@@ Line 1: / Line 1: @@
-This page discusses miscellaneous rank-2 temperaments tempering out [[126/125]], the starling comma or septimal semicomma.
+{{Technical data page}}
+This page discusses miscellaneous [[rank-2 temperament]]s tempering out [[126/125]], the starling comma or septimal semicomma.
 Temperaments discussed in families and clans are:
-* ''[[Pater]]'', {16/15, 126/125} → [[Father family #Pater|Father family]]
+* ''[[Pater]]'' (+16/15) → [[Father family #Pater|Father family]]
-* ''[[Flat]]'', {21/20, 25/24} → [[Dicot family #Flat|Dicot family]]
+* [[Meantone]] (+81/80) → [[Meantone family #Septimal meantone|Meantone family]]
-* ''[[Opossum]]'', {28/27, 126/125} → [[Trienstonic clan #Opossum|Trienstonic clan]]
+* ''[[Mavling]]'' (+135/128) → [[Mavila family #Mavling|Mavila family]]
-* ''[[Diminished]]'', {36/35, 50/49} → [[Dimipent family #Diminished|Dimipent family]] / [[Jubilismic clan #Diminished|jubilismic clan]]
+* ''[[Grackle]]'' (+32805/32768) → [[Schismatic family #Grackle|Schismatic family]]
-* [[Keemun]], {49/48, 126/125} → [[Kleismic family #Keemun|Kleismic family]]
+* ''[[Flattie]]'' (+21/20) → [[Dicot family #Flattie|Dicot family]]
-* ''[[Augene]]'', {64/63, 126/125} → [[Augmented family #Augene|Augmented family]]
+* [[Diaschismic]] (+2048/2025) → [[Diaschismic family #Septimal diaschismic|Diaschismic family]]
-* [[Meantone]], {81/80, 126/125} → [[Meantone family #Septimal meantone|Meantone family]]
+* [[Augene]] (+64/63) → [[Augmented family #Augene|Augmented family]]
-* [[Mavila]], {126/125, 135/128} → [[Pelogic family #Mavila|Pelogic family]]
+* [[Opossum]] (+28/27) → [[Trienstonic clan #Opossum|Trienstonic clan]]
-* [[Sensi]], {126/125, 245/243}, [[Sensipent family #Sensi|Sensipent family]] / [[Sensamagic clan #Sensi|sensamagic clan]]
+* [[Diminished (temperament)|Diminished]] (+36/35) → [[Diminished family #Septimal diminished|Diminished family]]
-* ''[[Gilead]]'', {126/125, 343/324} → [[Shibboleth family #Gilead|Shibboleth family]]
+* [[Wollemia]] (+2240/2187) → [[Tetracot family #Wollemia|Tetracot family]]
-* [[Muggles]], {126/125, 525/512} → [[Magic family #Muggles|Magic family]]
+* [[Muggles]] (+525/512) → [[Magic family #Muggles|Magic family]]
-* ''[[Diaschismic]]'', {126/125, 2048/2025} → [[Diaschismic family #Diaschismic|Diaschismic family]]
+* ''[[Passionate]]'' (+131072/127575) → [[Passion family #Passionate|Passion family]]
-* ''[[Wollemia]]'', {126/125, 2240/2187} → [[Tetracot family #Wollemia|Tetracot family]]
+* [[Keemun]] (+49/48) → [[Kleismic family #Keemun|Kleismic family]]
-* ''[[Unicorn]]'', {126/125, 10976/10935} → [[Unicorn family #Unicorn|Unicorn family]]
+* [[Sensi]] (+245/243), [[Sensipent family #Sensi|Sensipent family]]
-* ''[[Coblack]]'', {126/125, 16807/16384} → [[Trisedodge family #Coblack|Trisedodge family]] / [[Cloudy clan #Coblack|cloudy clan]]
+* ''[[Unicorn]]'' (+10976/10935) → [[Unicorn family #Unicorn|Unicorn family]]
-* ''[[Grackle]]'', {126/125, 32805/32768} → [[Schismatic family #Grackle|Schismatic family]]
+* ''[[Worschmidt]]'' (+33075/32768) → [[Würschmidt family #Worschmidt|Würschmidt family]]
-* ''[[Worschmidt]]'', {126/125, 33075/32768} → [[Würschmidt family #Worschmidt|Würschmidt family]]
+* [[Valentine]] (+1029/1024) → [[Gamelismic clan #Valentine|Gamelismic clan]]
-* ''[[Passionate]]'', {126/125, 131072/127575} → [[Passion family #Passionate|Passion family]]
+* ''[[Muscogee]]'' (+33756345/33554432) → [[Mabila family #Muscogee|Mabila family]]
-* ''[[Vishnean]]'', {126/125, 540225/524288} → [[Vishnuzmic family #Vishnean|Vishnuzmic family]]
+* ''[[Thuja]]'' (+65536/64827) → [[Buzzardsmic clan #Thuja|Buzzardsmic clan]]
-* ''[[Ditonic]]'', {126/125, 8751645/8388608} → [[Ditonmic family #Ditonic|Ditonmic family]]
+* ''[[Paraguay]]'' (+12005/11664) → [[Parakleismic family #Paraguay|Parakleismic family]]
-* ''[[Muscogee]]'', {126/125, 33756345/33554432} → [[Mabila family #Muscogee|Mabila family]]
+* ''[[Diton]]'' (+8751645/8388608) → [[Ditonmic family #Diton|Ditonmic family]]
+* ''[[Vishnean]]'' (+540225/524288) → [[Vishnu family #Vishnean|Vishnu family]]
+* ''[[Coblack]]'' (+16807/16384) → [[Trisedodge family #Coblack|Trisedodge family]]
-Since (6/5)<sup>3</sup> = 126/125 × 12/7, these temperaments tend to have a relatively small complexity for 6/5. They also possess the [[starling tetrad]], the 6/5-6/5-6/5-7/6 versions of the diminished seventh chord. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before [[12edo|12EDO]] established itself as the standard tuning, it is arguably more authentic to tune it as three stacked minor thirds and an augmented second, which is what it is in meantone, than as the modern version of four stacked very flat minor thirds.
+Considered below are myna, nusecond, oolong, vines, kumonga, cypress, bisemidim, casablanca, amigo, supersensi, and cobalt, sorted by increasing [[badness]].
+Since {{nowrap|(6/5)<sup>3</sup> {{=}} (126/125)⋅(12/7)}}, these temperaments tend to have a relatively small complexity for 6/5. They also possess the [[starling tetrad]], the 6/5–6/5–6/5–7/6 versions of the diminished seventh chord.
 == Myna ==
-: ''For the 5-limit version of this temperament, see [[High badness temperaments #Mynic]].''
 {{Main| Myna }}
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Mynic]].''
-In addition to 126/125, myna tempers out [[1728/1715]], the orwell comma, and [[2401/2400]], the breedsma. It can also be described as the 27&amp;31 temperament. It has 6/5 as a generator, and [[58edo|58EDO]] can be used as a tuning, with [[89edo|89EDO]] being a better one, and fans of round amounts in cents may like [[120edo|120EDO]]. It is also possible to tune myna with pure fifths by taking 6<sup>1/10</sup> as the generator. Myna extends naturally but with much increased complexity to the 11 and 13 limits.
+-limit myna is naturally found by establishing a structure of thirds, by making [[7/6]]–[[6/5]]–[[49/40]]–[[5/4]]–[[9/7]] all equidistant (the distances between which are [[36/35]], [[49/48]], and [[50/49]]). [[11-limit]] myna then arises from equating this neutral third to [[11/9]]. Myna's characteristic feature is that the pental thirds are tuned outwards so that the chroma between them ([[25/24]]) is twice the size of the interval between the pental and septimal thirds ([[36/35]]). In that sense, it is opposed to [[keemic temperaments]], in particular [[quasitemp]], where the distance between the pental and septimal thirds is the same as the chroma between the pental thirds and different from the septimal dieses.
-Subgroup: 2.3.5.7
+In terms of vanishing commas, in addition to 126/125, myna adds [[1728/1715]], the orwell comma, and [[2401/2400]], the breedsma. It can also be described as the {{nowrap| 27 & 31 }} temperament, and has a [[ploidacot]] signature of beta-decacot. It has [[~]][[6/5]] as a generator.
-[[Comma list]]: 126/125, 1728/1715
+[[58edo]] can be used as a tuning, with [[89edo]] being a better one, and fans of round cent values may like [[120edo]]. It is also possible to tune myna with pure fifths by taking 6<sup>1/10</sup> as the generator. Myna extends naturally but with much increased complexity to the 11- and 13-limit.
-[[Mapping]]: [{{val| 1 9 9 8 }}, {{val| 0 -10 -9 -7 }}]
+[[Subgroup]]: 2.3.5.7
-Mapping generators: ~2, ~5/3
+[[Comma list]]: 126/125, 1728/1715
-{{Multival|legend=1| 10 9 7 -9 -17 -9 }}
+{{Mapping|legend=1| 1 -1 0 1 | 0 10 9 7 }}
+: mapping generators: ~2, ~6/5
-[[POTE generator]]: ~6/5 = 310.146
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.3410{{c}}, ~6/5 = 309.9756{{c}}
+: [[error map]]: {{val| -0.659 -1.540 +3.467 +0.344 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 310.0880{{c}}
+: error map: {{val| 0.000 -1.075 +4.479 +1.790 }}
 [[Minimax tuning]]:
 * 7- and [[9-odd-limit]]: ~6/5 = {{monzo| 1/10 1/10 0 0}}
-: [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 9/10 9/10 0 0 }}, {{monzo| 17/10 7/10 0 0 }}]
+: {{monzo list| 1 0 0 0 | 0 1 0 0 | 9/10 9/10 0 0 | 17/10 7/10 0 0 }}
-: [[Eigenmonzo]]s (unchanged-intervals): 2, 3
+: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3
-{{Val list|legend=1| 27, 31, 58, 89 }}
+{{Optimal ET sequence|legend=1| 27, 31, 58, 89, 236cc }}
-[[Badness]]: 0.027044
+[[Badness]] (Sintel): 0.684
 === 11-limit ===
@@ Line 58: / Line 68: @@
 Comma list: 126/125, 176/175, 243/242
-Mapping: [{{val| 1 9 9 8 22 }}, {{val| 0 -10 -9 -7 -25 }}]
+Mapping: {{mapping| 1 -1 0 1 -3 | 0 10 9 7 25 }}
-POTE generator: ~6/5 = 310.144
+Optimal tunings:
+* WE: ~2 = 1199.3441{{c}}, ~6/5 = 309.9748{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 310.0982{{c}}
-Optimal GPV sequence: {{Val list| 27e, 31, 58, 89 }}
+{{Optimal ET sequence|legend=0| 27e, 31, 58, 89, 236cce }}
-Badness: 0.016842
+Badness (Sintel): 0.557
 ==== 13-limit ====
@@ Line 71: / Line 83: @@
 Comma list: 126/125, 144/143, 176/175, 196/195
-Mapping: [{{val| 1 9 9 8 22 0 }}, {{val| 0 -10 -9 -7 -25 5 }}]
+Mapping: {{mapping| 1 -1 0 1 -3 5 | 0 10 9 7 25 -5 }}
-POTE generator: ~6/5 = 310.276
+Optimal tunings:
+* WE: ~2 = 1198.6509{{c}}, ~6/5 = 309.9273{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 310.2218{{c}}
-Optimal GPV sequence: {{Val list| 27e, 31, 58 }}
+{{Optimal ET sequence|legend=0| 27e, 31, 58, 205cceff, 263ccdeefff }}
-Badness: 0.017125
+Badness (Sintel): 0.708
 ==== Minah ====
@@ Line 84: / Line 98: @@
 Comma list: 78/77, 91/90, 126/125, 176/175
-Mapping: [{{val| 1 9 9 8 22 20 }}, {{val| 0 -10 -9 -7 -25 -22 }}]
+Mapping: {{mapping| 1 -1 0 1 -3 -2 | 0 10 9 7 25 22 }}
-POTE generator: ~6/5 = 310.381
+Optimal tunings:
+* WE: ~2 = 1199.1929{{c}}, ~6/5 = 310.1724{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 310.3251{{c}}
-Optimal GPV sequence: {{Val list| 27e, 31f, 58f }}
+{{Optimal ET sequence|legend=0| 27e, 31f, 58f }}
-Badness: 0.027568
+Badness (Sintel): 1.14
 ==== Maneh ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 66/65, 105/104, 126/125, 540/539
+Comma list: 66/65, 105/104, 126/125, 243/242
-Mapping: [{{val| 1 9 9 8 22 23 }}, {{val| 0 -10 -9 -7 -25 -26 }}]
+Mapping: {{mapping| 1 -1 0 1 -3 -3 | 0 10 9 7 25 26 }}
-POTE generator: ~6/5 = 309.804
+Optimal tunings:
+* WE: ~2 = 1199.9109{{c}}, ~6/5 = 309.7815{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 309.7987{{c}}
-Optimal GPV sequence: {{Val list| 27eff, 31 }}
+{{Optimal ET sequence|legend=0| 27eff, 31 }}
-Badness: 0.029868
+Badness (Sintel): 1.23
 === Myno ===
@@ Line 110: / Line 128: @@
 Comma list: 99/98, 126/125, 385/384
-Mapping: [{{val| 1 9 9 8 -1 }}, {{val| 0 -10 -9 -7 6 }}]
+Mapping: {{mapping| 1 -1 0 1 5 | 0 10 9 7 -6 }}
-POTE generator: ~6/5 = 309.737
+Optimal tunings:
+* WE: ~2 = 1201.0652{{c}}, ~6/5 = 310.0121{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 309.7812{{c}}
-Optimal GPV sequence: {{Val list| 27, 31 }}
+{{Optimal ET sequence|legend=0| 27, 31 }}
-Badness: 0.033434
+Badness (Sintel): 1.11
 === Coleto ===
@@ Line 123: / Line 143: @@
 Comma list: 56/55, 100/99, 1728/1715
-Mapping: [{{val| 1 9 9 8 2 }}, {{val| 0 -10 -9 -7 2 }}]
+Mapping: {{mapping| 1 -1 0 1 4 | 0 10 9 7 -2 }}
-POTE generator: ~6/5 = 310.853
+Optimal tunings:
+* WE: ~2 = 1196.1024{{c}}, ~6/5 = 309.8434{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 310.6398{{c}}
-Optimal GPV sequence: {{Val list| 4, 23bc, 27e }}
+{{Optimal ET sequence|legend=0| 4, 23bc, 27e }}
-Badness: 0.048687
+Badness (Sintel): 1.61
-== Valentine ==
+== Nusecond ==
-{{Main| Valentine }}
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Nusecond]].''
-Valentine tempers out 1029/1024 and 6144/6125 as well as 126/125, so it also fits under the heading of the gamelismic clan. It has a generator of 21/20, which can be stripped of its 2 and taken as 3×7/5. In this respect it resembles miracle, with a generator of 3×5/7, and casablanca, with a generator of 5×7/3. These three generators are the simplest in terms of the relationship of tetrads in the [[The Seven Limit Symmetrical Lattices|lattice of 7-limit tetrads]]. Valentine can also be described as the 31&amp;46 temperament, and [[77edo|77EDO]], [[108edo|108EDO]] or [[185edo|185EDO]] make for excellent tunings, which also happen to be excellent tunings for starling temperament, the 126/125 planar temperament. Hence 7-limit valentine can be used whenever starling is wanted, with the extra tempering out of 1029/1024 having no discernible effect on tuning accuracy. Another tuning for valentine uses (3/2)<sup>1/9</sup> as a generator, giving pure 3/2 fifths. Valentine extends naturally to the 11-limit as {{multival| 9 5 -3 7 … }}, tempering out 121/120 and 441/440; 46EDO has a valentine generator 3\46 which is only 0.0117 cents sharp of the minimax generator, (11/7)<sup>1/10</sup>.
-Valentine is very closely related to [[Carlos Alpha]], the rank one nonoctave temperament of Wendy Carlos, as the generator chain of valentine is the same thing as Carlos Alpha. Indeed, the way Carlos uses Alpha in ''Beauty in the Beast'' suggests that she really intended Alpha to be the same thing as valentine, and that it is misdescribed as a rank one temperament. Carlos tells us that "[t]he melodic motions of Alpha are amazingly exotic and fresh, like you've never heard before", and since Alpha lives inside valentine this comment carries over and applies to it if you stick close melodically to generator steps, which is almost impossible not to do since the generator step is so small. MOS of 15, 16, 31 and 46 notes are available to explore these exotic and fresh melodies, or the less exotic ones you might cook up otherwise.
-Subgroup: 2.3.5
-[[Comma list]]: 1990656/1953125
-[[Mapping]]: [{{val| 1 1 2 }}, {{val| 0 9 5 }}]
-[[POTE generator]]: ~25/24 = 78.039
-{{Val list|legend=1| 15, 31, 46, 77, 123 }}
-[[Badness]]: 0.122765
-=== 7-limit ===
-Subgroup: 2.3.5.7
-[[Comma list]]: 126/125, 1029/1024
-[[Mapping]]: [{{val| 1 1 2 3 }}, {{val| 0 9 5 -3 }}]
-Mapping generators: ~2, ~21/20
-[[POTE generator]]: ~21/20 = 77.864
-[[Minimax tuning]]:
-* [[7-odd-limit]]: ~21/20 = {{monzo| 1/6 1/12 0 -1/12 }}
-: [{{monzo| 1 0 0 0 }}, {{monzo| 5/2 3/4 0 -3/4 }}, {{monzo| 17/6 5/12 0 -5/12 }}, {{monzo| 5/2 -1/4 0 1/4 }}]
-: [[Eigenmonzo]]s (unchanged-intervals): 2, 7/6
-* [[9-odd-limit]]: ~21/20 = {{monzo| 1/21 2/21 0 -1/21}}
-: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 47/21 10/21 0 -5/21 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
-: [[Eigenmonzo]]s (unchanged-intervals): 2, 9/7
-[[Algebraic generator]]: smaller root of ''x''<sup>2</sup> - 89''x'' + 92, or (89 - sqrt (7553))/2, at 77.8616 cents.
-{{Val list|legend=1| 15, 31, 46, 77, 185, 262cd }}
-[[Badness]]: 0.031056
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 121/120, 126/125, 176/175
-Mapping: [{{val| 1 1 2 3 3 }}, {{val| 0 9 5 -3 7 }}]
+Nusecond tempers out [[2430/2401]] and [[16875/16807]] in addition to 126/125, and may be described as {{nowrap| 31 & 70 }}. It has a neutral second generator of [[49/45]], two of which make up a 6/5 minor third since 2430/2401 is tempered out. Note that in the data below, the generator is its [[octave complement]] since eleven such generators [[octave reduction|octave reduced]] give the [[3/2|perfect fifth]]; its [[ploidacot]] is thus theta-hendecacot.
-Mapping generators: ~2, ~21/20
+[[31edo]] can be used as a tuning, or [[132edo]] with a val which is the sum of the [[patent val]]s for 31 and 101. Because 49/45 is flat of 12/11 by only 540/539, nusecond is more naturally thought of as an 11-limit temperament with a combined 12/11 and 11/10 as a generator, tempering out 99/98, 121/120 and 540/539. Because of all the neutral seconds, an exotic Middle Eastern sound comes naturally to nusecond. Mosses of 15, 23, or 31 notes are enough to give fuller effect to the harmony, but the 8-note mos might also be considered from the melodic point of view.
-POTE generator: ~21/20 = 77.881
+[[Subgroup]]: 2.3.5.7
-Minimax tuning:
-* [[11-odd-limit]]: ~21/20 = {{monzo| 0 0 0 -1/10 1/10 }}
-: [{{monzo| 1 0 0 0 0 }}, {{monzo| 1 0 0 -9/10 9/10 }}, {{monzo| 2 0 0 -1/2 1/2 }}, {{monzo| 3 0 0 3/10 -3/10 }}, {{monzo| 3 0 0 -7/10 7/10 }}]
-: Eigenmonzos (unchanged-intervals): 2, 11/7
-Algebraic generator: positive root of 4''x''<sup>3</sup> + 15''x''<sup>2</sup> - 21, or else Gontrand2, the smallest positive root of 4''x''<sup>7</sup> - 8''x''<sup>6</sup> + 5.
-Optimal GPV sequence: {{Val list| 15, 31, 46, 77, 262cdee, 339cdeee }}
-Badness: 0.016687
-==== Dwynwen ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 91/90, 121/120, 126/125, 176/175
-Mapping: [{{val| 1 1 2 3 3 2 }}, {{val| 0 9 5 -3 7 26 }}]
-POTE generator: ~21/20 = 78.219
-Optimal GPV sequence: {{Val list| 15, 31f, 46 }}
-Badness: 0.023461
-==== Lupercalia ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 66/65, 105/104, 121/120, 126/125
-Mapping: [{{val| 1 1 2 3 3 3 }}, {{val| 0 9 5 -3 7 11 }}]
-POTE generator: ~21/20 = 77.709
-Optimal GPV sequence: {{Val list| 15, 31, 77ff, 108eff, 139efff }}
-Badness: 0.021328
-==== Valentino ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 121/120, 126/125, 176/175, 196/195
-Mapping: [{{val| 1 1 2 3 3 5 }}, {{val| 0 9 5 -3 7 -20 }}]
-POTE generator: ~21/20 = 77.958
-Optimal GPV sequence: {{Val list| 15f, 31, 46, 77 }}
-Badness: 0.020665
-===== 17-limit =====
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 121/120, 126/125, 154/153, 176/175, 196/195
-Mapping: [{{val| 1 1 2 3 3 5 5 }}, {{val| 0 9 5 -3 7 -20 -14 }}]
-POTE generator: ~21/20 = 78.003
-Optimal GPV sequence: {{Val list| 15f, 31, 46, 77, 123e, 200ceg }}
-Badness: 0.016768
-==== Semivalentine ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 121/120, 126/125, 169/168, 176/175
-Mapping: [{{val| 2 2 4 6 6 7 }}, {{val| 0 9 5 -3 7 3 }}]
-POTE generator: ~21/20 = 77.839
-Optimal GPV sequence: {{Val list| 16, 30, 46, 62, 108ef }}
-Badness: 0.032749
-==== Hemivalentine ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 121/120, 126/125, 176/175, 343/338
-Mapping: [{{val| 1 1 2 3 3 4 }}, {{val| 0 18 10 -6 14 -9 }}]
-POTE generator: ~40/39 = 39.044
-Optimal GPV sequence: {{Val list| 30, 31, 61, 92f, 123f }}
-Badness: 0.047059
-=== Hemivalentino ===
-Subgroup: 2.3.5.7.11
-Comma list: 126/125, 243/242, 1029/1024
-Mapping: [{{val| 1 1 2 3 2 }}, {{val| 0 18 10 -6 45 }}]
-POTE generator: ~45/44 = 38.921
-Optimal GPV sequence: {{Val list| 31, 92e, 123, 154, 185 }}
-Badness: 0.061275
-==== 13-limit ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 126/125, 196/195, 243/242, 1029/1024
-Mapping: [{{val| 1 1 2 3 2 5 }}, {{val| 0 18 10 -6 45 -40 }}]
-POTE generator: ~45/44 = 38.948
-Optimal GPV sequence: {{Val list| 31, 92e, 123, 154 }}
-Badness: 0.057919
-==== Hemivalentoid ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 126/125, 144/143, 243/242, 343/338
-Mapping: [{{val| 1 1 2 3 2 4 }}, {{val| 0 18 10 -6 45 -9 }}]
-POTE generator: ~40/39 = 38.993
-Optimal GPV sequence: {{Val list| 31, 92ef, 123f }}
-Badness: 0.057931
-== Nusecond ==
-: ''For the 5-limit version of this temperament, see [[High badness temperaments #Nusecond]].''
-Nusecond tempers out 2430/2401 and 16875/16807 in addition to 126/125, and may be described as 31&amp;70. It has a neutral second generator of 49/45, two of which make up a 6/5 minor third since 2430/2401 is tempered out. [[31edo|31EDO]] can be used as a tuning, or [[132edo|132EDO]] with a val which is the sum of the [[patent val]]s for 31 and 101. Because 49/45 is flat of 12/11 by only 540/539, nusecond is more naturally thought of as an 11-limit temperament with a combined 12/11 and 11/10 as a generator, tempering out 99/98, 121/120 and 540/539. Because of all the neutral seconds, an exotic Middle Eastern sound comes naturally to nusecond. MOS of 15, 23, or 31 notes are enough to give fuller effect to the harmony, but the 8-note MOS might also be considered from the melodic point of view.
-Subgroup: 2.3.5.7
 [[Comma list]]: 126/125, 2430/2401
-[[Mapping]]: [{{val| 1 3 4 5 }}, {{val| 0 -11 -13 -17 }}]
+{{Mapping|legend=1| 1 -8 -9 -12 | 0 11 13 17 }}
+: mapping generators: ~2, ~49/27
-Mapping generators: ~2, ~49/45
-{{Multival|legend=1| 11 13 17 -5 -4 3 }}
-[[POTE generator]]: ~49/45 = 154.579
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.6138{{c}}, ~49/27 = 1045.0850{{c}}
+: [[error map]]: {{val| -0.386 -2.931 +3.267 +2.253 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/27 = 1045.3909{{c}}
+: error map: {{val| 0.000 -2.655 +3.768 +2.819 }}
 [[Minimax tuning]]:
 * [[7-odd-limit]]: ~49/45 = {{monzo| 4/13 0 -1/13 }}
-: [{{monzo| 1 0 0 0 }}, {{monzo| -5/13 0 11/13 0 }}, {{monzo| 0 0 1 0 }}, {{monzo| -3/13 0 17/13 0 }}]
+: {{monzo list| 1 0 0 0 | -5/13 0 11/13 0 | 0 0 1 0 | -3/13 0 17/13 0 }}
-: [[Eigenmonzo]]s (unchanged-intervals): 2, 5
+: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5
 * [[9-odd-limit]]: ~49/45 = {{monzo| 3/11 -1/11 }}
-: [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 5/11 13/11 0 0 }}, {{monzo| 4/11 17/11 0 0 }}]
+: {{monzo list| 1 0 0 0 | 0 1 0 0 | 5/11 13/11 0 0 | 4/11 17/11 0 0 }}
-: [[Eigenmonzo]]s (unchanged-intervals): 2, 3
+: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3
-{{Val list|legend=1| 8d, 23d, 31, 101, 132c, 163c }}
+{{Optimal ET sequence|legend=1| 8d, 23d, 31, 101, 132c, 163c }}
-[[Badness]]: 0.050389
+[[Badness]] (Sintel): 1.28
 === 11-limit ===
@@ Line 348: / Line 190: @@
 Comma list: 99/98, 121/120, 126/125
-Mapping: [{{val| 1 3 4 5 5 }}, {{val| 0 -11 -13 -17 -12 }}]
+Mapping: {{mapping| 1 -8 -9 -12 -7 | 0 11 13 17 12 }}
-Mapping generators: ~2, ~11/10
-POTE generator: ~11/10 = 154.645
+Optimal tunings:
+* WE: ~2 = 1200.3420{{c}}, ~11/6 = 1045.6528{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1045.3816{{c}}
 Minimax tuning:
-* [[11-odd-limit]]: ~11/10 = {{monzo| 1/10 -1/5 0 0 1/10 }}
+* [[11-odd-limit]]: ~11/6 = {{monzo| 9/10 1/5 0 0 -1/10 }}
 : [{{monzo| 1 0 0 0 0 }}, {{monzo| 19/10 11/5 0 0 -11/10 }}, {{monzo| 27/10 13/5 0 0 -13/10 }}, {{monzo| 33/10 17/5 0 0 -17/10 }}, {{monzo| 19/5 12/5 0 0 -6/5 }}]
-: Eigenmonzos (unchanged-intervals): 2, 11/9
+: unchanged-interval (eigenmonzo) basis: 2.11/9
 Algebraic generator: positive root of 15''x''<sup>2</sup> - 10''x'' - 7, or (5 + sqrt (130))/15, at 154.6652 cents. The recurrence converges very quickly.
-Optimal GPV sequence: {{Val list| 8d, 23de, 31, 101, 132ce, 163ce, 194cee }}
+{{Optimal ET sequence|legend=0| 8d, 23de, 31, 101 }}
-Badness: 0.025621
+Badness (Sintel): 0.847
 === 13-limit ===
@@ Line 370: / Line 212: @@
 Comma list: 66/65, 99/98, 121/120, 126/125
-Mapping: [{{val| 1 3 4 5 5 5 }}, {{val| 0 -11 -13 -17 -12 -10 }}]
+Mapping: {{mapping| 1 -8 -9 -12 -7 -5 | 0 11 13 17 12 10 }}
-POTE generator: ~11/10 = 154.478
+Optimal tunings:
+* WE: ~2 = 1198.9982{{c}}, ~11/6 = 1044.6488{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1045.4476{{c}}
-Optimal GPV sequence: {{Val list| 8d, 23de, 31, 70f, 101ff }}
+{{Optimal ET sequence|legend=0| 8d, 23de, 31 }}
-Badness: 0.023323
+Badness (Sintel): 0.964
 == Oolong ==
 {{Main| Oolong }}
-: ''For the 5-limit version of this temperament, see [[High badness temperaments #Oolong]].''
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Oolong]].''
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 126/125, 117649/116640
-[[Mapping]]: [{{val| 1 6 7 8 }}, {{val| 0 -17 -18 -20 }}]
+{{Mapping|legend=1| 1 -11 -11 -12 | 0 17 18 20 }}
+: mapping generators: ~2, ~5/3
-{{Multival|legend=1| 17 18 20 -11 -16 -4 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9188{{c}}, ~5/3 = 888.2606{{c}}
+: [[error map]]: {{val| -0.081 -0.632 +3.269 -2.640 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/3 = 888.3163{{c}}
+: error map: {{val| 0.000 -0.578 +3.379 -2.500 }}
-[[POTE generator]]: ~6/5 = 311.679
+{{Optimal ET sequence|legend=1| 23d, 27, 50, 77 }}
-{{Val list|legend=1| 27, 50, 77 }}
+[[Badness]] (Sintel): 1.86
-[[Badness]]: 0.073509
 === 11-limit ===
@@ Line 401: / Line 248: @@
 Comma list: 126/125, 176/175, 26411/26244
-Mapping: [{{val| 1 6 7 8 18 }}, {{val| 0 -17 -18 -20 -56 }}]
+Mapping: {{mapping| 1 -11 -11 -12 -38 | 0 17 18 20 56 }}
-POTE generator: ~6/5 = 311.587
+Optimal tunings:
+* WE: ~2 = 1198.9982{{c}}, ~5/3 = 888.0239{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 888.3941{{c}}
-Optimal GPV sequence: {{Val list| 27e, 77, 104c, 181c }}
+{{Optimal ET sequence|legend=0| 27e, 50e, 77, 104c }}
-Badness: 0.056915
+Badness (Sintel): 1.88
 === 13-limit ===
@@ Line 414: / Line 263: @@
 Comma list: 126/125, 176/175, 196/195, 13013/12960
-Mapping: [{{val| 1 6 7 8 18 5 }}, {{val| 0 -17 -18 -20 -56 -5 }}]
+Mapping: {{mapping| 1 -11 -11 -12 -38 0 | 0 17 18 20 56 5 }}
-POTE generator: ~6/5 = 311.591
+Optimal tunings:
+* WE: ~2 = 1199.5177{{c}}, ~5/3 = 888.0521{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 888.3959{{c}}
-Optimal GPV sequence: {{Val list| 27e, 77, 104c, 181c }}
+{{Optimal ET sequence|legend=0| 27e, 50e, 77, 104c }}
-Badness: 0.035582
+Badness (Sintel): 1.47
 == Vines ==
-: ''For the 5-limit version of this temperament, see [[High badness temperaments #Vines]].''
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Vines]].''
-Subgroup: 2.3.5.7
+Vines may be described as the {{nowrap| 46 & 50 }} temperament. It has a [[semi-octave]] period and a [[~]][[6/5]] generator. Eight generators minus three periods give the [[3/2|perfect fifth]], so the [[ploidacot]] for the temperament is diploid gamma-octacot. [[96edo]] in the 96d val may be recommended as a tuning.
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 126/125, 84035/82944
-[[Mapping]]: [{{val| 2 7 8 8 }}, {{val| 0 -8 -7 -5 }}]
+{{Mapping|legend=1| 2 -1 1 3 | 0 8 7 5 }}
+: mapping generators: ~343/240, ~6/5
-[[POTE generator]]: ~6/5 = 312.602
+[[Optimal tuning]]s:
+* [[WE]]: ~343/240 = 600.2436{{c}}, ~6/5 = 312.7294{{c}}
+: [[error map]]: {{val| +0.487 -0.363 +3.036 -4.448 }}
+* [[CWE]]: ~343/240 = 600.0000{{c}}, ~6/5 = 312.6547{{c}}
+: error map: {{val| 0.000 -0.717 +2.269 -5.552 }}
-{{Val list|legend=1| 42, 46, 96d, 142d, 238dd }}
+{{Optimal ET sequence|legend=1| 46, 96d, 142d }}
-[[Badness]]: 0.078049
+[[Badness]] (Sintel): 1.98
 === 11-limit ===
@@ Line 442: / Line 300: @@
 Comma list: 126/125, 385/384, 2401/2376
-Mapping: [{{val| 2 7 8 8 5 }}, {{val| 0 -8 -7 -5 4 }}]
+Mapping: {{mapping| 2 -1 1 3 9 | 0 8 7 5 -4 }}
-POTE generator: ~6/5 = 312.601
+Optimal tunings:
+* WE: ~99/70 = 600.2454{{c}}, ~6/5 = 312.7293{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~6/5 = 312.6282{{c}}
-Optimal GPV sequence: {{Val list| 42, 46, 96d, 142d, 238dd }}
+{{Optimal ET sequence|legend=0| 46, 96d, 142d }}
-Badness: 0.044499
+Badness (Sintel): 1.47
 === 13-limit ===
@@ Line 455: / Line 315: @@
 Comma list: 126/125, 196/195, 364/363, 385/384
-Mapping: [{{val| 2 7 8 8 5 5 }}, {{val| 0 -8 -7 -5 4 5 }}]
+Mapping: {{mapping| 2 -1 1 3 9 10 | 0 8 7 5 -4 -5 }}
-POTE generator: ~6/5 = 312.564
+Optimal tunings:
+* WE: ~55/39 = 600.3065{{c}}, ~6/5 = 312.7240{{c}}
+* CWE: ~55/39 = 600.0000{{c}}, ~6/5 = 312.5836{{c}}
-Optimal GPV sequence: {{Val list| 42, 46, 96d, 238ddf }}
+{{Optimal ET sequence|legend=0| 46, 96d }}
-Badness: 0.029693
+Badness (Sintel): 1.23
-== Kumonga ==
+== Xenial ==
-: ''For the 5-limit version of this temperament, see [[High badness temperaments #Kumonga]].''
+{{Main| Xenial }}
+: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Xenial]].''
-Subgroup: 2.3.5.7
+Named by [[User:Xenllium|Xenllium]] in 2026, xenial may be described as the {{nowrap| 19 & 70 }} temperament, splitting the [[8/3|perfect eleventh]] into nine equal parts, each for ~[[10/9]]. Equivalently, a stack of nine [[9/5]]s is equated with the [[3/2|perfect fifth]] above 7 [[octave]]s, so the [[ploidacot]] for the temperament is zeta-enneacot, and from this it derives its name.
-[[Comma list]]: 126/125, 12288/12005
+[[Subgroup]]: 2.3.5.7
-[[Mapping]]: [{{val| 1 4 4 3 }}, {{val| 0 -13 -9 -1 }}]
+[[Comma list]]: 126/125, 177147/175616
-{{Multival|legend=1| 13 9 1 -16 -35 -23 }}
+{{Mapping|legend=1| 1 -6 -12 -25 | 0 9 17 33 }}
+: mapping generators: ~2, ~9/5
-[[POTE generator]]: ~8/7 = 222.797
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0095{{c}}, ~9/5 = 1011.1532{{c}}
+: [[error map]]: {{val| +0.010 -1.634 +3.176 -1.009 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~9/5 = 1011.1456{{c}}
+: error map: {{val| 0.000 -1.644 +3.162 -1.021 }}
-{{Val list|legend=1| 16, 27, 43, 70, 167ccdd }}
+{{Optimal ET sequence|legend=1| 19, 51cd, 70, 89 }}
-[[Badness]]: 0.087500
+[[Badness]] (Sintel): 2.13
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 126/125, 176/175, 864/847
+Comma list: 126/125, 540/539, 16384/16335
-Mapping: [{{val| 1 4 4 3 7 }}, {{val| 0 -13 -9 -1 -19 }}]
+Mapping: {{mapping| 1 -6 -12 -25 22 | 0 9 17 33 -22 }}
-POTE generator: ~8/7 = 222.898
+Optimal tunings:
+* WE: ~2 = 1199.6137{{c}}, ~9/5 = 1010.8717{{c}}
+* CWE: ~2 = 1200.000{{c}}, ~9/5 = 1011.1915{{c}}
-Optimal GPV sequence: {{Val list| 16, 27e, 43, 70e }}
+{{Optimal ET sequence|legend=0| 19, 51cd, 70, 89 }}
-Badness: 0.043336
+Badness (Sintel): 2.31
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 78/77, 126/125, 144/143, 176/175
+Comma list: 126/125, 169/168, 540/539, 729/728
-Mapping: [{{val| 1 4 4 3 7 5 }}, {{val| 0 -13 -9 -1 -19 -7 }}]
+Mapping: {{mapping| 1 -6 -12 -25 22 -14 | 0 9 17 33 -22 21 }}
-POTE generator: ~8/7 = 222.961
+Optimal tunings:
+* WE: ~2 = 1199.8559{{c}}, ~9/5 = 1011.0911{{c}}
+* CWE: ~2 = 1200.000{{c}}, ~9/5 = 1011.2102{{c}}
-Optimal GPV sequence: {{Val list| 16, 27e, 43, 70e, 113cdee }}
+{{Optimal ET sequence|legend=0| 19, 51cd, 70, 89 }}
-Badness: 0.028920
+Badness (Sintel): 1.98
-== Thuja ==
+=== 17-limit ===
-: ''For the 5-limit version of this temperament, see [[High badness temperaments #Thuja]].''
+Subgroup: 2.3.5.7.11.13.17
-Subgroup: 2.3.5.7
+Comma list: 126/125, 169/168, 221/220, 256/255, 540/539
-[[Comma list]]: 126/125, 65536/64827
+Mapping: {{mapping| 1 -6 -12 -25 22 -14 26 | 0 9 17 33 -22 21 -26 }}
-[[Mapping]]: [{{val| 1 -4 0 7 }}, {{val| 0 12 5 -9 }}]
+Optimal tunings:
+* WE: ~2 = 1199.6970{{c}}, ~9/5 = 1010.9792{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~9/5 = 1011.2323{{c}}
-{{Multival|legend=1| 12 5 -9 -20 -48 -35 }}
+{{Optimal ET sequence|legend=0| 19, 51cd, 70, 89 }}
-[[POTE generator]]: ~175/128 = 558.605
+Badness (Sintel): 2.06
-{{Val list|legend=1| 15, 43, 58 }}
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
-[[Badness]]: 0.088441
+Comma list: 126/125, 169/168, 171/170, 221/220, 256/255, 540/539
-=== 11-limit ===
+Mapping: {{mapping| 1 -6 -12 -25 22 -14 26 27 | 0 9 17 33 -22 21 -26 -27 }}
-Subgroup: 2.3.5.7.11
-Comma list: 126/125, 176/175, 1344/1331
+Optimal tunings:
+* WE: ~2 = 1199.7741{{c}}, ~9/5 = 1011.0334{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~9/5 = 1011.2230{{c}}
-Mapping: [{{val| 1 -4 0 7 3 }}, {{val| 0 12 5 -9 1 }}]
+{{Optimal ET sequence|legend=0| 19, 51cdh, 70, 89 }}
-POTE generator: ~11/8 = 558.620
+Badness (Sintel): 2.03
-Optimal GPV sequence: {{Val list| 15, 43, 58 }}
+=== 23-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23
-Badness: 0.033078
+Comma list: 126/125, 162/161, 169/168, 171/170, 208/207, 221/220, 231/230
-=== 13-limit ===
+Mapping: {{mapping| 1 -6 -12 -25 22 -14 26 27 2 | 0 9 17 33 -22 21 -26 -27 3 }}
-Subgroup: 2.3.5.7.11.13
-Comma list: 126/125, 144/143, 176/175, 364/363
+Optimal tunings:
+* WE: ~2 = 1199.6628{{c}}, ~9/5 = 1010.9415{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~9/5 = 1011.2245{{c}}
-Mapping: [{{val| 1 -4 0 7 3 -7 }}, {{val| 0 12 5 -9 1 23 }}]
+{{Optimal ET sequence|legend=0| 19, 51cdh, 70, 89 }}
-POTE generator: ~11/8 = 558.589
+Badness (Sintel): 1.93
-Optimal GPV sequence: {{Val list| 15, 43, 58 }}
+== Kumonga ==
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Kumonga]].''
-Badness: 0.022838
+[[Subgroup]]: 2.3.5.7
-=== 17-limit ===
+[[Comma list]]: 126/125, 12288/12005
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 126/125, 144/143, 176/175, 221/220, 256/255
+{{Mapping|legend=1| 1 -9 -5 2 | 0 13 9 1 }}
+: mapping generators: ~2, ~7/4
-Mapping: [{{val| 1 -4 0 7 3 -7 12 }}, {{val| 0 12 5 -9 1 23 -17 }}]
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1198.0653{{c}}, ~7/4 = 975.6277{{c}}
+: [[error map]]: {{val| -1.935 -1.382 +4.009 +2.932 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 977.1096{{c}}
+: error map: {{val| 0.000 +0.470 +7.673 +8.284 }}
-POTE generator: ~11/8 = 558.509
+{{Optimal ET sequence|legend=1| 16, 27, 43, 70, 167ccdd }}
-Optimal GPV sequence: {{Val list| 15, 43, 58 }}
+[[Badness]] (Sintel): 2.21
-Badness: 0.022293
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-=== 19-limit ===
+Comma list: 126/125, 176/175, 864/847
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 96/95, 126/125, 144/143, 153/152, 176/175, 221/220
+Mapping: {{mapping| 1 -9 -5 2 -12 | 0 13 9 1 19 }}
-Mapping: [{{val| 1 -4 0 7 3 -7 12 1 }}, {{val| 0 12 5 -9 1 23 -17 7 }}]
+Optimal tunings:
+* WE: ~2 = 1197.9101{{c}}, ~7/4 = 975.4007{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 976.9964{{c}}
-POTE generator: ~11/8 = 558.504
+{{Optimal ET sequence|legend=0| 16, 27e, 43, 70e }}
-Optimal GPV sequence: {{Val list| 15, 43, 58h }}
+Badness (Sintel): 1.43
-Badness: 0.018938
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-=== 23-limit ===
+Comma list: 78/77, 126/125, 144/143, 176/175
-Subgroup: 2.3.5.7.11.13.17.19.23
-Comma list: 96/95, 126/125, 144/143, 153/152, 176/175, 221/220, 231/230
+Mapping: {{mapping| 1 -9 -5 2 -12 -2 | 0 13 9 1 19 7 }}
-Mapping: [{{val| 1 -4 0 7 3 -7 12 1 5 }}, {{val| 0 12 5 -9 1 23 -17 7 -1 }}]
+Optimal tunings:
+* WE: ~2 = 1198.4987{{c}}, ~7/4 = 975.8162{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 976.9677{{c}}
-POTE generator: ~11/8 = 558.522
+{{Optimal ET sequence|legend=0| 16, 27e, 43, 70e, 113cdee }}
-Optimal GPV sequence: {{Val list| 15, 43, 58hi }}
+Badness (Sintel): 1.19
-Badness: 0.016581
+== Bisemidim ==
+Bisemidim tempers out [[118098/117649]] and may be described as the {{nowrap| 50 & 58 }} temperament. It has a [[semi-octave]] period and a [[~]][[49/45]] generator. Nine generators minus a period give the [[3/2|perfect fifth]], so the [[ploidacot]] for the temperament is diploid alpha-enneacot. [[108edo]] and [[166edo]] in the 166cef val may be recommended as tunings.
-=== 29-limit ===
+[[Subgroup]]: 2.3.5.7
-The ''raison d'etre'' of this entry is the simple and accurate approximation of factor twenty-nine, the 2.5.11.21.29 subgroup being of especially good accuracy and simplicity.
-Subgroup: 2.3.5.7.11.13.17.19.23.29
+[[Comma list]]: 126/125, 118098/117649
-Comma list: 96/95, 116/115, 126/125, 144/143, 153/152, 176/175, 221/220, 231/230
+{{Mapping|legend=1| 2 1 2 2 | 0 9 11 15 }}
+: mapping generators: ~343/243, ~49/45
-Mapping: [{{val| 1 -4 0 7 3 -7 12 1 5 3 }}, {{val| 0 12 5 -9 1 23 -17 7 -1 4 }}]
+[[Optimal tuning]]s:
+* [[WE]]: ~343/243 = 599.8915{{c}}, ~49/45 = 144.5293{{c}}
+: [[error map]]: {{val| -0.217 -1.299 +3.292 -1.103 }}
+* [[CWE]]: ~343/243 = 600.0000{{c}}, ~49/45 = 144.5351{{c}}
+: error map: {{val| 0.000 -1.139 +3.572 -0.799 }}
-POTE generator: ~11/8 = 558.520
+{{Optimal ET sequence|legend=1| 50, 58, 108, 166c, 408ccc }}
-Optimal GPV sequence: {{Val list| 15, 43, 58hi }}
+[[Badness]] (Sintel): 2.47
-Badness: 0.013762
-== Cypress ==
-: ''For the 5-limit version of this temperament, see [[High badness temperaments #Cypress]].''
-Subgroup: 2.3.5.7
-[[Comma list]]: 126/125, 19683/19208
-[[Mapping]]: [{{val| 1 7 10 15 }}, {{val| 0 -12 -17 -27 }}]
-{{Multival|legend=1| 12 17 27 -1 9 15 }}
-[[POTE generator]]: ~135/98 = 541.828
-{{Val list|legend=1| 11cd, 20cd, 31, 206bcd, 237bcd, 268bcd, 299bcd, 330bbcd }}
-[[Badness]]: 0.099801
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 99/98, 126/125, 243/242
+Comma list: 126/125, 540/539, 1344/1331
-Mapping: [{{val| 1 7 10 15 17 }}, {{val| 0 -12 -17 -27 -30 }}]
+Mapping: {{mapping| 2 1 2 2 5 | 0 9 11 15 8 }}
-POTE generator: ~15/11 = 541.772
+Optimal tunings:
+* WE: ~99/70 = 599.6360{{c}}, ~12/11 = 144.5388{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~12/11 = 144.5623{{c}}
-Optimal GPV sequence: {{Val list| 11cdee, 20cde, 31, 144cd, 175cd, 206bcde, 237bcde }}
+{{Optimal ET sequence|legend=0| 50, 58, 108, 166ce, 224cee }}
-Badness: 0.042719
+Badness (Sintel): 1.36
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 66/65, 99/98, 126/125, 243/242
+Comma list: 126/125, 144/143, 196/195, 364/363
-Mapping: [{{val| 1 7 10 15 17 15 }}, {{val| 0 -12 -17 -27 -30 -25 }}]
+Mapping: {{mapping| 2 1 2 2 5 5 | 0 9 11 15 8 10 }}
-POTE generator: ~15/11 = 541.778
+Optimal tunings:
+* WE: ~55/39 = 599.5217{{c}}, ~12/11 = 144.5375{{c}}
+* CWE: ~55/39 = 600.0000{{c}}, ~12/11 = 144.5698{{c}}
-Optimal GPV sequence: {{Val list| 11cdeef, 20cdef, 31 }}
+{{Optimal ET sequence|legend=0| 50, 58, 166cef, 224ceeff }}
-Badness: 0.037849
+Badness (Sintel): 0.987
-== Bisemidim ==
+== Cypress ==
-Subgroup: 2.3.5.7
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Cypress]].''
-[[Comma list]]: 126/125, 118098/117649
+[[Subgroup]]: 2.3.5.7
-[[Mapping]]: [{{val| 2 1 2 2 }}, {{val| 0 9 11 15 }}]
+[[Comma list]]: 126/125, 19683/19208
-{{Multival|legend=1| 18 22 30 -7 -3 8 }}
+{{Mapping|legend=1| 1 -5 -7 -12 | 0 12 17 27 }}
-[[POTE generator]]: ~35/27 = 455.445
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.1652{{c}}, ~196/135 = 658.2622{{c}}
+: [[error map]]: {{val| +0.165 -3.634 +2.988 +2.272 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~196/135 = 658.1814{{c}}
+: error map: {{val| 0.000 -3.779 +2.769 +2.071 }}
-{{Val list|legend=1| 50, 58, 108, 166c, 408ccc }}
+{{Optimal ET sequence|legend=1| 11cd, 20cd, 31 }}
-[[Badness]]: 0.097786
+[[Badness]] (Sintel): 2.53
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 126/125, 540/539, 1344/1331
+Comma list: 99/98, 126/125, 243/242
-Mapping: [{{val| 2 1 2 2 5 }}, {{val| 0 9 11 15 8 }}]
+Mapping: {{mapping| 1 -5 -7 -12 -13 | 0 12 17 27 30 }}
-POTE generator: ~35/27 = 455.373
+Optimal tunings:
+* WE: ~2 = 1200.1117{{c}}, ~22/15 = 658.2892{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 658.2345{{c}}
-Optimal GPV sequence: {{Val list| 50, 58, 108, 166ce, 224cee }}
+{{Optimal ET sequence|legend=0| 11cdee, 20cde, 31, 144cd }}
-Badness: 0.041190
+Badness (Sintel): 1.41
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 126/125, 144/143, 196/195, 364/363
+Comma list: 66/65, 99/98, 126/125, 243/242
-Mapping: [{{val| 2 1 2 2 5 5 }}, {{val| 0 9 11 15 8 10 }}]
+Mapping: {{mapping| 1 -5 -7 -12 -13 -10 | 0 12 17 27 30 25 }}
-POTE generator: ~35/27 = 455.347
+Optimal tunings:
+* WE: ~2 = 1199.4328{{c}}, ~22/15 = 657.9111{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 658.1886{{c}}
-Optimal GPV sequence: {{Val list| 50, 58, 166cef, 224ceeff }}
+{{Optimal ET sequence|legend=0| 11cdeef, 20cdef, 31 }}
-Badness: 0.023877
+Badness (Sintel): 1.56
 == Casablanca ==
-: ''For the 5-limit version of this temperament, see [[High badness temperaments #Casablanca]].''
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Casablanca]].''
+Aside from 126/125, casablanca tempers out the no-threes comma [[823543/819200]] and also [[589824/588245]], and may be described as {{nowrap| 31 & 73 }} with a [[ploidacot]] signature of eta-19-cot. 61\135 or 75\166 supply good tunings for the generator, and 20- and 31-note [[mos scale]]s are available.
-Aside from 126/125, casablanca tempers out the no-threes comma 823543/819200 and also 589824/588245, and may also be described as 31&amp;73. 74\135 or 91\166 supply good tunings for the generator, and 20 and 31 note MOS are available.
+It may not seem like casablanca has much to offer, but peering under the hood a bit harder suggests otherwise. For one thing, the [[~]][[48/35]] generator is particularly interesting; like [[15/14]] and [[21/20]], it represents an interval between one vertex of a [[hexany]] and the opposite vertex, which makes it particularly simple with regard to the cubic lattice of tetrads.
-It may not seem like casablanca has much to offer, but peering under the hood a bit harder suggests otherwise. For one thing, the 35/24 generator is particularly interesting; like 15/14 and 21/20, it represents an interval between one vertex of a [[hexany]] and the opposite vertex, which makes it particularly simple with regard to the cubic lattice of tetrads. For another, if we add 385/384 to the list of commas, 35/24 is identified with 16/11, and casablanca is revealed as an 11-limit temperament with a very low complexity for 11 and not too high a one for 7; we might compare 1, 4, 14, 19, the generator steps to 11, 7, 5 and 3 respectively, with 1, 4, 10, 18, the steps to 3, 5, 7 and 11 in 11-limit meantone.
+If we add 385/384 to the list of commas, 48/35 is identified with [[11/8]], and casablanca is revealed as an [[11-limit]] temperament with a very low complexity for [[11/1|11]] and not too high a one for [[7/1|7]]; we might compare 1, 4, 14, 19, the generator steps to 11, 7, 5 and 3 respectively, with 1, 4, 10, 18, the steps to 3, 5, 7 and 11 in 11-limit [[meantone]].
-Subgroup: 2.3.5.7
+Marrakesh, named by [[Herman Miller]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19166.html#19186 Yahoo! Tuning Group | ''A rose by any other name . . .'']</ref>, is a more accurate 11-limit extension where the generator is identified with [[15/11]] as opposed to 11/8 in casablanca.
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 126/125, 589824/588245
-[[Mapping]]: [{{val| 1 12 10 5 }}, {{val| 0 -19 -14 -4 }}]
+{{Mapping|legend=1| 1 -7 -4 1 | 0 19 14 4 }}
+: mapping generators: ~2, ~48/35
-{{Multival|legend=1| 19 14 4 -22 -47 -30 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.6286{{c}}, ~48/35 = 542.0141{{c}}
+: [[error map]]: {{val| -0.371 -1.087 +3.370 -1.141 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~48/35 = 542.1684{{c}}
+: error map: {{val| 0.000 -0.756 +4.044 -0.152 }}
-[[POTE generator]]: ~35/24 = 657.818
+{{Optimal ET sequence|legend=1| 11b, 20b, 31, 104c, 135c, 166c }}
-{{Val list|legend=1| 11b, 20b, 31, 104c, 135c, 166c }}
+[[Badness]] (Sintel): 2.56
-[[Badness]]: 0.101191
 === 11-limit ===
@@ Line 713: / Line 605: @@
 Comma list: 126/125, 385/384, 2420/2401
-Mapping: [{{val| 1 12 10 5 4 }}, {{val| 0 -19 -14 -4 -1 }}]
+Mapping: {{mapping| 1 -7 -4 1 3 | 0 19 14 4 1 }}
-POTE generator: ~16/11 = 657.923
+Optimal tunings:
+* WE: ~2 = 1200.6404{{c}}, ~11/8 = 542.3659{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 542.0945{{c}}
-Optimal GPV sequence: {{Val list| 11b, 20b, 31 }}
+{{Optimal ET sequence|legend=0| 11b, 20b, 31 }}
-Badness: 0.067291
+Badness (Sintel): 2.22
 ==== 13-limit ====
@@ Line 726: / Line 620: @@
 Comma list: 126/125, 196/195, 385/384, 2420/2401
-Mapping: [{{val| 1 12 10 5 4 7 }}, {{val| 0 -19 -14 -4 -1 -6 }}]
+Mapping: {{mapping| 1 -7 -4 1 3 1 | 0 19 14 4 1 6 }}
-POTE generator: ~16/11 = 657.854
+Optimal tunings:
+* WE: ~2 = 1199.7367{{c}}, ~11/8 = 542.0269{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 542.1392{{c}}
-Optimal GPV sequence: {{Val list| 11b, 20b, 31 }}
+{{Optimal ET sequence|legend=0| 11b, 20b, 31 }}
+Badness (Sintel): 2.31
 === Marrakesh ===
@@ Line 737: / Line 635: @@
 Comma list: 126/125, 176/175, 14641/14580
-Mapping: [{{val| 1 12 10 5 21 }}, {{val| 0 -19 -14 -4 -32 }}]
+Mapping: {{mapping| 1 -7 -4 1 -11 | 0 19 14 4 32 }}
-POTE generator: ~22/15 = 657.791
+Optimal tunings:
+* WE: ~2 = 1199.6315{{c}}, ~15/11 = 542.0428{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/11 = 542.1958{{c}}
-Optimal GPV sequence: {{Val list| 31, 73, 104c, 135c }}
+{{Optimal ET sequence|legend=0| 31, 73, 104c, 135c }}
-Badness: 0.040539
+Badness (Sintel): 1.34
 ==== 13-limit ====
@@ Line 750: / Line 650: @@
 Comma list: 126/125, 176/175, 196/195, 14641/14580
-Mapping: [{{val| 1 12 10 5 21 -10 }}, {{val| 0 -19 -14 -4 -32 25 }}]
+Mapping: {{mapping| 1 -7 -4 1 -11 15 | 0 19 14 4 32 -25 }}
-POTE generator: ~22/15 = 657.756
+Optimal tunings:
+* WE: ~2 = 1199.3741{{c}}, ~15/11 = 541.9613{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/11 = 542.2361{{c}}
-Optimal GPV sequence: {{Val list| 31, 73, 104c, 135c, 239ccf }}
+{{Optimal ET sequence|legend=0| 31, 73, 104c, 135c, 239ccf }}
-Badness: 0.040774
+Badness (Sintel): 1.68
 ==== Murakuc ====
@@ Line 763: / Line 665: @@
 Comma list: 126/125, 144/143, 176/175, 1540/1521
-Mapping: [{{val| 1 12 10 5 21 7 }}, {{val| 0 -19 -14 -4 -32 -6 }}]
+Mapping: {{mapping| 1 -7 -4 1 -11 1 | 0 19 14 4 32 6 }}
-POTE generator: ~22/15 = 657.700
+Optimal tunings:
+* WE: ~2 = 1198.6578{{c}}, ~15/11 = 541.6930{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/11 = 542.2577{{c}}
-Optimal GPV sequence: {{Val list| 31, 104cff, 135cff }}
+{{Optimal ET sequence|legend=0| 31, 73f, 104cff }}
-Badness: 0.041395
+Badness (Sintel): 1.71
 == Amigo ==
-{{see also| High badness temperaments #Magus }}
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Magus]].''
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 126/125, 2097152/2083725
-[[Mapping]]: [{{val| 1 -2 2 9 }}, {{val| 0 11 1 -19 }}]
+{{Mapping|legend=1| 1 -2 2 9 | 0 11 1 -19 }}
+: mapping generators: ~2, ~5/4
-{{Multival|legend=1| 11 1 -19 -24 -61 -47 }}
-[[POTE generator]]: ~5/4 = 391.094
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.4354{{c}}, ~5/4 = 390.9104{{c}}
+: [[error map]]: {{val| -0.565 -0.811 +3.467 -1.206 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 391.0937{{c}}
+: error map: {{val| 0.000 +0.076 +4.780 +0.393 }}
-{{Val list|legend=1| 43, 46, 89, 135c, 359cc }}
+{{Optimal ET sequence|legend=1| 43, 46, 89, 135c, 359cc }}
-[[Badness]]: 0.110873
+[[Badness]] (Sintel): 2.81
 === 11-limit ===
@@ Line 793: / Line 700: @@
 Comma list: 126/125, 176/175, 16384/16335
-Mapping: [{{val| 1 -2 2 9 9 }}, {{val| 0 11 1 -19 -17 }}]
+Mapping: {{mapping| 1 -2 2 9 9 | 0 11 1 -19 -17 }}
-POTE generator: ~5/4 = 391.075
+Optimal tunings:
+* WE: ~2 = 1199.5267{{c}}, ~5/4 = 390.9211{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 391.0783{{c}}
-Optimal GPV sequence: {{Val list| 43, 46, 89, 135c, 224c }}
+{{Optimal ET sequence|legend=0| 43, 46, 89, 135c, 224c }}
-Badness: 0.043438
+Badness (Sintel): 1.44
 === 13-limit ===
@@ Line 806: / Line 715: @@
 Comma list: 126/125, 169/168, 176/175, 364/363
-Mapping: [{{val| 1 -2 2 9 9 5 }}, {{val| 0 11 1 -19 -17 -4 }}]
+Mapping: {{mapping| 1 -2 2 9 9 5 | 0 11 1 -19 -17 -4 }}
-POTE generator: ~5/4 = 391.073
+Optimal tunings:
+* WE: ~2 = 1199.8174{{c}}, ~5/4 = 391.0130{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 391.0737{{c}}
-Optimal GPV sequence: {{Val list| 43, 46, 89, 135cf, 224cf }}
+{{Optimal ET sequence|legend=0| 43, 46, 89 }}
-Badness: 0.030666
+Badness (Sintel): 1.27
 == Supersensi ==
-Supersensi (8d &amp; 43) has supermajor third as a generator like [[sensi]], but the no-fives comma 17496/16807 rather than 245/243 tempered out.
+Named by [[Xenllium]] in 2022, supersensi tempers out the no-fives comma [[17496/16807]], and may be described as {{nowrap| 8d & 43 }}. It has a ultramajor third generator, which is sharper than the generator for [[sensi]], hence the name. Its [[ploidacot]] is epsilon-15-cot.
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 126/125, 17496/16807
-[[Mapping]]: [{{val| 1 -4 -4 -5 }}, {{val| 0 15 17 21 }}]
+{{Mapping|legend=1| 1 -4 -4 -5 | 0 15 17 21 }}
+: mapping generators: ~2, ~343/270
-{{Multival|legend=1| 15 17 21 -8 -9 1 }}
-[[POTE generator]]: ~343/270 = 446.568
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.1406{{c}}, ~343/270 = 446.2478{{c}}
+: [[error map]]: {{val| -0.859 -4.800 +3.337 +6.675 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~343/270 = 446.5163{{c}}
+: error map: {{val| 0.000 -4.210 +4.464 +8.017 }}
-{{Val list|legend=1| 8d, 35, 43 }}
+{{Optimal ET sequence|legend=1| 8d, …, 35, 43 }}
-[[Badness]]: 0.148531
+[[Badness]] (Sintel): 3.76
 === 11-limit ===
@@ Line 836: / Line 750: @@
 Comma list: 99/98, 126/125, 864/847
-Mapping: [{{val| 1 -4 -4 -5 -1 }}, {{val| 0 15 17 21 12 }}]
+Mapping: {{mapping| 1 -4 -4 -5 -1 | 0 15 17 21 12 }}
-POTE generator: ~72/55 = 446.616
+Optimal tunings:
+* WE: ~2 = 1198.6099{{c}}, ~72/55 = 446.0983{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~72/55 = 446.5381{{c}}
-Optimal GPV sequence: {{Val list| 8d, 35, 43 }}
+{{Optimal ET sequence|legend=0| 8d, …, 35, 43 }}
-Badness: 0.059449
+Badness (Sintel): 1.97
 === 13-limit ===
@@ Line 849: / Line 765: @@
 Comma list: 78/77, 99/98, 126/125, 144/143
-Mapping: [{{val| 1 -4 -4 -5 -1 -3 }}, {{val| 0 15 17 21 12 18 }}]
+Mapping: {{mapping| 1 -4 -4 -5 -1 -3 | 0 15 17 21 12 18 }}
-POTE generator: ~13/10 = 446.598
+Optimal tunings:
+* WE: ~2 = 1198.9947{{c}}, ~13/10 = 446.2243{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~13/10 = 446.5420{{c}}
-Optimal GPV sequence: {{Val list| 8d, 35f, 43 }}
+{{Optimal ET sequence|legend=0| 8d, …, 35f, 43 }}
-Badness: 0.035258
+Badness (Sintel): 1.46
 === 17-limit ===
@@ Line 862: / Line 780: @@
 Comma list: 78/77, 99/98, 120/119, 126/125, 144/143
-Mapping: [{{val| 1 -4 -4 -5 -1 -3 0 }}, {{val| 0 15 17 21 12 18 11 }}]
+Mapping: {{mapping| 1 -4 -4 -5 -1 -3 0 | 0 15 17 21 12 18 11 }}
-POTE generator: ~13/10 = 446.631
+Optimal tunings:
+* WE: ~2 = 1198.7070{{c}}, ~13/10 = 446.1493{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~13/10 = 446.5645{{c}}
-Optimal GPV sequence: {{Val list| 8d, 35f, 43 }}
+{{Optimal ET sequence|legend=0| 8d, …, 35f, 43 }}
-Badness: 0.025907
+Badness (Sintel): 1.32
 == Cobalt ==
-The name of ''cobalt temperament'' comes from Cobalt, the 27th element.
+: ''For the 5-limit version, see [[27th-octave temperaments #Cobalt]].''
-Cobalt (27 &amp; 81) has a period of 1/27 octave and tempers out 126/125 and 540/539, as well as the [[Starling family #Aplonis|aplonis temperament]].
+Cobalt has a period of 1/27 octave and tempers out 126/125 and 540/539 as in the [[aplonis]] temperament. It may be described as {{nowrap| 27 & 81 }}.
-Subgroup: 2.3.5.7
+Cobalt was named by [[Xenllium]] in 2022 after the 27th element.
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 126/125, 40353607/40310784
-[[Mapping]]: [{{val|27 43 63 76}}, {{val|0 -1 -1 -1}}]
+{{Mapping|legend=1| 27 0 20 33 | 0 1 1 1 }}
+: mapping generators: ~36/35, ~3
-[[POTE generator]]: ~3/2 = 701.244
+[[Optimal tuning]]s:
+* [[WE]]: ~36/35 = 44.4363{{c}}, ~3/2 = 701.1154{{c}}
+: [[error map]]: {{val| -0.221 -1.060 +3.307 -1.534 }}
+* [[CWE]]: ~36/35 = 44.4444{{c}}, ~3/2 = 701.0414{{c}}
+: error map: {{val| 0.000 -0.914 +3.617 -1.118 }}
-{{Val list|legend=1| 27, 81, 108, 135c, 243c }}
+{{Optimal ET sequence|legend=1| 27, 81, 108, 135c }}
-[[Badness]]: 0.173308
+[[Badness]] (Sintel): 4.39
 === 11-limit ===
@@ Line 892: / Line 819: @@
 Comma list: 126/125, 540/539, 21609/21296
-Mapping: [{{val|27 43 63 76 94}}, {{val|0 -1 -1 -1 -2}}]
+Mapping: {{mapping| 27 0 20 33 8 | 0 1 1 1 2 }}
-POTE generator: ~3/2 = 700.001
+Optimal tunings:
+* WE: ~36/35 = 44.4418{{c}}, ~3/2 = 699.9594{{c}}
+* CWE: ~36/35 = 44.4444{{c}}, ~3/2 = 699.9386{{c}}
-Optimal GPV sequence: {{Val list| 27e, 81, 108 }}
+{{Optimal ET sequence|legend=0| 27e, 81, 108 }}
-Badness: 0.078060
+Badness (Sintel): 2.58
 ==== 13-limit ====
@@ Line 905: / Line 834: @@
 Comma list: 126/125, 144/143, 196/195, 21609/21296
-Mapping: [{{val|27 43 63 76 94 100}}, {{val|0 -1 -1 -1 -2 0}}]
+Mapping: {{mapping| 27 0 20 33 8 100 | 0 1 1 1 2 0 }}
-POTE generator: ~3/2 = 700.867
+Optimal tunings:
+* WE: ~36/35 = 44.4250{{c}}, ~3/2 = 700.5606{{c}}
+* CWE: ~36/35 = 44.4444{{c}}, ~3/2 = 700.5524{{c}}
-Optimal GPV sequence: {{Val list| 27e, 81, 108, 243ceef }}
+{{Optimal ET sequence|legend=0| 27e, 81, 108, 243ceef }}
-Badness: 0.057145
+Badness (Sintel): 2.36
 ===== Cobaltous =====
@@ Line 918: / Line 849: @@
 Comma list: 126/125, 144/143, 189/187, 196/195, 1452/1445
-Mapping: [{{val|27 43 63 76 94 100 111}}, {{val|0 -1 -1 -1 -2 0 -2}}]
+Mapping: {{mapping| 27 0 20 33 8 100 79 | 0 1 1 1 2 0 2 }}
-POTE generator: ~3/2 = 700.397
+Optimal tunings:
+* WE: ~36/35 = 44.4237{{c}}, ~3/2 = 700.0699{{c}}
+* CWE: ~36/35 = 44.4444{{c}}, ~3/2 = 700.0569{{c}}
-Optimal GPV sequence: {{Val list| 27eg, 81, 108g }}
+{{Optimal ET sequence|legend=0| 27eg, 81, 108g }}
-Badness: 0.042106
+Badness (Sintel): 2.14
 ====== 19-limit ======
@@ Line 931: / Line 864: @@
 Comma list: 126/125, 144/143, 171/170, 189/187, 196/195, 969/968
-Mapping: [{{val|27 43 63 76 94 100 111 115}}, {{val|0 -1 -1 -1 -2 0 -2 -1}}]
+Mapping: {{mapping| 27 0 20 33 8 100 79 99 | 0 1 1 1 2 0 2 1 }}
-POTE generator: ~3/2 = 700.429
+Optimal tunings:
+* WE: ~36/35 = 44.4227{{c}}, ~3/2 = 700.0859{{c}}
+* CWE: ~36/35 = 44.4444{{c}}, ~3/2 = 700.0852{{c}}
-Optimal GPV sequence: {{Val list| 27eg, 81, 108g }}
+{{Optimal ET sequence|legend=0| 27eg, 81, 108g }}
-Badness: 0.030415
+Badness (Sintel): 1.85
 ===== Cobaltic =====
@@ Line 944: / Line 879: @@
 Comma list: 126/125, 144/143, 196/195, 221/220, 12005/11968
-Mapping: [{{val|27 43 63 76 94 100 111}}, {{val|0 -1 -1 -1 -2 0 -3}}]
+Mapping: {{mapping| 27 0 20 33 8 100 -18 | 0 1 1 1 2 0 3 }}
-POTE generator: ~3/2 = 701.595
+Optimal tunings:
+* WE: ~36/35 = 44.4203{{c}}, ~3/2 = 701.2133{{c}}
+* CWE: ~36/35 = 44.4444{{c}}, ~3/2 = 701.2530{{c}}
-Optimal GPV sequence: {{Val list| 27eg, 81gg, 108, 135ce }}
+{{Optimal ET sequence|legend=0| 27eg, 108, 135ce }}
-Badness: 0.047163
+Badness (Sintel): 2.40
 ====== 19-limit ======
@@ Line 957: / Line 894: @@
 Comma list: 126/125, 144/143, 196/195, 210/209, 221/220, 1088/1083
-Mapping: [{{val|27 43 63 76 94 100 111 115}}, {{val|0 -1 -1 -1 -2 0 -3 -1}}]
+Mapping: {{mapping| 27 0 20 33 8 100 -18 72 | 0 1 1 1 2 0 3 1 }}
-POTE generator: ~3/2 = 701.673
+Optimal tunings:
+* WE: ~36/35 = 44.4177{{c}}, ~3/2 = 701.2519{{c}}
+* CWE: ~36/35 = 44.4444{{c}}, ~3/2 = 701.3143{{c}}
-Optimal GPV sequence: {{Val list| 27eg, 81gg, 108, 135ceh }}
+{{Optimal ET sequence|legend=0| 27eg, 108, 135ceh }}
-Badness: 0.034176
+Badness (Sintel): 2.08
 ==== Cobaltite ====
@@ Line 970: / Line 909: @@
 Comma list: 126/125, 169/168, 540/539, 975/968
-Mapping: [{{val|27 43 63 76 94 100}}, {{val|0 -1 -1 -1 -2 -1}}]
+Mapping: {{mapping| 27 0 20 33 8 57 | 0 1 1 1 2 1 }}
-POTE generator: ~3/2 = 699.179
+Optimal tunings:
+* WE: ~36/35 = 44.4177{{c}}, ~3/2 = 699.5121{{c}}
+* CWE: ~36/35 = 44.4444{{c}}, ~3/2 = 699.6606{{c}}
-Optimal GPV sequence: {{Val list| 27e, 54bdef, 81f, 108f }}
+{{Optimal ET sequence|legend=0| 27e, 54bdef, 81f }}
-Badness: 0.052732
+Badness (Sintel): 2.18
+== References ==
+[[Category:Starling temperaments| ]] <!-- main article -->
 [[Category:Temperament collections]]
-[[Category:Starling temperaments| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Myna]]
-[[Category:Rank 2]]

Starling temperaments: Difference between revisions