{{Mapping|legend=5| 1 0 0 -21 | 0 1 0 15 }}
 : mapping generators: ~2, ~3
@@ Line 685: / Line 678: @@
 Comma list: 896/891, 1331/1323
-Subgroup-val mapping: {{mapping| 1 0 -21 -14 | 0 1 15 11 }}
+{{Mapping|legend=2| 1 0 -21 -14 | 0 1 15 11 }}
-Gencom mapping: {{mapping| 1 0 0 -21 -14 | 0 1 0 15 11 }}
+{{Mapping|legend=4| 1 0 0 -21 -14 | 0 1 0 15 11 }}
 Optimal tunings:
@@ Line 702: / Line 695: @@
 Comma list: 169/168, 352/351, 364/363
-Subgroup-val mapping: {{mapping| 1 0 -21 -14 -9 | 0 1 15 11 8 }}
+{{Mapping|legend=2| 1 0 -21 -14 -9 | 0 1 15 11 8 }}
-Gencom mapping: {{mapping| 1 0 0 -21 -14 -9 | 0 1 0 15 11 8 }}
+{{Mapping|legend=4| 1 0 0 -21 -14 -9 | 0 1 0 15 11 8 }}
 Optimal tunings:
@@ Line 719: / Line 712: @@
 Comma list: 169/168, 208/207, 352/351, 364/363
-Subgroup-val mapping: {{mapping| 1 0 -21 -14 -9 -5 | 0 1 15 11 8 6 }}
+{{Mapping|legend=2| 1 0 -21 -14 -9 -5 | 0 1 15 11 8 6 }}
-Gencom mapping: {{mapping| 1 0 0 -21 -14 -9 0 0 -5 | 0 1 0 15 11 8 0 0 6 }}
+{{Mapping|legend=4| 1 0 0 -21 -14 -9 0 0 -5 | 0 1 0 15 11 8 0 0 6 }}
 Optimal tunings:
@@ Line 736: / Line 729: @@
 Comma list: 169/168, 208/207, 232/231, 352/351, 364/363
-Subgroup-val mapping: {{mapping| 1 0 -21 -14 -9 -5 -38 | 0 1 15 11 8 6 27 }}
+{{Mapping|legend=2| 1 0 -21 -14 -9 -5 -38 | 0 1 15 11 8 6 27 }}
-Gencom mapping: {{mapping| 1 0 0 -21 -14 -9 -5 0 0 -38 | 0 1 0 15 11 8 0 0 6 27 }}
+{{Mapping|legend=4| 1 0 0 -21 -14 -9 -5 0 0 -38 | 0 1 0 15 11 8 0 0 6 27 }}
 Optimal tunings:
@@ Line 765: / Line 758: @@
 [[Comma list]]: 17294403/16777216
-{{Mapping|legend=2| 1 0 3 | 0 8 -1 }}
+{{Mapping|legend=3| 1 0 3 | 0 8 -1 }}
 : mapping generators: ~2, ~8/7
@@ Line 779: / Line 772: @@
 === Hectosaros leap week ===
-This temperament may be described as the {{nowrap| 320 & 1803 }} temperament, in the 2.3.7.13.17.19 on the basis of the fact that 1803 tropical years make up almost exactly 100 saros cycles.
+This temperament may be described as the {{nowrap| 320 & 1803 }} temperament, in the 2.3.7.13.17.19. It is named after the fact that 1803 tropical years make up almost exactly 100 saros cycles.
 [[Subgroup]]: 2.3.7
@@ Line 785: / Line 778: @@
 [[Comma list]]: {{monzo| -50 -746 439 }}
-{{Mapping|legend=2| 1 -126 -214 | 0 439 746 }}
+{{Mapping|legend=3| 1 -126 -214 | 0 439 746 }}
 : mapping generators: ~2, ~{{monzo| -16 -243 143 }}
@@ Line 803: / Line 796: @@
 Comma list: {{monzo| -42 -2 -5 16 }}, {{monzo| 10 -46 29 -5 }}
-Subgroup-val mapping: {{mapping| 1 -126 -214 -80 | 0 439 746 288 }}
+{{Mapping|legend=2| 1 -126 -214 -80 | 0 439 746 288 }}
 Optimal tunings:
@@ Line 818: / Line 811: @@
 Comma list: 39337984/39328497, {{monzo| 0 -14 7 4 -3 }}, {{monzo| -18 -24 14 -1 5 }}
-Subgroup-val mapping: {{mapping| 1 -126 -214 -80 -18 | 0 439 746 288 76 }}
+{{Mapping|legend=2| 1 -126 -214 -80 -18 | 0 439 746 288 76 }}
 Optimal tunings:
@@ Line 833: / Line 826: @@
 Comma list: 10081799/10077696, 10754912/10744731, 39337984/39328497, 480024727/480020256
-Subgroup-val mapping: {{mapping| 1 -126 -214 -80 -18 -171 | 0 439 746 288 76 603 }}
+{{Mapping|legend=2| 1 -126 -214 -80 -18 -171 | 0 439 746 288 76 603 }}
 Optimal tunings:
@@ Line 852: / Line 845: @@
 [[Comma list]]: 243/242, 1083/1078
-{{Mapping|legend=2| 1 1 0 2 1 | 0 4 0 10 3 | 0 0 1 0 1 }}
+{{Mapping|legend=3| 1 1 0 2 1 | 0 4 0 10 3 | 0 0 1 0 1 }}
 : mapping generators: ~2, ~21/19, ~7
@@ Line 866: / Line 859: @@
 === Neutral ===
 See [[Rastmic clan #Neutral]].
-==== Namo ====
-See [[Rastmic clan #Namo]].
 === Io ===
 Io is a very low-complexity temperament which tempers out the undecimal quartertone [[33/32]]. This equates very different intervals (for example, the generator itself represents both [[3/2]] and [[16/11]]), and as such some consider it to be an [[exotemperament]]. It has an extremely wide generator range, but the most accurate tunings are generally inside the range of [[flattone]] temperament.
-The name ''io'' was coined by [[User:CompactStar|CompactStar]] in 2024 based on the [[Kite's color notation|color name]] ''ilo'', prior to which it could only be termed as "undecimal temperament" with 33/32 being known as the undecimal comma.
+The name ''io'' was coined by {{u|CompactStar}} in 2024 based on the [[Kite's color notation|color name]] ''ilo'', prior to which it could only be termed as "undecimal temperament" with 33/32 being known as the undecimal comma.
 [[Subgroup]]: 2.3.11
@@ Line 879: / Line 869: @@
 [[Comma list]]: 33/32
-{{Mapping|legend=2| 1 0 5 | 0 1 -1 }}
+{{Mapping|legend=3| 1 0 5 | 0 1 -1 }}
 : mapping generators: ~2, ~3
@@ Line 891: / Line 881: @@
 [[Badness]] (Sintel): 0.185
+=== Alphaxenean ===
+Alphaxenean tempers out the [[Alpharabian comma]], and equates a stack of four undecimal quartertones with the [[9/8|Pythagorean whole tone]]. It has a [[semi-octave]] period, and the generator can be taken to be the aforementioned undecimal quartertone or that plus a period, which represents ~[[16/11]]. The interval class of a perfect fifth is found by two generator steps and a period.
+[[Subgroup]]: 2.3.11
+[[Comma list]]: 131769/131072
+{{Mapping|legend=3| 2 1 8 | 0 2 -1 }}
+: mapping generators: ~363/256, ~16/11
+[[Optimal tuning]]s:
+* [[WE]]: ~363/256 = 600.1590{{c}}, ~16/11 = 650.8508{{c}}
+: [[error map]]: {{val| +0.318 -0.094 -0.897 }}
+* [[CWE]]: ~363/256 = 600.0000{{c}}, ~16/11 = 650.7321{{c}}
+: error map: {{val| 0.000 -0.491 -2.050 }}
+{{Optimal ET sequence|legend=1| 22, 24, 94, 118, 142, 450e, 592e, 1326beeee }}
+[[Badness]] (Sintel): 0.395
+=== Octatonic ===
+[[12/11]] is very close to one step of 8edo, and hence this temperament tempers out the [[undecimal octatonic comma]], the difference between a stack of eight 12/11's and the octave.
+[[Subgroup]]: 2.3.11
+[[Comma list]]: 214990848/214358881
+{{Mapping|legend=3| 8 0 15 | 0 1 1 }}
+: mapping generators: ~12/11, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~12/11 = 149.9917{{c}}, ~3/2 = 701.9324{{c}}
+: [[error map]]: {{val| -0.066 -0.089 +0.424 }}
+* [[CWE]]: ~12/11 = 150.0000{{c}}, ~3/2 = 701.9147{{c}}
+: error map: {{val| 0.000 -0.040 +0.597 }}
+{{Optimal ET sequence|legend=1| 8, 16, 24, 104, 128, 152, 176, 200, 1024e, 1224e, 1424e, 1624e }}
+[[Badness]] (Sintel): 0.515
+=== Betaxenean ===
+Betaxenean tempers out the [[Betarabian comma]]. It splits a [[3/1|perfect twelfth]] into two halves of [[512/297]]. [[Baragon]] is a full 11-limit extension that combines this temperament with [[godzilla]], albeit not as accurate as normal betaxenean.
+[[Subgroup]]: 2.3.11
+[[Comma list]]: 264627/262144
+{{Mapping|legend=3| 1 0 9 | 0 2 -7 }}
+: mapping generators: ~2, ~512/297
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.5931{{c}}, ~512/297 = 950.6872{{c}}
+: [[error map]]: {{val| +0.593 -0.581 -0.791 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~512/297 = 950.1972{{c}}
+: error map: {{val| 0.000 -1.561 -2.699 }}
+{{Optimal ET sequence|legend=1| 5, 14e, 19, 24, 125, 149, 173, 197e, 221e, 466bee, 687beee }}
+[[Badness]] (Sintel): 0.709
 === Infraug ===
@@ Line 897: / Line 947: @@
 [[Comma list]]: 729/704
-{{Mapping|legend=2| 1 0 -6 | 0 1 6 }}
+{{Mapping|legend=3| 1 0 -6 | 0 1 6 }}
 : mapping generators: ~2, ~3
@@ Line 910: / Line 960: @@
 [[Badness]] (Sintel): 0.734
-==== 2.3.11.13 ====
+==== 2.3.11.13 subgroup ====
 Subgroup: 2.3.11.13
 Comma list: 144/143, 729/704
-Subgrouo-val mapping: {{mapping| 1 0 -6 10 | 0 1 6 -4 }}
+{{Mapping|legend=2| 1 0 -6 10 | 0 1 6 -4 }}
 Optimal tunings:
@@ Line 930: / Line 980: @@
 Comma list: 363/361, 729/704
-Subgrouo-val mapping: {{mapping| 1 0 -6 -6 | 0 2 12 13 }}
+{{Mapping|legend=2| 1 0 -6 -6 | 0 2 12 13 }}
 : mapping generators: ~2, ~19/11
@@ Line 937: / Line 987: @@
 * CWE: ~2 = 1200.0000{{c}}, ~19/11 = 945.7779{{c}}
-{{Optimal ET sequence|legend=1| 14, 19, 33 }}
+{{Optimal ET sequence|legend=0| 14, 19, 33 }}
 Badness (Sintel): 1.59
@@ Line 946: / Line 996: @@
 [[Comma list]]: 4096/3993
-{{Mapping|legend=2| 1 0 4 | 0 3 -1 }}
+{{Mapping|legend=3| 1 0 4 | 0 3 -1 }}
 : mapping generators: ~2, ~16/11
@@ Line 968: / Line 1,018: @@
 Comma list: 512/507, 1352/1331
-Subgroup-val mapping: {{mapping| 1 -3 5 6 | 0 6 -2 -3 }}
+{{Mapping|legend=2| 1 -3 5 6 | 0 6 -2 -3 }}
 : mapping generators: ~2, ~22/13
@@ Line 986: / Line 1,036: @@
 [[Comma list]]: 10554638336/10460353203
-{{Mapping|legend=2| 1 1 0 | 0 5 21 }}
+{{Mapping|legend=3| 1 1 0 | 0 5 21 }}
 : mapping generators: ~2, ~88/81
@@ Line 1,004: / Line 1,054: @@
 Comma list: 352/351, 531674/531441
-Subgroup-val mapping: {{mapping| 1 1 0 3 | 0 5 21 6 }}
+{{Mapping|legend=2| 1 1 0 3 | 0 5 21 6 }}
 Optimal tunings:
@@ Line 1,013: / Line 1,063: @@
 Badness (Sintel): 0.415
+=== Profanity ===
+Profanity identifies [[11/9]] with 2\7.
+[[Subgroup]]: 2.3.11
+[[Comma list]]: 19487171/19131876
+{{Mapping|legend=3| 7 0 2 | 0 1 2 }}
+: mapping generators: ~1458/1331, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~1458/1331 = 171.4369{{c}}, ~3/2 = 702.9304{{c}}
+: [[error map]]: {{val| +0.058 +1.033 -2.467 }}
+* [[CWE]]: ~1458/1331 = 171.4286{{c}}, ~3/2 = 702.9442{{c}}
+: error map: {{val| 0.000 -0.989 -2.572 }}
+{{Optimal ET sequence|legend=1| 7, … 49, 56, 63, 70 }}
+[[Badness]] (Sintel): 3.03
 == Temperaments with a 2.3.13 gene ==
@@ Line 1,020: / Line 1,090: @@
 [[Comma list]]: 2197/2187
-{{Mapping|legend=2| 1 0 0 | 0 3 7 }}
+{{Mapping|legend=3| 1 0 0 | 0 3 7 }}
 : mapping generators: ~2, ~13/9
@@ Line 1,040: / Line 1,110: @@
 [[Comma list]]: 27/26
-{{Mapping|legend=2| 1 0 -1 | 0 1 3 }}
+{{Mapping|legend=3| 1 0 -1 | 0 1 3 }}
 : mapping generators: ~2, ~3
@@ Line 1,052: / Line 1,122: @@
 [[Badness]] (Sintel): 0.200
+=== Tridecapyth ===
+Tridecapyth sets a stack of ten [[9/8]]'s equal to [[13/4]]. It shows a way of giving a mapping of prime 13 to any temperament with an extremely accurate tuning of its fifth (like the [[53edo]] tuning of [[schismic]]). Interestingly, the mapping is ''so'' accurate that more optimized tunings of schismic that use a flatter fifth are not accurate enough to preserve the mapping – for 118edo we get the 118f [[val]] that takes the second-closest, flat mapping of prime 13, and the same is true for [[171edo]] where we get the 171f val. However, [[41edo]] uses this mapping, and so does [[94edo]], the val sum of 41 and 53. Thus it is of interest to flatter tunings of [[garibaldi]]/[[cassandra]] with fifths tending close to pure. If we add this mapping to 5-limit schismic instead we get [[tridecaschismic]].
+[[Subgroup]]: 2.3.13
+{{mapping|legend=2| 1 0 -28 | 0 1 20 }}
+: mapping generators: ~2, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9778{{c}}, ~3/2 = 702.0170{{c}}
+: [[error map]]: {{val| -0.022 +0.040 -0.011 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0283{{c}}
+: error map: {{val| 0.000 +0.070 -0.019 }}
+{{Optimal ET sequence|legend=1| 12, 29f, 41, 53, 94, 147, 494, 641, 788, 2217, 3005 }}
+[[Badness]] (Sintel): 0.211
 === Superflat ===
@@ Line 1,062: / Line 1,150: @@
 [[Comma list]]: 1053/1024
-{{Mapping|legend=2| 1 0 10 | 0 1 -4 }}
+{{Mapping|legend=3| 1 0 10 | 0 1 -4 }}
 : mapping generators: ~2, ~3
@@ Line 1,069: / Line 1,157: @@
 : [[error map]]: {{val| +3.129 -3.177 -4.349 }}
 * [[CWE]]: ~2 = 1200.0000{{c}} ~3/2 = 693.6081{{c}}
-: error map: {{val| 0.000 -8.347 +14.960 }}
+: error map: {{val| 0.000 -8.347 -14.960 }}
 {{Optimal ET sequence|legend=1| 5f, 7, 12, 19, 45f, 64f, 147bfff }}
@@ Line 1,082: / Line 1,170: @@
 [[Comma list]]: 816293376/815730721
-{{Mapping|legend=2| 1 -5 -7 | 0 8 13 }}
+{{Mapping|legend=3| 1 -5 -7 | 0 8 13 }}
 : mapping generators: ~2, ~3888/2197
@@ Line 1,095: / Line 1,183: @@
 Badness (Sintel): 0.135
-==== 2.3.13.23 ====
+==== 2.3.13.23 subgroup ====
 Subgroup: 2.3.13.23
 Comma list: 3888/3887, 12168/12167
-Subgroup-val mapping: {{mapping| 1 -5 -7 -7 | 0 8 13 14 }}
+{{Mapping|legend=2| 1 -5 -7 -7 | 0 8 13 14 }}
 Optimal tunings:
@@ Line 1,113: / Line 1,201: @@
 * [[Shoal17]]
-Music:
+; Music
 * [https://www.youtube.com/watch?v=bwGjN56iMM0 ''Moody Improvisation in the Shoal Temperament''] by [[Budjarn Lambeth]] (2025)
 === Glacier ===
-This 2.3.13-subgroup gene is not nearly as good as shoal, but it can extend extremely well to other no-5 subgroups. It is the common [[restriction]] of [[#Bleu|bleu]] and [[#Navy|navy]]. It is very well represented in [[26edo]], where a pure 13/12 can serve as the generator, but [[94edo]] provides a much better tuning.
+This 2.3.13-subgroup gene is not nearly as good as shoal, but it can extend extremely well to other no-5 subgroups. It is the common [[restriction]] of [[#Bleu|bleu]] and [[#Navy|navy]]. It is very well represented in [[26edo]], where a nearly pure 13/12 can serve as the generator, but [[94edo]] provides a much better tuning.
 [[Subgroup]]: 2.3.13
@@ Line 1,123: / Line 1,211: @@
 [[Comma list]]: 373248/371293
-{{Mapping|legend=2| 1 1 3 | 0 5 6 }}
+{{Mapping|legend=3| 1 1 3 | 0 5 6 }}
 : mapping generators: ~2, ~13/12
@@ Line 1,138: / Line 1,226: @@
 == Temperaments with a higher-limit gene ==
 === Semitonic ===
+Note that [[34edo]] and [[46edo]] also support this temperament but do not appear in the optimal ET sequence due to their sharp fifths, but they are on opposite sides of the just-17's tuning such that 34 + 46 = [[80edo]] is effectively a pure [[consistent circle]] of 80 [[17/16]]'s; all of these are good tunings for the related temperament [[srutal]] in 2.3.5.17 (sometimes called [[srutal archagall]] to distinguish it from diaschismic, which prefers tunings with a more just fifth), but the accuracy of primes 7, 11 and 13 varies depending on the tuning; especially, 34edo's 7 is extremely sharp and its 11 not much better.
 [[Subgroup]]: 2.3.17
 [[Comma list]]: [[289/288]]
-{{Mapping|legend=2| 2 0 5 | 0 1 1 }}
+{{Mapping|legend=3| 2 0 5 | 0 1 1 }}
+: mapping generators: ~17/12, ~3
-: sval mapping generators: ~17/12, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~17/12 = 600.1471{{c}}, ~3/2 = 701.9563{{c}} (~17/16 = 101.8091{{c}})
+: [[error map]]: {{val| +0.294 +0.295 -1.969 }}
+* [[CWE]]: ~17/12 = 600.0000{{c}}, ~3/2 = 702.0260{{c}} (~17/16 = 102.0260{{c}})
+: error map: {{val| 0.000 +0.071 -2.929 }}
-: [[gencom]]: [17/12 3; 289/288]
+{{Optimal ET sequence|legend=1| 10, 12, 58, 70, 82, 94, 106, 118, 224g }}
-[[Optimal tuning]] ([[CTE]]): ~17/12 = 1\2, ~3/2 = 702.3472 (~17/16 = 102.3472)
+[[Badness]] (Sintel): 0.0454
-{{Optimal ET sequence|legend=1| 12, 58, 70, 82, 94, 106, 118, 224g }}
+=== Boethian ===
+Boethian is a [[5L 2s|diatonic-based]] temperament that makes [[513/512]] vanish, so that the major third (C–E) is ~[[24/19]] and the minor third (C–E♭) is ~[[19/16]]. As such, it functions as a 2.3.19-subgroup analogue of [[meantone]], though the small size of the comma puts it at [[schismic]] level of accuracy. In particular, the equal temperaments in the tuning spectrum up to 1/2-comma (flattened) boethian temperament (very close to [[12edo]]) are included in the schismic tuning spectrum in the 5-limit, so boethian intersects with schismic in the prime-5 infill extension thereof, called [[nestoria]], which also tempers out [[361/360]], the difference between 19/18 and 20/19 or between 19/15 and 24/19.
-[[Tp tuning #T2 tuning|RMS error]]: 0.2247 cents
+[[Subgroup]]: 2.3.19
-=== Gigapyth ===
+[[Comma list]]: 513/512
-[[Subgroup]]: 2.3.85
-[[Comma list]]: 2.3.85 {{val|-40 1 6 }}
+{{Mapping|legend=3| 1 0 9 | 0 1 -3 }}
+: mapping generators: ~2, ~3
-{{mapping|legend=2| 1 4 6 | 0 -6 1 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.2498{{c}}, ~3/2 = 701.4958{{c}}
-: mapping generators: ~2, ~85/64
+: [[error map]]: {{val| +0.250 -0.209 -0.501 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.3445{{c}}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~85/64 = 483.034
+: error map: {{val| 0.000 -0.610 -1.547 }}
-[[Support]]ing [[ET]]s:	5, 47, 52, 57, 62, 67, 72, 77*, 82*, 87*, 92*, 139*, 149*, 159**
-<nowiki>*</nowiki>Wart for 85
-==== 2.3.7.85 subgroup ====
-[[Subgroup]]: 2.3.7.85
-[[Comma list]]: 1029/1024, 7225/7203
-{{mapping|legend=2| 1 4 2 6 | 0 -6 2 1}}
-: mapping generators: ~2, ~85/64
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~85/64 = 483.031
-[[Support]]ing [[ET]]s:	5, 47, 52, 57, 62, 67, 72, 77*, 82*, 87*, 92*, 139*, 149*, 159**
-<nowiki>*</nowiki>Wart for 85
-=== Dog ===
-The dog temperament is based by [[2L 5s]] or [[7L 2s]] scale that makes [[81/76]] vanish, so [[19/16]] is a major third. It can be viewed as a 2.3.19 subgroup analogue of [[Pelogic family|mavila]].
-Subgroup: 2.3.19
-[[Comma list]]: 81/76
-[[Gencom]]: [2 4/3; 81/76]
-[[Mapping|Sval mapping]]: [{{val|1 2 6}}, {{val|0 -1 -4}}]
-[[Tp tuning|POL2 generator]]: ~4/3 = 521.403
-{{Optimal ET sequence|legend=1| 5h, 7, 16, 23 }}
+{{Optimal ET sequence|legend=1| 5, 7, 12, 41, 53, 65, 77, 219, 296, 1557bhhhh, 1853bhhhh }}
-[[Tp tuning #T2 tuning|RMS error]]: 4.943 cents
+[[Badness]] (Sintel): 0.0294
-=== Boethian ===
+=== Deviaug ===
-Boethian is a [[5L 2s|diatonic-based]] temperament that makes [[513/512]] vanish, so that the major third (C–E) is ~[[24/19]] and the minor third (C–E♭) is ~[[19/16]]. As such, it functions as a 2.3.19-subgroup analogue of [[meantone]], though the small size of the comma puts it at [[schismic]] level of accuracy. In particular, the equal temperaments in the tuning spectrum up to 1/2-comma (flattened) boethian temperament (very close to [[12edo]]) are included in the schismic tuning spectrum in the 5-limit, so boethian intersects with schismic in the prime-5 infill extension thereof, called [[nestoria]], which also tempers out [[361/360]], the difference between 19/18 and 20/19 or between 19/15 and 24/19.
+Deviaug tempers out [[6912/6859]] in the 2.3.19 subgroup, setting [[24/19]] to 1/3 of an octave.
 [[Subgroup]]: 2.3.19
-[[Comma list]]: [[513/512]]
+[[Comma list]]: 6912/6859
-{{Mapping|legend=2| 1 0 9 | 0 1 -3 }}
+{{Mapping|legend=3| 3 0 8 | 0 1 1 }}
-: mapping generators: ~2, ~3
+: mapping generators: ~24/19, ~3
-[[Optimal tuning]] (CTE): ~2 = 1200.0000{{c}}, ~3/2 = 701.3288{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~24/19 = 399.8571{{c}}, ~3/2 = 701.9795{{c}}
+: [[error map]]: {{val| -0.429 -0.404 +2.894 }}
+* [[CWE]]: ~24/19 = 400.0000{{c}}, ~3/2 = 701.8810{{c}}
+: error map: {{val| 0.000 -0.074 +4.368 }}
-{{Optimal ET sequence|legend=1| 5, 7, 12, 41, 53, 65, 77, 219, 296 }}
+{{Optimal ET sequence|legend=1| 9, 12, 75, 87, 99, 111, 123h, 135h }}
-[[Badness]] (Smith): 0.000374
+[[Badness]] (Sintel): 0.237
 === Lipsett ===
-Lipsett temperament is a pleasantly melodic little temperament with a highly useable 5-tone and 9-tone mos. It is audibly similar to [[semaphore]] temperament, so it could be thought of as semaphore but for the 23rd harmonic instead of the 7th. It is named for Arthur Lipsett, the director off the Canadian short film ’21-87’. Leia’s prison cell in Star Wars is numbered ‘2187’, as a nod to the influence the film had on George Lucas.
+Lipsett is a pleasantly melodic little temperament with a highly usable 5-tone and 9-tone mos. It is audibly similar to [[semaphore]] temperament, so it could be thought of as semaphore but for the 23rd harmonic instead of the 7th. It is named for Arthur Lipsett, the director of the Canadian short film ''21-87''. Leia's prison cell in ''Star Wars'' is numbered 2187, as a nod to the influence the film had on George Lucas.
 [[Subgroup]]: 2.3.23
-[[Comma list]]: [[2187/2116]]
+[[Comma list]]: 2187/2116
-{{Mapping|legend=2| 1 0 -1 | 0 2 7}}
+{{Mapping|legend=3| 1 0 -1 | 0 2 7 }}
+: mapping generators: ~2, ~46/27
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~46/27 = 948.526
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.5339{{c}}, ~46/27 = 948.5629{{c}}
+: [[error map]]: {{val| +0.534 -4.829 +11.132 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~46/27 = 948.3272{{c}}
+: error map: {{val| 0.000 -5.301 +10.016 }}
 {{Optimal ET sequence|legend=1| 5, 14, 19, 43, 62i, 81i }}
-[[Badness]] (Smith): 8.998 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.801
 === Porpoise ===
@@ Line 1,237: / Line 1,310: @@
 [[Comma list]]: 24576/24389
-[[Mapping]]: [{{val|1 2 5}}, {{val|0 3 -1}}]
+{{Mapping|legend=3| 1 2 5 | 0 -3 -1 }}
+: mapping generators: ~2, ~32/29
-[[CTE tuning|CTE generator]]: ~32/29 = 166.067
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.5519{{c}}, ~32/29 = 165.7453{{c}}
+: [[error map]]: {{val| -0.448 -0.087 +2.437 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~32/29 = 165.9004{{c}}
+: error map: {{val| 0.000 +0.344 +4.522 }}
 {{Optimal ET sequence|legend=1| 7, 22, 29, 94, 123, 152j, 275jj, 427jjj }}
-=== Sematology ===
+[[Badness]] (Sintel): 0.317
-This temperament tempers out 4107/4096 and thus equates 2 [[37/32]]'s with [[4/3]].
-[[Subgroup]]: 2.3.37
+=== Jackpot ===
+Named by {{u|CompactStar}} in 2024, jackpot tempers out the [[7-29-comma]] in 2.3.29, setting 32/29 to one step of [[7edo]] with an independent generator for the [[3/1|3rd harmonic]]. The name refers to the [[Temperament merging|EDO join]] of 7 & 77.
-[[Comma list]]: 4107/4096
+[[Subgroup]]: 2.3.29
-[[Gencom]]: [2 37/32; 4107/4096]
+[[Comma list]]: 17249876309/17179869184
-[[Mapping]]: [{{val|1 1 5}}, {{val|0 -2 1}}]
+{{Mapping|legend=3| 7 0 34 | 0 1 0 }}
+: mapping generators: ~32/29, ~3
-[[POTE generator]]: ~[[37/32]] = 249.075
+[[Optimal tuning]]s:
+* [[WE]]: ~32/29 = 171.4434{{c}}, ~3/2 = 701.8515{{c}}
+: [[error map]]: {{val| +0.103 -0.000 -0.503 }}
+* [[CWE]]: ~32/29 = 171.4286{{c}}, ~3/2 = 701.8456{{c}}
+: error map: {{val| 0.000 -0.109 -1.006 }}
-{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 53, 77, 130 }}
+{{Optimal ET sequence|legend=1| 7, 42, 49, 56, 63, 70, 77, 147, 224 }}
-==== 2.3.7.37 subgroup ====
+[[Badness]] (Sintel): 1.02
-[[Subgroup]]: 2.3.7.37
-[[Comma list]]: 4107/4096, 259/256
+=== Sematology ===
+This temperament tempers out [[4107/4096]] and thus equates a stack of two [[37/32]]'s with [[4/3]].
-[[Gencom]]: [2 37/32; 4107/4096 259/256]
+[[Subgroup]]: 2.3.37
-[[Mapping]]: [{{val|1 1 1 5}}, {{val|0 -2 -1 1}}]
+[[Comma list]]: 4107/4096
-[[POTE generator]]: ~[[37/32]] = 247.782
+{{Mapping|legend=3| 1 0 6 | 0 2 -1 }}
+: mapping generators: ~2, ~64/37
-{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 53d }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.2184{{c}}, ~64/37 = 950.9546{{c}}
-==== 2.3.5.37 subgroup ====
+: [[error map]]: {{val| +0.218 -0.046 -0.988 }}
-It is difficult to extend sematology to include 5, due the 5th harmonic being quite high-complexity.
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~64/37 = 950.8250{{c}}
+: error map: {{val| 0.000 -0.305 -2.169 }}
-[[Subgroup]]: 2.3.5.37
-[[Comma list]]: 4107/4096, 17592186044416/17562397269605
-[[Gencom]]: [2 37/32; 4107/4096 17592186044416/17562397269605]
-[[Mapping]]: [{{val|1 1 4 5}}, {{val|0 -2 -8 1}}]
-[[POTE generator]]: ~[[37/32]] = 251.393
-{{Optimal ET sequence|legend=1| 5, 14c, 19, 43, 62 }}
+{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 53, 77, 130, 443l, 573ll, 703ll, 1536blllll }}
-===== 2.3.5.7.37 subgroup =====
+[[Badness]] (Sintel): 0.0690
-[[Subgroup]]: 2.3.5.7.37
-[[Comma list]]: 4107/4096, 17592186044416/17562397269605, 259/256
-[[Gencom]]: [2 37/32; 4107/4096 17592186044416/17562397269605 259/256]
-[[Mapping]]: [{{val|1 1 4 1 5}}, {{val|0 -2 -8 -1 1}}]
-[[POTE generator]]: ~[[37/32]] = 251.204
-{{Optimal ET sequence|legend=1| 5, 14c, 19 }}
 === Reversed mavila ===
@@ Line 1,304: / Line 1,368: @@
 [[Comma list]]: 81/74
-[[Gencom]]: [2 4/3; 81/74]
+{{Mapping|legend=3| 1 0 -1 | 0 1 4 }}
+: mapping generators: ~2, ~3
-[[Mapping]]: [{{val|1 1 0}}, {{val|0 -1 12}}]
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1201.9908{{c}}, ~3/2 = 676.4865{{c}}
+: [[error map]]: {{val| +1.991 -23.478 +60.575 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 676.7603{{c}}
+: error map: {{val| 0.000 -25.195 +55.697 }}
-[[POTE generator]]: ~4/3 = 521.397
+{{Optimal ET sequence|legend=1| 2, 5l, 7l, 9, 16l }}
-{{Optimal ET sequence|legend=1| 5l, 7l, 9, 16l }}
+[[Badness]] (Sintel): 0.623
 === Reversed meantone ===
 {{Main| Reversed meantone }}
-Subgroup: 2.3.41
+[[Subgroup]]: 2.3.41
 [[Comma list]]: 82/81
-[[Gencom]]: [2 4/3; 82/81]
+{{Mapping|legend=3| 1 0 -1 | 0 1 4 }}
+: mapping generators: ~2, ~3
-[[Mapping|Sval mapping]]: [{{val|1 2 7}}, {{val|0 -1 -4}}]
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.6907{{c}}, ~3/2 = 705.3096{{c}}
-[[Tp tuning|POL2 generator]]: ~4/3 = 494.509
+: [[error map]]: {{val| -0.309 +3.045 -8.752 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 705.2699{{c}}
-{{Optimal ET sequence|legend=1| 5, 12, 17 }}
+: error map: {{val| 0.000 +3.315 -7.983 }}
-==== 2.3.7.41 subgroup ====
-Subgroup: 2.3.7.41
-[[Comma list]]: 64/63, 82/81
-[[Gencom]]: [2 4/3; 64/63 82/81]
-[[Mapping|Sval mapping]]: [{{val| 1 2 2 7 }}, {{val| 0 -1 2 -4 }}]
-[[POTE generator]]: ~4/3 = 490.0323
-[[TOP tuning|TOP generator]]s: ~2 = 1197.2342, ~4/3 = 488.9029
-{{Optimal ET sequence|legend=1| 5, 12, 17, 22, 49 }}
-==== 2.3.7.11.41 subgroup ====
-Subgroup: 2.3.7.11.41
-[[Comma list]]: 64/63, 82/81, 99/98
-[[Gencom]]: [2 4/3; 64/63 82/81 99/98]
-[[Mapping|Sval mapping]]: [{{val| 1 2 2 1 7 }}, {{val| 0 -1 2 6 -4 }}]
-[[POTE generator]]: ~4/3 = 492.1787
-[[TOP tuning|TOP generator]]s: ~2 = 1197.9683, ~4/3 = 491.3454
+{{Optimal ET sequence|legend=1| 5, 12, 17, 97m, 114m, 131m }}
-{{Optimal ET sequence|legend=1| 5, 12, 17, 22, 39d }}
+[[Badness]] (Sintel): 0.0841
-[[Category:Temperament collections]]
+[[Category:Catalogs of subgroup temperaments]]
-[[Category:Subgroup temperaments]]
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Rank 2]]

No-fives subgroup temperaments: Difference between revisions