@@ Line 15: / Line 15: @@
 * Jubilic ([[50/49]]) → [[Jubilismic clan #Jubilic|Jubilismic clan]]
 * Didacus ([[3136/3125]]) → [[Hemimean clan #Didacus|Hemimean clan]]
-* Mercy ([[823543/819200]]) → [[Quince clan #Mercy|Quince clan]]
-* Llywelyn a.k.a. shoe ([[4194304/4117715]]) → [[Llywelynsmic clan #Llywelyn a.k.a. shoe|Llywelynsmic clan]]
 * Sidewalk ([[823543/800000]]) → [[2023/2000 #Sidewalk]]
-=== Rainy ===
-In rainy, three generators make an [[8/7]]; five generators make a [[5/4]]. It is the no-3's [[restriction]] of [[tertiaseptal]] (and [[valentine]]), notable theoretically as it equates ([[2/1]])/([[5/4]])<sup>3</sup> (128/125, the lesser diesis) with ([[2/1]])/([[8/7]])<sup>5</sup> (the 2.7-subgroup [[cloudy comma]], which is similar to the 2.5-subgroup lesser diesis in that tempering it out tunes the 8/7 about 8.8{{cent}} sharp, while tempering out 128/125 similarly sharpens the 5/4 by about 13.7{{cent}}). By tempering out their difference, stacked 5's and stacked 7's become easier to navigate, using the general-purpose diesis to simplify clusters.
-A highly notable tuning of rainy not shown here is [[311edo]], which is 140 + 171 so tuned between them.
-[[Subgroup]]: 2.5.7
-[[Comma list]]: [[2100875/2097152]]
-{{Mapping|legend=3| 1 2 3 | 0 5 -3 }}
-{{Mapping|legend=5| 1 0 2 3 | 0 0 5 -3 }}
-: mapping generators: ~2, ~256/245
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1200.0939{{c}}, ~256/245 = 77.2107{{c}}
-: [[error map]]: {{val| +0.094 -0.072 -0.176 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~256/245 = 77.2093{{c}}
-: error map: {{val| 0.000 -0.267 -0.454 }}
-{{Optimal ET sequence|legend=1| 15, 16, 31, 109, 140, 171, 373, 544, 1259, 1803d }}
-[[Badness]] (Sintel): 0.156
 === Augment ===
@@ Line 72: / Line 46: @@
 Comma list: 56/55, 128/125
-Subgroup-val mapping: {{mapping| 3 7 0 2 | 0 0 1 1 }}
+{{Mapping|legend=2| 3 7 0 2 | 0 0 1 1 }}
-Gencom mapping: {{mapping| 3 0 7 0 2 | 0 0 0 1 1 }}
+{{Mapping|legend=4| 3 0 7 0 2 | 0 0 0 1 1 }}
 Optimal tunings:
@@ Line 83: / Line 57: @@
 Badness (Sintel): 0.196
+=== Mabilic ===
+{{Main| Mabilic and trismegistus }}
+{{See also| Chromatic pairs #Mabilic }}
+Mabilic is the no-3 [[restriction]] of [[mavila family #Armodue|armodue]] (7 & 16), [[magic family #Trismegistus|trismegistus]] (16 & 25), and [[mabila family #Semabila|semabila]] (25 & 34). It is the 7 & 9 temperament in the [[2.5.7 subgroup]], and tempers out [[1071875/1048576]], the mabilisma. [[Weak extension]]s of mabilic include [[archytas clan #Sixix|sixix]] (7 & 25), [[vishnu family #Vishnean|vishnean]] (16 & 34), [[marvel temperaments #Septimin|septimin]] (9 & 41) and [[tetracot family #Monkey|monkey]] (7 & 34).
+[[Subgroup]]: 2.5.7
+[[Comma list]]: 1071875/1048576
+{{Mapping|legend=3| 1 1 5 | 0 3 -5 }}
+{{Mapping|legend=5| 1 0 1 5 | 0 0 3 -5 }}
+: mapping generators: ~2, ~175/128
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1201.2543{{c}}, ~175/128 = 527.7872{{c}}
+: [[error map]]: {{val| +1.254 -1.698 -1.491 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~175/128 = 527.2041{{c}}
+: error map: {{val| 0.000 -4.701 -4.846 }}
+{{Optimal ET sequence|legend=1| 7, 9, 16, 25, 41, 66, 305ccdd, 371ccddd }}
+[[Badness]] (Sintel): 1.70
+=== Ostara ===
+Ostara is a temperament that is derived from 93 & 524 solar calendar leap rule scale, interpreted in general no-3's 19-limit. It is a weak extension of the unnamed 2.5.7-subgroup 28 & 31 temperament, which tempers out 8589934592/8544921875.
+Subgroup: 2.5.7.11
+Comma list: 8589934592/8544921875, 30691800524/30517578125
+{{Mapping|legend=2| 1 1 20 -49 | 0 3 -39 119 }}
+: mapping generators: ~2, ~5120/3773
+Optimal tunings:
+* WE: ~2 = 1199.9115{{c}}, ~5120/3773 = 528.9650{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~5120/3773 = 529.0037{{c}}
+{{Optimal ET sequence|legend=0| 93, 245e, 338, 955c, 1386c }}
+Badness (Sintel): 11.7
+==== 2.5.7.11.13 subgroup ====
+Subgroup: 2.5.7.11.13
+Comma list: 1001/1000, 34420736/34328125, 5670699008/5661858125
+{{Mapping|legend=2| 1 1 20 -49 35 | 0 3 -39 119 -71 }}
+Optimal tunings:
+* WE: ~2 = 1199.9194{{c}}, ~1664/1225 = 528.9681{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~1664/1225 = 529.0036{{c}}
+{{Optimal ET sequence|legend=0| 93, 245e, 338, 431, 1386c }}
+Badness (Sintel): 3.42
+==== 2.5.7.11.13.17 subgroup ====
+Subgroup: 2.5.7.11.13.17
+Comma list: 1001/1000, 32768/32725, 147968/147875, 537824/537251
+{{Mapping|legend=2| 1 1 20 -49 35 42 | 0 3 -39 119 -71 -86 }}
+Optimal tunings:
+* WE: ~2 = 1199.9054{{c}}, ~1664/1225 = 528.9628{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~1664/1225 = 529.0046{{c}}
+{{Optimal ET sequence|legend=0| 93, 338, 431, 955c, 1386cg }}
+Badness (Sintel): 1.99
+==== 2.5.7.11.13.17.19 subgroup ====
+Subgroup: 2.5.7.11.13.17.19
+Comma list: 1001/1000, 2128/2125, 3328/3325, 16807/16796, 147968/147875
+{{Mapping|legend=2| 1 1 20 -49 35 42 21 | 0 3 -39 119 -71 -86 -38 }}
+Optimal tunings:
+* WE: ~2 = 1199.9081{{c}}, ~19/14 = 528.9639{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~19/14 = 529.0045{{c}}
+{{Optimal ET sequence|legend=0| 93, 338, 431, 955c, 1386cg }}
+Badness (Sintel): 1.29
 === Frostburn ===
+{{Redirect|Frostburn|the software developer|Lumi Pakkanen}}
 Frostburn is the common [[restriction]] of [[magic family #Quadrimage|quadrimage]] and [[subgroup temperaments #Baldy|baldy]].
@@ Line 109: / Line 173: @@
 Comma list: 245/242, 625/616
-Subgroup-val mapping: {{mapping| 1 3 4 5 | 0 -4 -7 -9 }}
+{{Mapping|legend=2| 1 3 4 5 | 0 -4 -7 -9 }}
 : mapping generators: ~2, ~28/25
@@ Line 120: / Line 184: @@
 Badness (Sintel): 0.463
-=== Mabilic ===
+=== Rainy ===
-{{Main| Mabilic and trismegistus }}
+In rainy, three generators make an [[8/7]]; five generators make a [[5/4]]. It is the no-3's [[restriction]] of [[tertiaseptal]] (and [[valentine]]), notable theoretically as it equates ([[2/1]])/([[5/4]])<sup>3</sup> (128/125, the lesser diesis) with ([[2/1]])/([[8/7]])<sup>5</sup> (the 2.7-subgroup [[cloudy comma]], which is similar to the 2.5-subgroup lesser diesis in that tempering it out tunes the 8/7 about 8.8{{cent}} sharp, while tempering out 128/125 similarly sharpens the 5/4 by about 13.7{{cent}}). By tempering out their difference, stacked 5's and stacked 7's become easier to navigate, using the general-purpose diesis to simplify clusters.
-{{See also| Chromatic pairs #Mabilic }}
+A highly notable tuning of rainy not shown here is [[311edo]], which is 140 + 171 so tuned between them.
+[[Subgroup]]: 2.5.7
+[[Comma list]]: [[2100875/2097152]]
+{{Mapping|legend=3| 1 2 3 | 0 5 -3 }}
+{{Mapping|legend=5| 1 0 2 3 | 0 0 5 -3 }}
+: mapping generators: ~2, ~256/245
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0939{{c}}, ~256/245 = 77.2107{{c}}
+: [[error map]]: {{val| +0.094 -0.072 -0.176 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~256/245 = 77.2093{{c}}
+: error map: {{val| 0.000 -0.267 -0.454 }}
+{{Optimal ET sequence|legend=1| 15, 16, 31, 109, 140, 171, 373, 544, 1259, 1803d }}
+[[Badness]] (Sintel): 0.156
+=== Llywelyn a.k.a. shoe ===
+Llywelyn a.k.a. shoe is the common [[restriction]] of [[gamelismic clan #Gorgo|gorgo]] (16 & 21), [[breedsmic temperaments #Gorgik|gorgik]] (21 & 37), and [[gariboh clan #Semaja|semaja]] (16 & 37). It can be described as 16 & 21, and tempers out the [[llywelynsma]]. Its generator is a flattened [[~]][[8/7]] whole tone, seven of which give the interval class of [[5/1|5]]. Its [[ploidacot]] is alpha-heptaseph. [[Weak extension]]s to the full 7-limit include [[marvel temperaments #Misneb|misneb]] (21 & 32), which splits 8/7 into two for [[15/14]]~[[16/15]] each, [[archytas clan #Ultrapyth|ultrapyth]] (32 & 37), which splits [[16/7]] into two for a [[3/2|perfect fifth]], and [[buzzardsmic clan #Septimal buzzard|buzzard]] (53 & 58), which splits 16/7 into three, each for [[21/16]].
+; Scales
+* [[Shoe5]], [[Shoe6]], [[Shoe11]], [[Shoe16]]
+[[Subgroup]]: 2.5.7
+[[Comma list]]: 4194304/4117715
+{{Mapping|legend=3| 1 1 3 | 0 7 -1 }}
+{{Mapping|legend=5| 1 0 1 3 | 0 0 7 -1 }}
+: mapping generators: ~2, ~8/7
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.1974{{c}}, ~8/7 = 226.7586{{c}}
+: [[error map]]: {{val| -0.803 +0.194 +2.008 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 226.8388{{c}}
+: error map: {{val| 0.000 +1.558 +4.335 }}
+{{Optimal ET sequence|legend=1| 5, 11c, 16, 21, 37, 164d }}
+[[Badness]] (Sintel): 2.06
+==== 2.5.7.11 subgroup ====
+Subgroup: 2.5.7.11
+Comma list: 176/175, 1310720/1294139
+{{Mapping|legend=2| 1 1 3 1 | 0 7 -1 13 }}
+{{Mapping|legend=4| 1 0 1 3 1 | 0 0 7 -1 13 }}
+Optimal tunings:
+* WE: ~2 = 1199.1784{{c}}, ~8/7 = 226.9582{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 227.0438{{c}}
+{{Optimal ET sequence|legend=0| 16, 21, 37, 206cd, 243cd, …, 354ccdd }}
+Badness (Sintel): 0.651
+==== 2.5.7.11.13 subgroup ====
+Subgroup: 2.5.7.11.13
+Comma list: 176/175, 640/637, 847/845
+{{Mapping|legend=2| 1 1 3 1 2 | 0 7 -1 13 9 }}
+{{Mapping|legend=4| 1 0 1 3 1 2 | 0 0 7 -1 13 9 }}
+Optimal tunings:
+* WE: ~2 = 1199.1643{{c}}, ~8/7 = 226.9495{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 227.0315{{c}}
+{{Optimal ET sequence|legend=0| 16, 21, 37, 206cdf, 243cdf, …, 354ccddff }}
+Badness (Sintel): 0.319
+==== 2.5.7.11.13.17 subgroup ====
+Subgroup: 2.5.7.11.13.17
+Comma list: 176/175, 221/220, 640/637, 847/845
+{{Mapping|legend=2| 1 1 3 1 2 2 | 0 7 -1 13 9 11 }}
+{{Mapping|legend=4| 1 0 1 3 1 2 2 | 0 0 7 -1 13 9 11 }}
+Optimal tunings:
+* WE: ~2 = 1199.3162{{c}}, ~8/7 = 227.1125{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 227.1774{{c}}
+{{Optimal ET sequence|legend=0| 16, 21, 37, 95 }}
+Badness (Sintel): 0.458
-Mabilic is the no-3 [[restriction]] of [[mavila family #Armodue|armodue]], [[mabila family #Semabila|semabila]], and [[magic family #Trismegistus|trismegistus]]. It is the 7 & 9 temperament in the [[2.5.7 subgroup]], and tempers out [[1071875/1048576]], the mabilisma.
+=== Mercy ===
+Named by {{u|KingHyperio}} in 2021, mercy is the common restriction of [[gamelismic clan #Miracle|miracle]] and [[porwell temperaments #Countermiracle|countermiracle]]. It tempers out the [[quince comma]]. In this temperament, two generators make [[~]][[8/7]], five make ~[[7/5]], and seven make ~[[8/5]]. The [[ploidacot]] for this temperament is omega-heptaseph. [[Weak extension]]s of this temperament include [[starling temperaments #Cassablanca|cassablanca]], [[octagar temperaments #Slendi|slendi]], [[ragismic microtemperaments #Quincy|quincy]], [[septischismic clan #Cotoneum|cotoneum]], and [[varunismic temperaments #Octowerck|octowerck]].
 [[Subgroup]]: 2.5.7
-[[Comma list]]: 1071875/1048576
+[[Comma list]]: 823543/819200
+{{Mapping|legend=3| 1 3 3 | 0 -7 -2 }}
+{{Mapping|legend=5| 1 0 3 3 | 0 0 -7 -2 }}
+: mapping generators: ~2, ~343/320
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.2169{{c}}, ~343/320 = 116.3116{{c}}
+: [[error map]]: {{val| +0.217 +0.156 -0.798 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~343/320 = 116.2576{{c}}
+: error map: {{val| 0.000 -0.117 -1.341 }}
+{{Optimal ET sequence|legend=1| 10, 21, 31, 134, 165, 196, 227, 485d, 712d, 1197dd }}
+[[Badness]] (Sintel): 0.428
+==== 2.5.7.13 subgroup ====
+Presented here is a low-accuracy extension, which may be thought of as a way to conceptualize the 2.5.7.13.17.19 subgroup of [[31edo]].
+Subgroup: 2.5.7.13
+Comma list: 343/338, 640/637
+{{Mapping|legend=2| 1 3 3 4 | 0 -7 -2 -3 }}
+{{Mapping|legend=4| 1 0 3 3 0 4 | 0 0 -7 -2 0 -3 }}
+Optimal tunings:
+* WE: ~2 = 1199.2166{{c}}, ~14/13 = 116.0181{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 116.2099{{c}}
+{{Optimal ET sequence|legend=0| 10, 21, 31 }}
+Badness (Sintel): 0.546
+==== 2.5.7.13.17 subgroup ====
+Subgroup: 2.5.7.13.17
+Comma list: 170/169, 224/221, 343/338
+{{Mapping|legend=2| 1 3 3 4 4 | 0 -7 -2 -3 1 }}
+{{Mapping|legend=4| 1 0 3 3 0 4 4 | 0 0 -7 -2 0 -3 1 }}
+Optimal tunings:
+* WE: ~2 = 1198.5476{{c}}, ~14/13 = 115.6294{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 115.9132{{c}}
+{{Optimal ET sequence|legend=0| 10, 21, 31, 83fg }}
+Badness (Sintel): 0.451
+==== 2.5.7.13.17.19 subgroup ====
+Subgroup: 2.5.7.13.17.19
+Comma list: 170/169, 224/221, 343/338, 476/475
-{{Mapping|legend=3| 1 1 5 | 0 3 -5 }}
+{{Mapping|legend=2| 1 3 3 4 4 3 | 0 -7 -2 -3 1 13 }}
-{{Mapping|legend=5| 1 0 1 5 | 0 0 3 -5 }}
+{{Mapping|legend=4| 1 0 3 3 0 4 4 3 | 0 0 -7 -2 0 -3 1 13 }}
-: mapping generators: ~2, ~175/128
-[[Optimal tuning]]s:
+Optimal tunings:
-* [[WE]]: ~2 = 1201.2543{{c}}, ~175/128 = 527.7872{{c}}
+* WE: ~2 = 1198.4839{{c}}, ~14/13 = 115.5700{{c}}
-: [[error map]]: {{val| +1.254 -1.698 -1.491 }}
+* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 115.7299{{c}}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~175/128 = 527.2041{{c}}
-: error map: {{val| 0.000 -4.701 -4.846 }}
-{{Optimal ET sequence|legend=1| 7, 9, 16, 25, 41, 66, 305ccdd, 371ccddd }}
+{{Optimal ET sequence|legend=0| 10h, 21, 31, 52f, 83fg }}
-[[Badness]] (Sintel): 1.70
+Badness (Sintel): 0.759
 === Huntington ===
@@ Line 174: / Line 388: @@
 Comma list: 640/637, 10985/10976
-Subgroup-val mapping: {{mapping| 1 -4 0 3 | 0 9 4 1 }}
+{{Mapping|legend=2| 1 -4 0 3 | 0 9 4 1 }}
-Gencom mapping: {{mapping| 1 0 -4 0 0 3 | 0 0 9 4 0 1 }}
+{{Mapping|legend=4| 1 0 -4 0 0 3 | 0 0 9 4 0 1 }}
 : mapping generators: ~2, ~13/8
@@ Line 196: / Line 410: @@
 Comma list: 170/169, 640/637, 5525/5488
-Subgroup-val mapping: {{mapping| 1 -4 0 3 9 | 0 9 4 1 -7 }}
+{{Mapping|legend=2| 1 -4 0 3 9 | 0 9 4 1 -7 }}
-Gencom mapping: {{mapping| 1 0 -4 0 0 3 9 | 0 0 9 4 0 1 -7 }}
+{{Mapping|legend=4| 1 0 -4 0 0 3 9 | 0 0 9 4 0 1 -7 }}
 Optimal tunings:
@@ Line 207: / Line 421: @@
 Badness (Sintel): 0.504
-=== Ostara ===
-Ostara is a temperament that is derived from 93 & 524 solar calendar leap rule scale, interpreted in general no-3's 19-limit. It is a weak extension of the unnamed 2.5.7-subgroup 28 & 31 temperament, which tempers out 8589934592/8544921875.
-Subgroup: 2.5.7.11
-Comma list: 8589934592/8544921875, 30691800524/30517578125
-Subgroup-val mapping: {{mapping| 1 1 20 -49 | 0 3 -39 119 }}
-: mapping generators: ~2, ~5120/3773
-Optimal tunings:
-* WE: ~2 = 1199.9115{{c}}, ~5120/3773 = 528.9650{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~5120/3773 = 529.0037{{c}}
-{{Optimal ET sequence|legend=0| 93, 245e, 338, 955c, 1386c }}
-Badness (Sintel): 11.7
-==== 2.5.7.11.13 subgroup ====
-Subgroup: 2.5.7.11.13
-Comma list: 1001/1000, 34420736/34328125, 5670699008/5661858125
-Subgroup-val mapping: {{mapping| 1 1 20 -49 35 | 0 3 -39 119 -71 }}
-Optimal tunings:
-* WE: ~2 = 1199.9194{{c}}, ~1664/1225 = 528.9681{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~1664/1225 = 529.0036{{c}}
-{{Optimal ET sequence|legend=0| 93, 245e, 338, 431, 1386c }}
-Badness (Sintel): 3.42
-==== 2.5.7.11.13.17 subgroup ====
-Subgroup: 2.5.7.11.13.17
-Comma list: 1001/1000, 32768/32725, 147968/147875, 537824/537251
-Subgroup-val mapping: {{mapping| 1 1 20 -49 35 42 | 0 3 -39 119 -71 -86 }}
-Optimal tunings:
-* WE: ~2 = 1199.9054{{c}}, ~1664/1225 = 528.9628{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~1664/1225 = 529.0046{{c}}
-{{Optimal ET sequence|legend=0| 93, 338, 431, 955c, 1386cg }}
-Badness (Sintel): 1.99
-==== 2.5.7.11.13.17.19 subgroup ====
-Subgroup: 2.5.7.11.13.17.19
-Comma list: 1001/1000, 2128/2125, 3328/3325, 16807/16796, 147968/147875
-Subgroup-val mapping: {{mapping| 1 1 20 -49 35 42 21 | 0 3 -39 119 -71 -86 -38 }}
-Optimal tunings:
-* WE: ~2 = 1199.9081{{c}}, ~19/14 = 528.9639{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~19/14 = 529.0045{{c}}
-{{Optimal ET sequence|legend=0| 93, 338, 431, 955c, 1386cg }}
-Badness (Sintel): 1.29
 === Bastille ===
@@ Line 321: / Line 472: @@
 Comma list: 847/845, 1001/1000
-Subgroup-val mapping: {{mapping| 1 0 -2 3 2 | 0 1 1 1 1 | 0 0 4 -3 -1 }}
+{{Mapping|legend=2| 1 0 -2 3 2 | 0 1 1 1 1 | 0 0 4 -3 -1 }}
 Optimal tunings:
@@ Line 336: / Line 487: @@
 Comma list: 170/169, 221/220, 847/845
-Subgroup-val mapping: {{mapping| 1 0 -2 3 2 3 | 0 1 1 1 1 1 | 0 0 4 -3 -1 -2 }}
+{{Mapping|legend=2| 1 0 -2 3 2 3 | 0 1 1 1 1 1 | 0 0 4 -3 -1 -2 }}
 Optimal tunings:
@@ Line 349: / Line 500: @@
 Temperaments discussed elsewhere include:
 * Jacobin superfamily ([[6656/6655]]) → [[The Jacobins]]
+=== Sephiroth ===
+{{See also| Chromatic pairs #Sephiroth }}
+Sephiroth is the common [[restriction]] of [[magic family #Muggles|muggles]] and [[avicennmic temperaments #Submerged|submerged]].
+[[Subgroup]]: 2.5.11
+[[Comma list]]: 34375/32768
+{{Mapping|legend=3| 1 0 15 | 0 1 -5 }}
+{{Mapping|legend=5| 1 0 0 0 15 | 0 0 1 0 -5 }}
+: mapping generators: ~2, ~5
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1203.3290{{c}}, ~5/4 = 373.6097{{c}}
+: [[error map]]: {{val| +3.329 -6.046 -2.722 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 372.1586{{c}}
+: error map: {{val| 0.000 -14.155 -12.111 }}
+{{Optimal ET sequence|legend=0| 3, 10, 13, 16, 29, 132cceee }}
+[[Badness]] (Sintel): 1.85
+==== 2.5.11.13 subgroup ====
+Subgroup: 2.5.11.13
+Comma list: 65/64, 6875/6656
+{{Mapping|legend=2| 1 0 15 6 | 0 1 -5 -1 }}
+{{Mapping|legend=4| 1 0 0 0 15 6 | 0 0 1 0 -5 -1 }}
+Optimal tunings:
+* WE: ~2 = 1203.3825{{c}}, ~5/4 = 373.6318{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 372.1519{{c}}
+{{Optimal ET sequence|legend=0| 3, 10, 13, 16, 29, 132cceeeff }}
+Badness (Sintel): 0.410
+==== 2.5.11.13.17 subgroup ====
+Subgroup: 2.5.11.13.17
+Comma list: 65/64, 170/169, 221/220
+{{Mapping|legend=2| 1 0 15 6 11 | 0 1 -5 -1 -3 }}
+{{Mapping|legend=4| 1 0 0 0 15 6 11 | 0 0 1 0 -5 -1 -3 }}
+Optimal tunings:
+* WE: ~2 = 1203.6741{{c}}, ~5/4 = 373.3775{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 371.6773{{c}}
+{{Optimal ET sequence|legend=0| 3, 10, 13, 16, 29g, 129ccceeffgggg }}
+Badness (Sintel): 0.299
 === Wizz ===
 {{See also| Chromatic pairs #Wizz }}
-Wizz, the 6 & 16 temperament in the 2.5.11 subgroup, tempers out [[15625/15488]], and is the common [[restriction]] of [[astrology]] and [[wizard]].
+Wizz, the 6 & 16 temperament in the 2.5.11 subgroup, tempers out [[15625/15488]], and is the common [[restriction]] of [[jubilismic clan #Astrology|astrology]] and [[stearnsmic clan #Wizard|wizard]].
 [[Subgroup]]: 2.5.11
@@ Line 393: / Line 602: @@
 === Movila ===
-This temperament has a structure very similar to [[mavila]] but is somewhat more accurate because the generator is a flat [[11/8]] rather than a sharp [[4/3]]. The major third is still ~[[5/4]], but the minor third is now ~[[64/55]] instead of ~[[6/5]].
+This temperament has a structure very similar to [[mavila family #Mavila|mavila]] but is somewhat more accurate because the generator is a flat [[11/8]] rather than a sharp [[4/3]]. The major third is still ~[[5/4]], but the minor third is now ~[[64/55]] instead of ~[[6/5]].
 [[Subgroup]]: 2.5.11
@@ Line 411: / Line 620: @@
 [[Badness]] (Sintel): 0.718
-=== Sephiroth ===
-{{See also| Chromatic pairs #Sephiroth }}
-Sephiroth is the common [[restriction]] of [[muggles]] and [[submerged]].
-[[Subgroup]]: 2.5.11
-[[Comma list]]: 34375/32768
-{{Mapping|legend=3| 1 0 15 | 0 1 -5 }}
-{{Mapping|legend=5| 1 0 0 0 15 | 0 0 1 0 -5 }}
-: mapping generators: ~2, ~5
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1203.3290{{c}}, ~5/4 = 373.6097{{c}}
-: [[error map]]: {{val| +3.329 -6.046 -2.722 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 372.1586{{c}}
-: error map: {{val| 0.000 -14.155 -12.111 }}
-{{Optimal ET sequence|legend=0| 3, 10, 13, 16, 29, 132cceee }}
-[[Badness]] (Sintel): 1.85
-==== 2.5.11.13 subgroup ====
-Subgroup: 2.5.11.13
-Comma list: 65/64, 6875/6656
-Subgroup-val mapping: {{mapping| 1 0 15 6 | 0 1 -5 -1 }}
-Gencom mapping: {{mapping| 1 0 0 0 15 6 | 0 0 1 0 -5 -1 }}
-Optimal tunings:
-* WE: ~2 = 1203.3825{{c}}, ~5/4 = 373.6318{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 372.1519{{c}}
-{{Optimal ET sequence|legend=0| 3, 10, 13, 16, 29, 132cceeeff }}
-Badness (Sintel): 0.410
-==== 2.5.11.13.17 subgroup ====
-Subgroup: 2.5.11.13.17
-Comma list: 65/64, 170/169, 221/220
-Subgroup-val mapping: {{mapping| 1 0 15 6 11 | 0 1 -5 -1 -3 }}
-Gencom mapping: {{mapping| 1 0 0 0 15 6 11 | 0 0 1 0 -5 -1 -3 }}
-Optimal tunings:
-* WE: ~2 = 1203.6741{{c}}, ~5/4 = 373.3775{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 371.6773{{c}}
-{{Optimal ET sequence|legend=0| 3, 10, 13, 16, 29g, 129ccceeffgggg }}
-Badness (Sintel): 0.299
 === Trader ===
@@ Line 475: / Line 626: @@
 [[Comma list]]: 26/25
-{{Mapping|legend=3| 1 2 3 | 0 1 2 }}
+{{Mapping|legend=3| 1 0 -1 | 0 1 2 }}
-: mapping generators, ~2, ~5/4
+: mapping generators, ~2, ~5
 [[Optimal tuning]]s:
@@ Line 537: / Line 688: @@
 === Argument ===
-Argument tempers out [[1372/1331]] in the 2.7.11 subgroup. It is the no-3 [[restriction]] of [[#Augment|augment]].
+Argument tempers out [[1372/1331]] in the 2.7.11 subgroup, equating [[14/11]] to a step of [[3edo]]. It is the no-3 [[restriction]] of [[#Augment|augment]].
 [[Subgroup]]: 2.7.11
@@ Line 556: / Line 707: @@
 [[Badness]] (Sintel): 0.475
-=== Score ===
+=== Scaevola ===
-{{See also| Chromatic pairs #Score }}
+Scaevola is the 2.7.11-subgroup temperament tempering out 14641/14336, with a generator of [[11/8]] and mapping +4 generators to [[7/4]]. Two strong extensions are [[#Score|score]] to 2.7.11.13 and [[subgroup temperaments #Joan|joan]] to 2.9.7.11.
+Scaevola has a structure that is very similar to [[mavila family #Mavila|mavila]], but whereas mavila has a "fifth" of [[3/2]], "major third" of [[5/4]], and "minor third" of [[6/5]], scaevola has a "fifth" of [[16/11]], "major third" of [[14/11]], and "minor third" of [[8/7]], substituting mavila's 4:5:6 for 11:14:16. Essentially, Scaevola can be seen as a counterpart of mavila for fifths even flatter than [[9edo]], such as [[11edo]]'s fifth.
-Score is a low-accuracy [[extension]] of the unnamed 2.7.11-subgroup temperament tempering out 14641/14336.
+It was named by [[CompactStar]] in 2026, referring to ''{{w|Scaevola}}'' (the genus of flowering plants), which is meant to sound reminiscent of ''score'' and ''mavila'' (the score and joan temperaments were actually named prior to this temperament).
-[[Subgroup]]: 2.7.11.13
+[[Subgroup]]: 2.7.11
-[[Comma list]]: 343/338, 847/832
+[[Comma list]]: 14641/14336
-{{Mapping|legend=3| 1 1 3 1 | 0 4 1 6 }}
+{{Mapping|legend=3| 1 1 3 | 0 4 1 }}
-{{Mapping|legend=5| 1 0 0 1 3 1 | 0 0 0 4 1 6 }}
+{{Mapping|legend=5| 1 0 0 1 3 | 0 0 0 4 1 }}
 : mapping generators: ~2, ~11/8
 [[Optimal tuning]]s:
-* [[WE]]: ~2 = 1201.5484{{c}}, ~11/8 = 540.7963{{c}}
+* [[WE]]: ~2 = 1201.2479{{c}}, ~11/8 = 542.1162{{c}}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/8 = 540.5091{{c}}
+: [[error map]]: {{val| +1.248 +0.887 -5.458 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/8 = 541.9403{{c}}
+: error map: {{val| 0.000 -1.065 -9.378 }}
+{{Optimal ET sequence|legend=1| 2, 7d, 9, 11, 20, 31, 51, 82e, 113e, 195eee }}
+[[Badness]] (Sintel): 0.578
+==== Score ====
+{{See also| Chromatic pairs #Score }}
+Score is an extension of scaevola that maps [[13/8]] to +6 generators.
+Subgroup: 2.7.11.13
+Comma list: 343/338, 847/832
+{{Mapping|legend=2| 1 1 3 1 | 0 4 1 6 }}
+{{Mapping|legend=4| 1 0 0 1 3 1 | 0 0 0 4 1 6 }}
+Optimal tunings:
+* WE: ~2 = 1201.5484{{c}}, ~11/8 = 540.7963{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 540.5091{{c}}
-{{Optimal ET sequence|legend=1| 9, 11, 20 }}
+{{Optimal ET sequence|legend=0| 9, 11, 20 }}
-[[Badness]] (Sintel): 0.368
+Badness (Sintel): 0.368
 === Bossier ===
@@ Line 607: / Line 783: @@
 Comma list: 1573/1568, 15488/15379
-Subgroup-val mapping: {{mapping| 1 0 1 3 | 0 8 7 2 }}
+{{Mapping|legend=2| 1 0 1 3 | 0 8 7 2 }}
-Gencom mapping: {{mapping|| 1 0 0 0 1 3 | 0 0 0 8 7 2 }}
+{{Mapping|legend=4| 1 0 0 0 1 3 | 0 0 0 8 7 2 }}
 Optimal tunings:
@@ Line 704: / Line 880: @@
 [[Comma list]]: 1352/1331
-{{Mapping|legend=3| 1 3 3 | 0 2 3 }}
+{{Mapping|legend=3| 1 1 0 | 0 2 3 }}
-{{Mapping|legend=5| 1 0 0 0 3 3 | 0 0 0 0 2 3 }}
+{{Mapping|legend=5| 1 0 0 0 1 0 | 0 0 0 0 2 3 }}
-: mapping generators, ~2, ~13/11
+: mapping generators: ~2, ~26/11
 [[Optimal tuning]]s:
@@ Line 858: / Line 1,034: @@
 [[Badness]] (Sintel): 0.106
-[[Category:Temperament collections]]
+[[Category:Catalogs of subgroup temperaments]]
-[[Category:Subgroup temperaments]]
+[[Category:Catalogs of rank-2 temperaments]]

No-threes subgroup temperaments: Difference between revisions

FloraC (talk | contribs)