@@ Line 1: / Line 1: @@
 {{Technical data page}}
-This page discusses miscellaneous rank-2 temperaments tempering out {{monzo|-5 2 2 -1}} = [[225/224]], the marvel comma or septimal kleisma.
+This page discusses miscellaneous [[rank-2 temperament|rank-2]] [[regular temperament|temperaments]] [[tempering out]] [[225/224]], the marvel comma or septimal kleisma.
 Temperaments considered in families and clans are:
-* ''[[Pelogic]]'' → [[Mavila family #Pelogic|Mavila family]] (+21/20 or 135/128, generated by the fifth with 5/4 mapped to the m3)
+* ''[[Pelogic]]'' (+21/20 or 135/128) → [[Mavila family #Pelogic|Mavila family]]
-* [[Meantone]] → [[Meantone family #Septimal meantone|Meantone family]] (+81/80 or 126/125, generated by the fifth with 5/4 mapped to the M3)
+* [[Meantone]] (+81/80 or 126/125) → [[Meantone family #Septimal meantone|Meantone family]]
-* [[Garibaldi]] → [[Schismatic family #Garibaldi|Schismatic family]] (+3125/3087, generated by the fifth with 5/4 mapped to the d4)
+* [[Garibaldi]] (+3125/3087) → [[Schismatic family #Garibaldi|Schismatic family]]
-* [[Pajara]] → [[Diaschismic family #Pajara|Diaschismic family]] (+50/49 or 64/63, generated by the fifth with a semioctave period)
+* [[Pajara]] (+50/49 or 64/63) → [[Diaschismic family #Pajara|Diaschismic family]]
-* ''[[Sharpie]]'' → [[Dicot family #Sharpie|Dicot family]] (+25/24 or 28/27, fifth sliced in two)
+* ''[[Sharpie]]'' (+25/24 or 28/27) → [[Dicot family #Sharpie|Dicot family]]
-* ''[[Immune]]'' → [[Immunity family #Immune|Immunity family]] (+781250/750141, twelfth sliced in two)
+* ''[[Immune]]'' (+781250/750141) → [[Immunity family #Immune|Immunity family]]
-* ''[[August]]'' → [[Augmented family #August|Augmented family]] (+36/35 or 128/125, generated by the fifth with a 1/3-octave period)
+* ''[[August]]'' (+36/35 or 128/125) → [[Augmented family #August|Augmented family]]
-* ''[[Fog]]'' → [[Misty family #Fog|Misty family]] (+156250/151263, generated by the fifth with a 1/3-octave period)
+* ''[[Fog]]'' (+156250/151263) → [[Misty family #Fog|Misty family]]
-* [[Negri]] → [[Slendro clan #Negri|Slendro clan]] (+49/48, fourth sliced in four)
+* [[Bunya]] (+15625/15309) → [[Tetracot family #Bunya|Tetracot family]]
-* [[Magic]] → [[Magic family #Magic|Magic family]] (+245/243, twelfth sliced in five)
+* [[Negri]] (+49/48) → [[Semaphoresmic clan #Negri|Semaphoresmic clan]]
-* ''[[Passive]]'' → [[Passion family #Passive|Passion family]] (+256/245, fourth sliced in five)
+* [[Magic]] (+245/243) → [[Magic family #Magic|Magic family]]
-* ''[[Quintapole]]'' → [[Quintaleap family #Quintapole|Quintaleap family]] (+7812500/7411887, fourth sliced in five)
+* ''[[Passive]]'' (+256/245) → [[Passion family #Passive|Passion family]]
-* ''[[Houborizic]]'' → [[Amity family #Houborizic|Amity family]] (+1250000/1240029, eleventh sliced in five)
+* ''[[Houborizic]]'' (+1250000/1240029) → [[Amity family #Houborizic|Amity family]]
-* ''[[Qintosec]]'' → [[Quintosec family #Qintosec|Quintosec family]] (+2560000/2470629, generated by the classical minor second with a 1/5-octave period)
+* ''[[Qintosec]]'' (+2560000/2470629) → [[Quintosec family #Qintosec|Quintosec family]]
-* [[Miracle]] → [[Gamelismic clan #Miracle|Gamelismic clan]] (+1029/1024, fifth sliced in six)
+* [[Miracle]] (+1029/1024) → [[Gamelismic clan #Miracle|Gamelismic clan]]
-* [[Catakleismic]] → [[Kleismic family #Catakleismic|Kleismic family]] (+4375/4374, twelfth sliced in six)
+* [[Catakleismic]] (+4375/4374) → [[Kleismic family #Catakleismic|Kleismic family]]
-* ''[[Marvo]]'' → [[Gravity family #Marvo|Gravity family]] (+78125000/78121827, two octaves and a fifth sliced in six)
+* ''[[Marvo]]'' (+78125000/78121827) → [[Gravity family #Marvo|Gravity family]]
-* [[Orwell]] → [[Semicomma family #Orwell|Semicomma family]] (+1728/1715, twelfth sliced in seven)
+* [[Orwell]] (+1728/1715) → [[Semicomma family #Orwell|Semicomma family]]
-* ''[[Snipes]]''  → [[Wesley family #Snipes|Wesley family]] (+6125/5832, two octaves and a fourth sliced in seven)
+* ''[[Snipes]]'' (+6125/5832)  → [[Wesley family #Snipes|Wesley family]]
-* ''[[Submajor]]'' → [[Buzzardsmic clan #Submajor|Buzzardsmic clan]] (+65536/64827, two octaves and a fourth sliced in eight)
+* ''[[Demibuzzard]]'' (+65536/64827) → [[Buzzardsmic clan #Demibuzzard|Buzzardsmic clan]]
-* ''[[Escapist]]'' → [[Escapade family #Escapist|Escapade family]] (+65625/65536, fourth sliced in nine)
+* ''[[Escapist]]'' (+65625/65536) → [[Escapade family #Escapist|Escapade family]]
-* ''[[Decic]]'' → [[Cloudy clan #Decic|Cloudy clan]] (+16807/16384, generated by the fifth with a 1/10-octave period)
+* ''[[Amavil]]'' (+17496/16807) → [[Mabila family #Amavil|Mabila family]]
-* ''[[Amavil]]'' → [[Mabila family #Amavil|Mabila family]] (+17496/16807, four octaves and a fourth sliced in ten)
+* ''[[Betic]]'' (+1071875/1062882) → [[Sycamore family #Betic|Sycamore family]]
-* ''[[Betic]]'' → [[Sycamore family #Betic|Sycamore family]] (+1071875/1062882, fifth sliced in eleven)
+* [[Compton]] (+250047/250000) → [[Compton family #Compton|Compton family]]
-* ''[[Hendeca]]'' → [[11th-octave temperaments #Hendeca|11th-octave temperaments]] (+122880/117649, generated by the fifth with a 1/11-octave period)
+* ''[[Raccoon]]'' (+41943040/40353607) → [[Vavoom family #Raccoon|Vavoom family]]
-* ''[[Compton]]'' → [[Compton family #Compton|Compton family]] (+250047/250000, generated by the classical major third with a 1/12-octave period)
+* ''[[Maquila]]'' (+30233088/28824005) → [[Maquila family #Septimal maquila|Maquila family]]
-* ''[[Raccoon]]'' → [[Vavoom family #Raccoon|Vavoom family]] (+41943040/40353607, twelfth sliced in seventeen)
+* ''[[Gammy]]'' (+94143178827/91913281250) → [[Gammic family #Gammy|Gammic family]]
-* ''[[Maquila]]'' → [[Maquila family #Septimal maquila|Maquila family]] (+30233088/28824005, seven octaves and a fifth sliced in seventeen)
-* ''[[Gammy]]'' → [[Gammic family #Gammy|Gammic family]] (+94143178827/91913281250, fifth sliced in twenty)
-Considered below are wizard, tritonic, septimin, slender, triton, merman, marvolo, amavil, enneaportent, alphorn, tertiosec, gwazy, and gracecordial.
+Considered below are wizard, tritonic, septimin, merman, slender, triton, marvolo, decic, enneaportent, gracecordial, alphorn, misneb, untriton, naiadical, quintannic, hendeca, gwazy, and tertiosec, in the order of increasing [[badness]].
-Since {{nowrap|(5/4)<sup>2</sup> {{=}} 225/224 × 14/9}}, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.
+Since {{nowrap|(5/4)<sup>2</sup> {{=}} (225/224)⋅(14/9)}}, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.
 The melodic signature of marvel temperaments is that 16/15 and 15/14 are tempered to be equal. Hence 8/7 can be divided into two equal parts.
@@ Line 43: / Line 41: @@
 == Wizard ==
 {{Main| Wizard }}
-: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Wizard]].''
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Wizard]].''
-Wizard has a semi-octave period and is generated by an interval that is best treated as ~17/15. The semi-octave complement of this interval is ~5/4. Wizard can be described as {{nowrap|22 &amp; 72}}. Its ploidacot is diploid alpha-hexacot, so six generator steps plus a semi-octave period gives the [[3/1|perfect twelfth]]. [[72edo]], [[94edo]], and especially [[166edo]] are good tunings for it.
+Wizard has a [[semi-octave]] period and is generated by an interval that can be treated as [[~]][[17/15]]. The semi-octave complement of this interval is ~[[5/4]]. Wizard can be described as {{nowrap| 22 & 72 }}. Its [[ploidacot]] is diploid alpha-hexacot, so six generator steps plus a semi-octave period gives the [[3/1|perfect twelfth]]. [[72edo]], [[94edo]], and especially [[166edo]] are good tunings for it.
 [[Subgroup]]: 2.3.5.7
@@ Line 52: / Line 50: @@
 {{Mapping|legend=1| 2 1 5 2 | 0 6 -1 10 }}
 : mapping generators: ~1225/864, ~245/216
 [[Optimal tuning]]s:
-* [[CTE]]: ~1225/864 = 600.000, ~245/216 = 216.919
+* [[WE]]: ~1225/864 = 600.3438{{c}}, ~245/216 = 216.8680{{c}}
-: [[error map]]: {{val| 0.000 -0.443 -3.232 +0.361 }}
+: [[error map]]: {{val| +0.688 -0.403 -1.463 +0.541 }}
-* [[POTE]]: ~1225/864 = 600.000, ~245/216 = 216.744
+* [[CWE]]: ~1225/864 = 600.0000{{c}}, ~245/216 = 216.7977{{c}}
-: error map: {{val| 0.000 -1.492 -3.057 -1.388 }}
+: error map: {{val| 0.000 -1.169 -3.111 -0.849 }}
-{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 382c }}
+{{Optimal ET sequence|legend=1| 22, 50, 72, 238c, 310c, 382c, 454bccd }}
-[[Badness]] (Smith): 0.040846
+[[Badness]] (Sintel): 1.03
 === 11-limit ===
@@ Line 73: / Line 70: @@
 Optimal tunings:
-* CTE: ~99/70 = 600.000, ~25/22 = 216.900
+* WE: ~99/70 = 600.3051{{c}}, ~25/22 = 216.8782{{c}}
-* POTE: ~99/70 = 600.000, ~25/22 = 216.768
+* CWE: ~99/70 = 600.0000{{c}}, ~25/22 = 216.7961{{c}}
 {{Optimal ET sequence|legend=0| 22, 50, 72, 166, 238c, 310c }}
-Badness (Smith): 0.018539
+Badness (Sintel): 0.613
 ==== Lizard ====
@@ Line 88: / Line 85: @@
 Optimal tunings:
-* CTE: ~55/39 = 600.000, ~25/22 = 216.703
+* WE: ~55/39 = 600.4824{{c}}, ~25/22 = 216.7852{{c}}
-* POTE: ~55/39 = 600.000, ~25/22 = 216.711
+* CWE: ~55/39 = 600.0000{{c}}, ~25/22 = 216.6247{{c}}
-{{Optimal ET sequence|legend=0| 22, 50, 72, 122, 194df }}
+{{Optimal ET sequence|legend=0| 22, 50, 72 }}
-Badness (Smith): 0.021781
+Badness (Sintel): 0.900
 ===== 17-limit =====
@@ Line 103: / Line 100: @@
 Optimal tunings:
-* CTE: ~17/12 = 600.000, ~17/15 = 216.748
+* WE: ~17/12 = 600.5032{{c}}, ~17/15 = 216.8002{{c}}
-* POTE: ~17/12 = 600.000, ~17/15 = 216.619
+* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.6361{{c}}
-{{Optimal ET sequence|legend=0| 22, 50, 72, 122g, 194dfg }}
+{{Optimal ET sequence|legend=0| 22, 50, 72 }}
-Badness (Smith): 0.014536
+Badness (Sintel): 0.741
 ===== 19-limit =====
@@ Line 118: / Line 115: @@
 Optimal tunings:
-* CTE: ~17/12 = 600.000, ~17/15 = 216.677
+* WE: ~17/12 = 600.4698{{c}}, ~17/15 = 216.6925{{c}}
-* POTE: ~17/12 = 600.000, ~17/15 = 216.523
+* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.5434{{c}}
 {{Optimal ET sequence|legend=0| 22h, 50, 72, 122g, 194dfg }}
-Badness (Smith): 0.015702
+Badness (Sintel): 0.955
 ==== Gizzard ====
@@ Line 133: / Line 130: @@
 Optimal tunings:
-* CTE: ~99/70 = 600.000, ~25/22 = 216.928
+* WE: ~99/70 = 600.2896{{c}}, ~25/22 = 216.9343{{c}}
-* POTE: ~99/70 = 600.000, ~25/22 = 216.830
+* CWE: ~99/70 = 600.0000{{c}}, ~25/22 = 216.8501{{c}}
 {{Optimal ET sequence|legend=0| 22f, 72, 166, 238cf }}
-Badness (Smith): 0.020252
+Badness (Sintel): 0.837
 ===== 17-limit =====
@@ Line 148: / Line 145: @@
 Optimal tunings:
-* CTE: ~17/12 = 600.000, ~17/15 = 216.943
+* WE: ~17/12 = 600.3227{{c}}, ~17/15 = 216.9414{{c}}
-* POTE: ~17/12 = 600.000, ~17/15 = 216.825
+* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.8469{{c}}
 {{Optimal ET sequence|legend=0| 22f, 72, 166g, 238cfg }}
-Badness (Smith): 0.013624
+Badness (Sintel): 0.694
 ===== 19-limit =====
@@ Line 163: / Line 160: @@
 Optimal tunings:
-* CTE: ~17/12 = 600.000, ~17/15 = 216.918
+* WE: ~17/12 = 600.2637{{c}}, ~17/15 = 216.9570{{c}}
-* POTE: ~17/12 = 600.000, ~17/15 = 216.862
+* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.8687{{c}}
 {{Optimal ET sequence|legend=0| 72, 94, 166g }}
-Badness (Smith): 0.014810
+Badness (Sintel): 0.901
 === Mage ===
@@ Line 178: / Line 175: @@
 Optimal tunings:
-* CTE: ~77/54 = 600.000, ~55/48 = 217.247
+* WE: ~77/54 = 600.6486{{c}}, ~55/48 = 217.1099{{c}}
-* POTE: ~77/54 = 600.000, ~55/48 = 216.876
+* CWE: ~77/54 = 600.0000{{c}}, ~55/48 = 216.9841{{c}}
 {{Optimal ET sequence|legend=0| 22, 50e, 72ee }}
-Badness (Smith): 0.057799
+Badness (Sintel): 1.91
 == Tritonic ==
-: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Tritonic]].''
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Tritonic]].''
+Tritonic tempers out [[50421/50000]] and may be described as the {{nowrap| 29 & 31 }} temperament. It splits the [[6/1|6th]] [[harmonic]] into five generators of [[~]][[10/7]] [[tritone]]s, hence the name. Its [[ploidacot]] is beta-pentacot. [[60edo]] may be used as a tuning, which in the 11-limit entails the 60e val.
 [[Subgroup]]: 2.3.5.7
@@ Line 192: / Line 191: @@
 [[Comma list]]: 225/224, 50421/50000
-{{Mapping|legend=1| 1 4 -3 -3 | 0 -5 11 12 }}
+{{Mapping|legend=1| 1 -1 8 9 | 0 5 -11 -12 }}
+: mapping generators: ~2, ~10/7
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~7/5 = 580.286
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1201.3539{{c}}, ~10/7 = 620.4131{{c}}
+: [[error map]]: {{val| +1.354 -1.243 -0.027 -1.598 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 619.6778{{c}}
+: error map: {{val| 0.000 -3.566 -2.769 -4.959 }}
 {{Optimal ET sequence|legend=1| 29, 31, 60, 91, 122, 213bcd }}
-[[Badness]]: 0.047578
+[[Badness]] (Sintel): 1.20
 === 11-limit ===
@@ Line 205: / Line 209: @@
 Comma list: 121/120, 225/224, 441/440
-Mapping: {{mapping| 1 4 -3 -3 2 | 0 -5 11 12 3 }}
+Mapping: {{mapping| 1 -1 8 9 5 | 0 5 -11 -12 -3 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.267
+Optimal tunings:
+* WE: ~2 = 1201.7116{{c}}, ~10/7 = 620.6166{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6890{{c}}
-{{Optimal ET sequence|legend=1| 29, 31, 60e }}
+{{Optimal ET sequence|legend=0| 29, 31, 60e, 91e, 213bcdeee }}
-Badness: 0.023659
+Badness (Sintel): 0.782
 ==== 13-limit ====
@@ Line 218: / Line 224: @@
 Comma list: 105/104, 121/120, 196/195, 275/273
-Mapping: {{mapping| 1 4 -3 -3 2 -5 | 0 -5 11 12 3 18 }}
+Mapping: {{mapping| 1 -1 8 9 5 13 | 0 5 -11 -12 -3 -18 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.108
+Optimal tunings:
+* WE: ~2 = 1201.5355{{c}}, ~10/7 = 620.6855{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.8469{{c}}
-{{Optimal ET sequence|legend=1| 29, 31, 60e }}
+{{Optimal ET sequence|legend=0| 29, 31, 60e }}
-Badness: 0.022993
+Badness (Sintel): 0.950
 ==== 17-limit ====
@@ Line 231: / Line 239: @@
 Comma list: 105/104, 121/120, 154/153, 196/195, 273/272
-Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 | 0 -5 11 12 3 18 25 }}
+Mapping: {{mapping| 1 -1 8 9 5 13 17 | 0 5 -11 -12 -3 -18 -25 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.055
+Optimal tunings:
+* WE: ~2 = 1201.5260{{c}}, ~10/7 = 620.7330{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.8986{{c}}
-{{Optimal ET sequence|legend=1| 29g, 31, 60e }}
+{{Optimal ET sequence|legend=0| 29g, 31, 60e }}
-Badness: 0.019093
+Badness (Sintel): 0.973
 ==== 19-limit ====
@@ Line 244: / Line 254: @@
 Comma list: 77/76, 105/104, 121/120, 153/152, 196/195, 273/272
-Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 -3 | 0 -5 11 12 3 18 25 15 }}
+Mapping: {{mapping| 1 -1 8 9 5 13 17 12 | 0 5 -11 -12 -3 -18 -25 -15 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.026
+Optimal tunings:
+* WE: ~2 = 1201.3100{{c}}, ~10/7 = 620.6509{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.9328{{c}}
-{{Optimal ET sequence|legend=1| 29g, 31, 60e }}
+{{Optimal ET sequence|legend=0| 29g, 31, 60e }}
-Badness: 0.017010
+Badness (Sintel): 1.03
 ==== 23-limit ====
@@ Line 257: / Line 269: @@
 Comma list: 77/76, 105/104, 115/114, 121/120, 153/152, 161/160, 196/195
-Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 -3 5 | 0 -5 11 12 3 18 25 15 -1 }}
+Mapping: {{mapping| 1 -1 8 9 5 13 17 12 4 | 0 5 -11 -12 -3 -18 -25 -15 1 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.009
+Optimal tunings:
+* WE: ~2 = 1201.4074{{c}}, ~10/7 = 620.7185{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.9548{{c}}
-{{Optimal ET sequence|legend=1| 29g, 31, 60e }}
+{{Optimal ET sequence|legend=0| 29g, 31, 60e }}
-Badness: 0.014471
+Badness (Sintel): 1.04
 === Tritoni ===
@@ Line 270: / Line 284: @@
 Comma list: 225/224, 385/384, 27783/27500
-Mapping: {{mapping| 1 4 -3 -3 17 | 0 -5 11 12 -28 }}
+Mapping: {{mapping| 1 -1 8 9 -11 | 0 5 -11 -12 28 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.389
+Optimal tunings:
+* WE: ~2 = 1201.0888{{c}}, ~10/7 = 620.1733{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6146{{c}}
-{{Optimal ET sequence|legend=1| 31, 91, 122, 153d }}
+{{Optimal ET sequence|legend=0| 31, 91, 122, 153d }}
-Badness: 0.045456
+Badness (Sintel): 1.50
 == Septimin ==
-: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Septimin]].''
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Septimin]].''
+Septimin may be described as the {{nowrap| 41 & 50 }} temperament. It is generated by a septimal minor third ([[7/6]]), which gives rise to the name, but the generator can be taken to be the [[octave complement]], [[12/7]], such that eleven of them [[octave reduction|octave reduced]] give the [[3/2|perfect fifth]]; its [[ploidacot]] is thus eta-hendecacot. [[91edo]] may be recommended as a tuning.
 [[Subgroup]]: 2.3.5.7
@@ Line 285: / Line 303: @@
 [[Comma list]]: 225/224, 84035/82944
-{{Mapping|legend=1| 1 4 1 5 | 0 -11 6 -10 }}
+{{Mapping|legend=1| 1 -7 7 -5 | 0 11 -6 10 }}
+: mapping generators: ~2, ~12/7
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~7/6 = 263.632
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1201.2452{{c}}, ~12/7 = 937.3394{{c}}
+: [[error map]]: {{val| +1.245 +0.062 -1.633 -1.658 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~12/7 = 936.4036{{c}}
+: error map: {{val| 0.000 -1.516 -4.735 -4.790 }}
 {{Optimal ET sequence|legend=1| 41, 91, 132d }}
-[[Badness]]: 0.054502
+[[Badness]] (Sintel): 1.38
 === 11-limit ===
@@ Line 298: / Line 321: @@
 Comma list: 225/224, 245/242, 385/384
-Mapping: {{mapping| 1 4 1 5 5 | 0 -11 6 -10 -7 }}
+Mapping: {{mapping| 1 -7 7 -5 -2 | 0 11 -6 10 7 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~7/6 = 263.634
+Optimal tunings:
+* WE: ~2 = 1200.8059{{c}}, ~12/7 = 936.9952{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3906{{c}}
-{{Optimal ET sequence|legend=1| 41, 91, 223cdef }}
+{{Optimal ET sequence|legend=0| 41, 91, 223cdef }}
-Badness: 0.031309
+Badness (Sintel): 1.04
 === 13-limit ===
@@ Line 311: / Line 336: @@
 Comma list: 105/104, 144/143, 196/195, 245/242
-Mapping: {{mapping| 1 4 1 5 5 7 | 0 -11 6 -10 -7 -15 }}
+Mapping: {{mapping| 1 -7 7 -5 -2 -8 | 0 11 -6 10 7 15 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~7/6 = 263.700
+Optimal tunings:
+* WE: ~2 = 1200.5990{{c}}, ~12/7 = 936.7670{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3196{{c}}
-{{Optimal ET sequence|legend=1| 41, 91 }}
+{{Optimal ET sequence|legend=0| 41, 91 }}
-Badness: 0.023117
+Badness (Sintel): 0.955
 == Merman ==
-: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Merman]].''
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Merman]].''
+Merman may be described as the {{nowrap| 41 & 43 }} temperament. Like [[#Tritonic|tritonic]], it is generated by a [[~]][[10/7]] [[tritone]], but here, seven generator steps give the [[interval class]] of [[3/1|3]]. The [[ploidacot]] for this temperament is gamma-heptacot.
+The name was likely derived from {{w|Triton (mythology)|''Triton''}}, which was in turn derived from ''tritonic''.
 [[Subgroup]]: 2.3.5.7
@@ Line 326: / Line 357: @@
 [[Comma list]]: 225/224, 2500000/2470629
-{{Mapping|legend=1| 1 5 -5 -5 | 0 -7 15 16 }}
+{{Mapping|legend=1| 1 -2 10 11 | 0 7 -15 -16 }}
+: mapping generators: ~2, ~10/7
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~7/5 = 585.585
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.3898{{c}}, ~10/7 = 614.6413{{c}}
+: [[error map]]: {{val| +0.390 -0.435 -1.630 +1.634 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 614.4073{{c}}
+: error map: {{val| 0.000 -1.104 -2.423 +0.657 }}
 {{Optimal ET sequence|legend=1| 41, 84, 125 }}
-[[Badness]]: 0.055078
+[[Badness]] (Sintel): 1.39
 === 11-limit ===
@@ Line 339: / Line 375: @@
 Comma list: 225/224, 441/440, 1344/1331
-Mapping: {{mapping| 1 5 -5 -5 2 | 0 -7 15 16 3 }}
+Mapping: {{mapping| 1 -2 10 11 5 | 0 7 -15 -16 -3 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 585.606
+Optimal tunings:
+* WE: ~2 = 1199.9578{{c}}, ~10/7 = 614.3720{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.3943{{c}}
-{{Optimal ET sequence|legend=1| 41, 84, 125e }}
+{{Optimal ET sequence|legend=0| 41, 84, 125e }}
-Badness: 0.036383
+Badness (Sintel): 1.20
-=== 13-limit ===
+==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
 Comma list: 144/143, 225/224, 364/363, 441/440
-Mapping: {{mapping| 1 5 -5 -5 2 12 | 0 -7 15 16 3 -17 }}
+Mapping: {{mapping| 1 -2 10 11 5 -5 | 0 7 -15 -16 -3 17 }}
+Optimal tunings:
+* WE: ~2 = 1199.7422{{c}}, ~10/7 = 614.2110{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.3442{{c}}
+{{Optimal ET sequence|legend=0| 41, 84, 125e, 209ef, 293ef }}
+Badness (Sintel): 1.14
+=== Mermaid ===
+Subgroup: 2.3.5.7.11
+Comma list: 225/224, 385/384, 532400/531441
+Mapping: {{mapping| 1 -2 10 11 -16 | 0 7 -15 -16 38 }}
+Optimal tunings:
+* WE: ~2 = 1199.4973{{c}}, ~10/7 = 614.7004{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.4470{{c}}
+{{Optimal ET sequence|legend=0| 41, 84e, 125, 166 }}
+Badness (Sintel): 1.46
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 225/224, 325/324, 385/384, 10648/10647
+Mapping: {{mapping| 1 -2 10 11 22 32 | 0 7 -15 -16 38 58 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 585.657
+Optimal tunings:
+* WE: ~2 = 1200.5126{{c}}, ~10/7 = 614.7152{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.4562{{c}}
-{{Optimal ET sequence|legend=1| 41, 84, 125e, 209ef, 293ef }}
+{{Optimal ET sequence|legend=0| 41, 84ef, 125f, 166 }}
-Badness: 0.027544
+Badness (Sintel): 1.47
 == Slender ==
-Slender ({{nowrap|31 &amp; 32}}) tempers out the [[Hewuermera temperaments|hewuermera comma]] in addition to the marvel comma. This temperament has a generator of [[49/48]], 3 of which equal marvel's 16/15~15/14, and 10 generators is 5/4.
+Slender tempers out the [[hewuermera comma]] in addition to the marvel comma, and may be described as the {{nowrap| 31 & 32 }} temperament. This temperament has a generator of [[49/48]], three of which equal marvel's [[16/15]][[~]][[15/14]], and ten generators give [[5/4]]. Its [[ploidacot]] is omega-13-cot.
+The name was likely derived from ''slendro diesis'', one of the names for the interval 49/48.
 [[Subgroup]]: 2.3.5.7
@@ Line 368: / Line 440: @@
 {{Mapping|legend=1| 1 2 2 3 | 0 -13 10 -6 }}
+: mapping generators: ~2, ~49/48
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~49/48 = 38.413
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.3816{{c}}, ~49/48 = 38.4256{{c}}
+: [[error map]]: {{val| +0.382 -0.725 -1.295 +1.765 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/48 = 38.4079{{c}}
+: error map: {{val| 0.000 -1.257 -2.235 +0.727 }}
-{{Optimal ET sequence|legend=1| 31, 94, 125 }}
+{{Optimal ET sequence|legend=1| 31, 94, 125, 406c }}
-[[Badness]]: 0.056934
+[[Badness]] (Sintel): 1.44
 === 11-limit ===
@@ Line 382: / Line 459: @@
 Mapping: {{mapping| 1 2 2 3 4 | 0 -13 10 -6 -17 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~49/48 = 38.387
+Optimal tunings:
+* WE: ~2 = 1199.4983{{c}}, ~49/48 = 38.4030{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 38.3775{{c}}
-{{Optimal ET sequence|legend=1| 31, 63, 94, 125 }}
+{{Optimal ET sequence|legend=0| 31, 63, 94, 125 }}
-Badness: 0.025342
+Badness (Sintel): 0.838
 === 13-limit ===
@@ Line 395: / Line 474: @@
 Mapping: {{mapping| 1 2 2 3 4 3 | 0 -13 10 -6 -17 22 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~49/48 = 38.314
+Optimal tunings:
+* WE: ~2 = 1200.1728{{c}}, ~49/48 = 38.3192{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 38.3129{{c}}
-{{Optimal ET sequence|legend=1| 31, 63, 94 }}
+{{Optimal ET sequence|legend=0| 31, 63, 94 }}
-Badness: 0.025913
+Badness (Sintel): 1.07
 == Triton ==
-: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Stump]].''
+: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Stump]].''
+Triton may be described as the {{nowrap| 19 & 21 }} temperament. Like [[#Tritonic|tritonic]], it is generated by a [[~]][[10/7]] [[tritone]], but here, three generator steps give the [[interval class]] of [[3/1|3]]. The [[ploidacot]] for this temperament is alpha-tricot.
 [[Subgroup]]: 2.3.5.7
@@ Line 409: / Line 492: @@
 {{Mapping|legend=1| 1 0 6 7 | 0 3 -7 -8 }}
+: mapping generators: ~2, ~10/7
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~7/5 = 568.865
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1203.3828{{c}}, ~10/7 = 632.9137{{c}}
+: [[error map]]: {{val| +3.383 -3.214 +3.587 -8.457 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 630.9827{{c}}
+: error map: {{val| 0.000 -9.007 -3.192 -16.687 }}
 {{Optimal ET sequence|legend=1| 2, 17d, 19, 78bd, 97bd }}
-[[Badness]]: 0.059245
+[[Badness]] (Sintel): 1.50
 === 11-limit ===
@@ Line 423: / Line 511: @@
 Mapping: {{mapping| 1 0 6 7 4 | 0 3 -7 -8 -1 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 569.144
+Optimal tunings:
+* WE: ~2 = 1201.3875{{c}}, ~10/7 = 631.5852{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 630.8007{{c}}
-{{Optimal ET sequence|legend=1| 2, 17d, 19, 59bde, 78bde, 97bde }}
+{{Optimal ET sequence|legend=0| 2, 17d, 19 }}
-Badness: 0.045675
+Badness (Sintel): 1.51
 == Marvolo ==
@@ Line 435: / Line 525: @@
 {{Mapping|legend=1| 1 2 1 1 | 0 -6 19 26 }}
+: mapping generators: ~2, ~21/20
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~21/20 = 83.348
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.7714{{c}}, ~21/20 = 83.4014{{c}}
+: [[error map]]: {{val| +0.772 -0.820 -0.916 +0.381 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 83.3640{{c}}
+: error map: {{val| 0.000 -2.139 -2.398 -1.362 }}
-{{Optimal ET sequence|legend=1| 29, 43, 72, 619bcd, 691bcd }}
+{{Optimal ET sequence|legend=1| 29, 43, 72, 619bbccd, 691bbccd }}
-[[Badness]]: 0.083338
+[[Badness]] (Sintel): 2.11
 === 11-limit ===
@@ Line 449: / Line 544: @@
 Mapping: {{mapping| 1 2 1 1 2 | 0 -6 19 26 21 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~21/20 = 83.340
+Optimal tunings:
+* WE: ~2 = 1200.7075{{c}}, ~21/20 = 83.3888{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3564{{c}}
-{{Optimal ET sequence|legend=1| 29, 43, 72 }}
+{{Optimal ET sequence|legend=0| 29, 43, 72 }}
-Badness: 0.028965
+Badness (Sintel): 0.958
 === 13-limit ===
@@ Line 462: / Line 559: @@
 Mapping: {{mapping| 1 2 1 1 2 3 | 0 -6 19 26 21 10 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~21/20 = 83.330
+Optimal tunings:
+* WE: ~2 = 1200.9467{{c}}, ~21/20 = 83.3956{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3516{{c}}
-{{Optimal ET sequence|legend=1| 29, 43, 72, 115f }}
+{{Optimal ET sequence|legend=0| 29, 43, 72 }}
-Badness: 0.021470
+Badness (Sintel): 0.887
 === 17-limit ===
@@ Line 475: / Line 574: @@
 Mapping: {{mapping| 1 2 1 1 2 3 2 | 0 -6 19 26 21 10 30 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~21/20 = 83.330
+Optimal tunings:
+* WE: ~2 = 1200.9606{{c}}, ~21/20 = 83.4030{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3594{{c}}
-{{Optimal ET sequence|legend=1| 29g, 43, 72 }}
+{{Optimal ET sequence|legend=0| 29g, 43, 72 }}
-Badness: 0.014924
+Badness (Sintel): 0.760
 === 19-limit ===
@@ Line 488: / Line 589: @@
 Mapping: {{mapping| 1 2 1 1 2 3 2 3 | 0 -6 19 26 21 10 30 18 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~21/20 = 83.330
+Optimal tunings:
+* WE: ~2 = 1200.7625{{c}}, ~21/20 = 83.3895{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3551{{c}}
+{{Optimal ET sequence|legend=0| 29g, 43, 72 }}
+Badness (Sintel): 0.895
+== Decic ==
+{{Main| Decic }}
-{{Optimal ET sequence|legend=1| 29g, 43, 72 }}
+Named by [[Xenllium]] in 2021, decic tempers out 16807/16384, the [[cloudy comma]], and {{monzo| 11 -10 -10 10 }}, the [[linus comma]], in addition to the marvel comma. It may be described as the {{nowrap| 50 & 60 }} temperament, with a period of 1/10 octave and a [[ploidacot]] signature of decaploid monocot. It is [[support]]ed by [[10edo|10-]], [[50edo|50-]], and [[60edo]].
-Badness: 0.014722
+It can be extended to the 11-, 13-, and 17-limit by adding [[385/384]], [[105/104]], and [[170/169]] to the comma list in this order.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 225/224, 16807/16384
+{{Mapping|legend=1| 10 0 39 28 | 0 1 -1 0 }}
+: mapping generators: ~15/14, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~15/14 = 120.1837{{c}}, ~3/2 = 699.7654{{c}} (~49/48 = 21.3366{{c}})
+: [[error map]]: {{val| +1.837 -0.353 -0.753 -3.683 }}
+* [[CWE]]: ~15/14 = 120.0000{{c}}, ~3/2 = 698.8236{{c}} (~49/48 = 21.1764{{c}})
+: error map: {{val| 0.000 -3.131 -5.137 -8.826 }}
+{{Optimal ET sequence|legend=1| 10, 30b, 40, 50, 60, 110d, 170cdd }}
+[[Badness]] (Sintel): 2.26
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 225/224, 385/384, 3087/3025
+Mapping: {{mapping| 10 0 39 28 3 | 0 1 -1 0 2 }}
+Optimal tunings:
+* WE: ~15/14 = 120.1406{{c}}, ~3/2 = 697.6075{{c}} (~56/55 = 23.2360{{c}})
+* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 697.0142{{c}} (~56/55 = 22.9858{{c}})
+{{Optimal ET sequence|legend=0| 10, 40, 50 }}
+Badness (Sintel): 2.11
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 105/104, 144/143, 196/195, 2200/2197
+Mapping: {{mapping| 10 0 39 28 3 37 | 0 1 -1 0 2 0 }}
+Optimal tunings:
+* WE: ~15/14 = 120.1166{{c}}, ~3/2 = 697.6705{{c}} (~78/77 = 23.0289{{c}})
+* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 697.1492{{c}} (~78/77 = 22.8508{{c}})
+{{Optimal ET sequence|legend=0| 10, 40, 50 }}
+Badness (Sintel): 1.52
+==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 105/104, 144/143, 170/169, 196/195, 221/220
+Mapping: {{mapping| 10 0 39 28 3 37 25 | 0 1 -1 0 2 0 1 }}
+Optimal tunings:
+* WE: ~15/14 = 120.1262{{c}}, ~3/2 = 697.8185{{c}} (~78/77 = 22.9388{{c}})
+* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 697.2757{{c}} (~78/77 = 22.7243{{c}})
+{{Optimal ET sequence|legend=0| 10, 40, 50 }}
+Badness (Sintel): 1.28
+=== Splendecic ===
+Splendecic (50 & 60e) is an alternative extension of decic, tempering out 1617/1600, 2401/2376 and 4375/4356 in the 11-limit. As a temperament of the [[fantastic]] rank-3 temperament, its name is a portmanteau of ''splendid'' and ''decic''.
+Subgroup: 2.3.5.7.11
+Comma list: 225/224, 1617/1600, 2401/2376
+Mapping: {{mapping| 10 0 39 28 82 | 0 1 -1 0 -3 }}
+Optimal tunings:
+* WE: ~15/14 = 120.1874{{c}}, ~3/2 = 699.6085{{c}} (~99/98 = 21.5156{{c}})
+* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 698.3531{{c}} (~99/98 = 21.6469{{c}})
+{{Optimal ET sequence|legend=0| 10e, 40e, 50, 60e, 110de, 170cddee }}
+Badness (Sintel): 1.98
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 105/104, 196/195, 1001/1000, 1188/1183
+Mapping: {{mapping| 10 0 39 28 82 37 | 0 1 -1 0 -3 0 }}
+Optimal tunings:
+* WE: ~15/14 = 120.1565{{c}}, ~3/2 = 699.2756{{c}} (~91/90 = 21.6631{{c}})
+* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 698.2480{{c}} (~91/90 = 21.7520{{c}})
+{{Optimal ET sequence|legend=0| 10e, 40e, 50, 60e, 110de }}
+Badness (Sintel): 1.57
+==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 105/104, 170/169, 196/195, 289/288, 375/374
+Mapping: {{mapping| 10 0 39 28 82 37 25 | 0 1 -1 0 -3 0 1 }}
+Optimal tunings:
+* WE: ~15/14 = 120.1571{{c}}, ~3/2 = 699.2892{{c}} (~91/90 = 21.6536{{c}})
+* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 698.3144{{c}} (~91/90 = 21.6856{{c}})
+{{Optimal ET sequence|legend=0| 10e, 50, 60e, 110deg }}
+Badness (Sintel): 1.33
+=== Prodecic ===
+Prodecic (50e & 60e) is an alternative extension of decic, tempering out 441/440, 1375/1372 and 4375/4356 in the 11-limit. As a temperament of the [[prodigy]] rank-3 temperament, its name is a portmanteau of ''prodigy'' and ''decic''.
+Subgroup: 2.3.5.7.11
+Comma list: 225/224, 441/440, 5929/5832
+Mapping: {{mapping| 10 0 39 28 -13 | 0 1 -1 0 3 }}
+Optimal tunings:
+* WE: ~15/14 = 120.2024{{c}}, ~3/2 = 701.3908{{c}} (~55/54 = 19.8237{{c}})
+* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 700.5235{{c}} (~55/54 = 19.4765{{c}})
+{{Optimal ET sequence|legend=0| 10, 50e, 60e }}
+Badness (Sintel): 2.20
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 105/104, 196/195, 275/273, 5929/5832
+Mapping: {{mapping| 10 0 39 28 -13 37 | 0 1 -1 0 3 0 }}
+Optimal tunings:
+* WE: ~15/14 = 120.1654{{c}}, ~3/2 = 701.4683{{c}} (~91/90 = 19.5242{{c}})
+* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 700.7175{{c}} (~91/90 = 19.2825{{c}})
+{{Optimal ET sequence|legend=0| 10, 50e, 60e }}
+Badness (Sintel): 1.73
+==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 105/104, 154/153, 170/169, 196/195, 289/288
+Mapping: {{mapping| 10 0 39 28 -13 37 25 | 0 1 -1 0 3 0 1 }}
+Optimal tunings:
+* WE: ~15/14 = 120.1577{{c}}, ~3/2 = 701.3950{{c}} (~91/90 = 19.5514{{c}})
+* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 700.6932{{c}} (~91/90 = 19.3068{{c}})
+{{Optimal ET sequence|legend=0| 10, 50e, 60e }}
+Badness (Sintel): 1.41
 == Enneaportent ==
@@ Line 500: / Line 766: @@
 {{Mapping|legend=1| 9 0 28 11 | 0 2 -1 2 }}
+: mapping generators: ~2592/2401, ~12005/6912
-: Mapping generators: ~2592/2401, ~12005/6912
+[[Optimal tuning]]s:
+* [[WE]]: ~2592/2401 = 133.4174{{c}}, ~12005/6912 = 950.7667{{c}} (~1728/1715 = 16.8452{{c}})
+: [[error map]]: {{val| +0.756 -0.422 -1.395 +0.298 }}
+* [[CWE]]: ~2592/2401 = 133.3333{{c}}, ~12005/6912 = 950.2969{{c}} (~1728/1715 = 16.9636{{c}})
+: error map: {{val| 0.000 -1.361 -3.277 -1.565 }}
-[[Optimal tuning]] ([[POTE]]): ~2592/2401 = 133.3333, ~12005/6912 = 950.1680 (~1728/1715 = 16.8347)
+{{Optimal ET sequence|legend=1| 9, 54, 63, 72, 495bccd, 567bcccd }}
-{{Optimal ET sequence|legend=1| 9, 63, 72, 495bcd }}
+[[Badness]] (Sintel): 2.37
-[[Badness]]: 0.093679
 === 11-limit ===
@@ Line 516: / Line 785: @@
 Mapping: {{mapping| 9 0 28 11 24 | 0 2 -1 2 1 }}
-Optimal tuning (POTE): ~121/112 = 133.3333, ~210/121 = 950.1873 (~99/98 = 16.8540)
+Optimal tunings:
+* WE: ~121/112 = 133.4071{{c}}, ~210/121 = 950.7131{{c}} (~99/98 = 16.8633{{c}})
+* CWE: ~121/112 = 133.3333{{c}}, ~210/121 = 950.2994{{c}} (~99/98 = 16.9661{{c}})
-{{Optimal ET sequence|legend=1| 9, 63, 72, 423cd, 495bcd }}
+{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}
-Badness: 0.030426
+Badness (Sintel): 1.01
 === 13-limit ===
@@ Line 529: / Line 800: @@
 Mapping: {{mapping| 9 0 28 11 24 19 | 0 2 -1 2 1 2 }}
-Optimal tuning (POTE): ~14/13 = 133.3333, ~26/15 = 950.2867 (~105/104 = 16.9534)
+Optimal tunings:
+* WE: ~14/13 = 133.4245{{c}}, ~26/15 = 950.9362{{c}} (~105/104 = 16.9650{{c}})
+* CWE: ~14/13 = 133.3333{{c}}, ~26/15 = 950.4364{{c}} (~99/98 = 17.1031{{c}})
-{{Optimal ET sequence|legend=1| 9, 63, 72, 279cf }}
+{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}
-Badness: 0.022322
+Badness (Sintel): 0.922
 == Gracecordial ==
-: ''For the 5-limit version of this temperament, see [[Schismic–Pythagorean equivalence continuum #Gracecordial (5-limit)]].''
+: ''For the 5-limit version, see [[Schismic–Pythagorean equivalence continuum #Gracecordial (5-limit)]].''
 [[Subgroup]]: 2.3.5.7
@@ Line 543: / Line 816: @@
 {{Mapping|legend=1| 1 0 34 63 | 0 1 -20 -38 }}
+: mapping generators: ~2, ~3
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~3/2 = 700.824
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.4904{{c}}, ~3/2 = 701.1103{{c}}
+: [[error map]]: {{val| +0.490 -0.354 -1.655 +1.241 }}
+* [[CWE]]: ~2 = 1200.3333{{c}}, ~3/2 = 700.8112{{c}}
+: error map: {{val| 0.000 -1.144 -2.537 +0.349 }}
-{{Optimal ET sequence|legend=1| 12, 113, 125, 238c, 363c }}
+{{Optimal ET sequence|legend=1| 12, …, 113, 125, 238c, 363c }}
-[[Badness]]: 0.096279
+[[Badness]] (Sintel): 2.44
 === 11-limit ===
@@ Line 557: / Line 835: @@
 Mapping: {{mapping| 1 0 34 63 -90 | 0 1 -20 -38 59 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.834
+Optimal tunings:
+* WE: ~2 = 1200.5571{{c}}, ~3/2 = 701.1589{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8328{{c}}
-{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125, 238c }}
+{{Optimal ET sequence|legend=0| 12e, 113, 125, 238c }}
-Badness: 0.089588
+Badness (Sintel): 2.96
 ==== 13-limit ====
@@ Line 570: / Line 850: @@
 Mapping: {{mapping| 1 0 34 63 -90 -66 | 0 1 -20 -38 59 44 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.841
+Optimal tunings:
+* WE: ~2 = 1200.6282{{c}}, ~3/2 = 701.2080{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8421{{c}}
-{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cf }}
+{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}
-Badness: 0.052235
+Badness (Sintel): 2.16
 ==== 17-limit ====
@@ Line 583: / Line 865: @@
 Mapping: {{mapping| 1 0 34 63 -90 -66 -7 | 0 1 -20 -38 59 44 7 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.841
+Optimal tunings:
+* WE: ~2 = 1200.5058{{c}}, ~3/2 = 701.1360{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8414{{c}}
-{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cf }}
+{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}
-Badness: 0.038565
+Badness (Sintel): 1.96
 ==== 19-limit ====
@@ Line 596: / Line 880: @@
 Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 | 0 1 -20 -38 59 44 7 -3 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.842
+Optimal tunings:
+* WE: ~2 = 1200.4418{{c}}, ~3/2 = 701.0999{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8425{{c}}
-{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cf }}
+{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}
-Badness: 0.028165
+Badness (Sintel): 1.71
 ==== 23-limit ====
@@ Line 609: / Line 895: @@
 Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 | 0 1 -20 -38 59 44 7 -3 30 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.843
+Optimal tunings:
+* WE: ~2 = 1200.4641{{c}}, ~3/2 = 701.1145{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8444{{c}}
-{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 238cfi }}
+{{Optimal ET sequence|legend=0| 12e, 113, 238cfi }}
-Badness: 0.021879
+Badness (Sintel): 1.57
 ==== 29-limit ====
@@ Line 622: / Line 910: @@
 Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 | 0 1 -20 -38 59 44 7 -3 30 34 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.842
+Optimal tunings:
+* WE: ~2 = 1200.4400{{c}}, ~3/2 = 701.0986{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8428{{c}}
-{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cfi }}
+{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}
-Badness: 0.018011
+Badness (Sintel): 1.50
 ==== 31-limit ====
@@ Line 635: / Line 925: @@
 Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 -79 | 0 1 -20 -38 59 44 7 -3 30 34 53 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.838
+Optimal tunings:
+* WE: ~2 = 1200.4178{{c}}, ~3/2 = 701.0822{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8396{{c}}
-{{Optimal ET sequence|legend=1| 12e, 101cdek, 113, 125f, 238cfi }}
+{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}
-Badness: 0.016007
+Badness (Sintel): 1.53
 === Gracecord ===
@@ Line 648: / Line 940: @@
 Mapping: {{mapping| 1 0 34 63 89 | 0 1 -20 -38 -54 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.885
+Optimal tunings:
+* WE: ~2 = 1200.6064{{c}}, ~3/2 = 701.2398{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8718{{c}}
-{{Optimal ET sequence|legend=1| 12, 101cd, 113 }}
+{{Optimal ET sequence|legend=0| 12, …, 101cd, 113 }}
-Badness: 0.066964
+Badness (Sintel): 2.21
 ==== 13-limit ====
@@ Line 661: / Line 955: @@
 Mapping: {{mapping| 1 0 34 63 89 113 | 0 1 -20 -38 -54 -69 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.890
+Optimal tunings:
+* WE: ~2 = 1200.6225{{c}}, ~3/2 = 701.2539{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8781{{c}}
-{{Optimal ET sequence|legend=1| 12f, 101cdf, 113 }}
+{{Optimal ET sequence|legend=0| 12f, …, 101cdf, 113 }}
-Badness: 0.044196
+Badness (Sintel): 1.83
 ==== 17-limit ====
@@ Line 674: / Line 970: @@
 Mapping: {{mapping| 1 0 34 63 89 113 -7 | 0 1 -20 -38 -54 -69 7 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.870
+Optimal tunings:
+* WE: ~2 = 1200.3308{{c}}, ~3/2 = 701.0632{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8654{{c}}
-{{Optimal ET sequence|legend=1| 12f, 101cdf, 113 }}
+{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}
-Badness: 0.036637
+Badness (Sintel): 1.87
 ==== 19-limit ====
@@ Line 687: / Line 985: @@
 Mapping: {{mapping| 1 0 34 63 89 113 -7 9 | 0 1 -20 -38 -54 -69 7 -3 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.866
+Optimal tunings:
+* WE: ~2 = 1200.2658{{c}}, ~3/2 = 701.0213{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8629{{c}}
-{{Optimal ET sequence|legend=1| 12f, 101cdf, 113 }}
+{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}
-Badness: 0.027559
+Badness (Sintel): 1.68
 == Alphorn ==
@@ Line 698: / Line 998: @@
 [[Comma list]]: 225/224, 5764801/5668704
-{{Mapping|legend=1| 1 9 0 13 | 0 -16 5 -22 }}
+{{Mapping|legend=1| 1 -7 5 -9 | 0 16 -5 22 }}
+: mapping generators: ~2, ~35/24
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~48/35 = 556.221
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1201.3004{{c}}, ~35/24 = 644.4767{{c}}
+: [[error map]]: {{val| +1.300 +0.569 -2.195 -2.043 }}
+* [[CWE]]: ~2 = 1200.3333{{c}}, ~35/24 = 643.8137{{c}}
+: error map: {{val| 0.000 -0.936 -5.382 -4.924 }}
-{{Optimal ET sequence|legend=1| 28d, 41, 151cd, 192cd, 233cd }}
+{{Optimal ET sequence|legend=1| 13d, 28d, 41, 151cd, 192cdd, 233ccdd }}
-[[Badness]]: 0.129258
+[[Badness]] (Sintel): 3.27
 === 11-limit ===
@@ Line 711: / Line 1,016: @@
 Comma list: 225/224, 385/384, 12250/11979
-Mapping: {{mapping| 1 9 0 13 3 | 0 -16 5 -22 1 }}
+Mapping: {{mapping| 1 -7 5 -9 4 | 0 16 -5 22 -1 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~11/8 = 556.144
+Optimal tunings:
+* WE: ~2 = 1200.5123{{c}}, ~16/11 = 644.1307{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~16/11 = 643.8662{{c}}
-{{Optimal ET sequence|legend=1| 28d, 41, 315cde }}
+{{Optimal ET sequence|legend=0| 13d, 28d, 41 }}
-Badness: 0.073459
+Badness (Sintel): 2.43
 == Misneb ==
-: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Misneb]].''
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Misneb]].''
 [[Subgroup]]: 2.3.5.7
@@ Line 726: / Line 1,033: @@
 [[Comma list]]: 225/224, 4194304/4117715
-{{Mapping|legend=1| 1 3 1 3 | 0 -15 14 -2 }}
+{{Mapping|legend=1| 1 -12 15 1 | 0 15 -14 2 }}
+: mapping generators: ~2, ~15/8
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~16/15 = 113.235
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.7642{{c}}, ~15/8 = 1086.5513{{c}}
+: [[error map]]: {{val| -0.236 -0.856 -1.569 +4.041 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~15/8 = 1086.7633{{c}}
+: error map: {{val| 0.000 -0.506 -0.999 +4.701 }}
 {{Optimal ET sequence|legend=1| 21, 32, 53 }}
-[[Badness]]: 0.140970
+[[Badness]] (Sintel): 3.57
 === 11-limit ===
@@ Line 739: / Line 1,051: @@
 Comma list: 99/98, 176/175, 1310720/1294139
-Mapping: {{mapping| 1 3 1 3 1 | 0 -15 14 -2 26 }}
+Mapping: {{mapping| 1 -12 15 1 27 | 0 15 -14 2 -26 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~16/15 = 113.323
+Optimal tunings:
+* WE: ~2 = 1200.1654{{c}}, ~15/8 = 1086.8269{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.6766{{c}}
-{{Optimal ET sequence|legend=1| 21, 32e, 53, 127, 180de }}
+{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}
-Badness: 0.085390
+Badness (Sintel): 2.82
 ==== 13-limit ====
@@ Line 752: / Line 1,066: @@
 Comma list: 99/98, 176/175, 640/637, 847/845
-Mapping: {{mapping| 1 3 1 3 1 2 | 0 -15 14 -2 26 18 }}
+Mapping: {{mapping| 1 -12 15 1 27 20 | 0 15 -14 2 -26 -18 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~16/15 = 113.323
+Optimal tunings:
+* WE: ~2 = 1200.1687{{c}}, ~15/8 = 1086.8295{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.6757{{c}}
-{{Optimal ET sequence|legend=1| 21, 32e, 53, 127, 180de }}
+{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}
-Badness: 0.045569
+Badness (Sintel): 1.88
 === Musneb ===
@@ Line 767: / Line 1,083: @@
 Mapping: {{mapping| 1 3 1 3 6 | 0 -15 14 -2 -27 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~16/15 = 113.142
+Optimal tunings:
+* WE: ~2 = 1200.0839{{c}}, ~15/8 = 1086.9343{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.8593{{c}}
-{{Optimal ET sequence|legend=1| 32, 53, 191de, 244cddee, 297cddee }}
+{{Optimal ET sequence|legend=0| 21e, 32, 53 }}
-Badness: 0.087333
+Badness (Sintel): 2.89
 == Untriton ==
-: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Untriton]].''
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Untriton]].''
+Named by [[Petr Pařízek]] in 2011<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>, untriton may be described as the {{nowrap| 51 & 53 }} temperament. Like [[#Tritonic|tritonic]], it is generated by a [[~]][[10/7]] [[tritone]], but here, nine generator steps give the [[interval class]] of [[3/1|3]]. The [[ploidacot]] for this temperament is delta-enneacot.
 [[Subgroup]]: 2.3.5.7
@@ Line 780: / Line 1,100: @@
 [[Comma list]]: 225/224, 125000000/121060821
-{{Mapping|legend=1| 1 6 -7 -7 | 0 -9 19 20 }}
+{{Mapping|legend=1| 1 -3 12 13 | 0 9 -19 -20 }}
+: mapping generators: ~2, ~10/7
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~7/5 = 588.641
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.8275{{c}}, ~10/7 = 611.2710{{c}}
+: [[error map]]: {{val| -0.172 +0.002 -2.533 +3.511 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 611.3614{{c}}
+: error map: {{val| 0.000 +0.298 -2.181 +3.946 }}
-{{Optimal ET sequence|legend=1| 51, 53, 316cd, 369cdd, 422cdd }}
+{{Optimal ET sequence|legend=1| 51, 53 }}
-[[Badness]]: 0.143976
+[[Badness]] (Sintel): 3.64
 === 11-limit ===
@@ Line 793: / Line 1,118: @@
 Comma list: 121/120, 225/224, 22000/21609
-Mapping: {{mapping| 1 6 -7 -7 1 | 0 -9 19 20 5 }}
+Mapping: {{mapping| 1 -3 12 13 6 | 0 9 -19 -20 -5 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 588.626
+Optimal tunings:
+* WE: ~2 = 1200.3591{{c}}, ~10/7 = 611.5569{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3690{{c}}
-{{Optimal ET sequence|legend=1| 51, 53 }}
+{{Optimal ET sequence|legend=0| 51, 53 }}
-Badness: 0.074295
+Badness (Sintel): 2.46
 === 13-limit ===
@@ Line 806: / Line 1,133: @@
 Comma list: 121/120, 225/224, 275/273, 1040/1029
-Mapping: {{mapping| 1 6 -7 -7 1 -12 | 0 -9 19 20 5 32 }}
+Mapping: {{mapping| 1 -3 12 13 6 20 | 0 9 -19 -20 -5 -32 }}
+Optimal tunings:
+* WE: ~2 = 1200.4078{{c}}, ~10/7 = 611.5536{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3392{{c}}
+{{Optimal ET sequence|legend=0| 51f, 53 }}
+Badness (Sintel): 1.96
+== Naiadical ==
+Named by [[Xenllium]] in 2026, naiadical may be described as the {{nowrap| 21 & 29 }} temperament.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 225/224, 823543/800000
+{{Mapping|legend=1| 1 -4 11 9 | 0 9 -14 -10 }}
+: mapping generators: ~2, ~32/21
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1202.1198{{c}}, ~32/21 = 745.4675{{c}}
+: [[error map]]: {{val| +2.120 -1.227 +0.459 -4.423 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~32/21 = 744.1318{{c}}
+: error map: {{val| 0.000 -4.769 -4.159 -10.144 }}
+{{Optimal ET sequence|legend=1| 21, 29, 50, 79d, 129cdd, 179bcddd }}
+[[Badness]] (Sintel): 3.67
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 225/224, 245/242, 1617/1600
+Mapping: {{Mapping| 1 -4 11 9 14 | 0 9 -14 -10 -17 }}
+Optimal tunings:
+* WE: ~2 = 1201.9008{{c}}, ~21/16 = 745.3867{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~32/21 = 744.1777{{c}}
+{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}
+Badness (Sintel): 2.00
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 105/104, 196/195, 245/242, 1001/1000
+Mapping: {{Mapping| 1 -4 11 9 14 13 | 0 9 -14 -10 -17 -15 }}
+Optimal tunings:
+* WE: ~2 = 1201.7863{{c}}, ~20/13 = 745.3344{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.1931{{c}}
+{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}
+Badness (Sintel): 1.43
-Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 588.654
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
-{{Optimal ET sequence|legend=1| 51f, 53 }}
+Comma list: 105/104, 170/169, 196/195, 221/220, 245/242
-Badness: 0.047441
+Mapping: {{Mapping| 1 -4 11 9 14 13 14 | 0 9 -14 -10 -17 -15 -16 }}
+Optimal tunings:
+* WE: ~2 = 1201.9208{{c}}, ~20/13 = 745.3976{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.1669{{c}}
+{{Optimal ET sequence|legend=0| 21, 29g, 50, 79dg }}
+Badness (Sintel): 1.26
 == Quintannic ==
+Named by [[Scott Dakota]], quintannic may be described as the {{nowrap| 43 & 60 }} temperament.
 [[Subgroup]]: 2.3.5.7
@@ Line 820: / Line 1,216: @@
 {{Mapping|legend=1| 1 1 5 7 | 0 5 -23 -36 }}
+: mapping generators: ~2, ~10000/9261
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~10000/9261 = 139.838
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.9803{{c}}, ~10000/9261 = 139.9522{{c}}
+: [[error map]]: {{val| +0.980 -1.214 -0.313 -0.243 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~10000/9261 = 139.8184{{c}}
+: error map: {{val| 0.000 -2.863 -2.136 -2.287 }}
 {{Optimal ET sequence|legend=1| 43, 60, 103, 266bcd, 369bcd }}
-[[Badness]]: 0.150565
+[[Badness]] (Sintel): 3.81
 === 11-limit ===
@@ Line 834: / Line 1,235: @@
 Mapping: {{mapping| 1 1 5 7 8 | 0 5 -23 -36 -39 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~320/297 = 139.827
+Optimal tunings:
+* WE: ~2 = 1201.0031{{c}}, ~320/297 = 139.9435{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~320/297 = 139.8053{{c}}
-{{Optimal ET sequence|legend=1| 43, 60e, 103 }}
+{{Optimal ET sequence|legend=0| 43, 60e, 103, 369bcdeee, 472bbcddeee }}
-Badness: 0.052590
+Badness (Sintel): 1.74
 === 13-limit ===
@@ Line 847: / Line 1,250: @@
 Mapping: {{mapping| 1 1 5 7 8 3 | 0 5 -23 -36 -39 6 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~13/12 = 139.812
+Optimal tunings:
+* WE: ~2 = 1200.8354{{c}}, ~13/12 = 139.9095{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.7997{{c}}
-{{Optimal ET sequence|legend=1| 43, 60e, 103 }}
+{{Optimal ET sequence|legend=0| 43, 60e, 103 }}
-Badness: 0.032730
+Badness (Sintel): 1.35
 === 17-limit ===
@@ Line 860: / Line 1,265: @@
 Mapping: {{mapping| 1 1 5 7 8 3 7 | 0 5 -23 -36 -39 6 -25 }}
-Optimal tuning (POTE): ~2 = 1200.000, ~13/12 = 139.815
+Optimal tunings:
+* WE: ~2 = 1200.7402{{c}}, ~13/12 = 139.9015{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.8038{{c}}
+{{Optimal ET sequence|legend=0| 43, 60e, 103 }}
+Badness (Sintel): 1.17
+== Hendeca ==
+{{Distinguish| Hendec }}
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Hendecatonic]].''
+Hendeca tempers out the same 5-limit comma as [[porwell temperaments #Hendecatonic|hendecatonic]], and has a period of 1/11 octave. However, in this temperament, nine periods represent [[7/4]], the same as [[keemic temperaments #Undeka|undeka]]. It can be tuned to [[22edo]] or [[33edo]] using the [[patent val]], or [[55edo]] using the 55d val. It was named by [[Xenllium]] in 2025 as a low-accuracy variant of hendecatonic.
+[[Subgroup]]: 2.3.5.7
-{{Optimal ET sequence|legend=1| 43, 60e, 103 }}
+[[Comma list]]: 225/224, 122880/117649
-Badness: 0.023038
+{{Mapping|legend=1| 11 0 43 31 | 0 1 -1 0 }}
+: mapping generators: ~16/15, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~16/15 = 108.9526{{c}}, ~3/2 = 702.4215{{c}}
+: [[error map]]: {{val| -1.521 -1.055 -2.252 +8.705 }}
+* [[CWE]]: ~16/15 = 109.0909{{c}}, ~3/2 = 703.2071{{c}}
+: error map: {{val| 0.000 +1.252 +1.388 +12.992 }}
+{{Optimal ET sequence|legend=1| 22, 55d, 77d, 99dd }}
+[[Badness]] (Sintel): 4.37
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 121/120, 225/224, 352/343
+Mapping: {{mapping| 11 0 43 31 38 | 0 1 -1 0 0 }}
+Optimal tunings:
+* WE: ~16/15 = 109.0109{{c}}, ~3/2 = 702.5746{{c}}
+* CWE: ~16/15 = 109.0909{{c}}, ~3/2 = 703.0395{{c}}
+{{Optimal ET sequence|legend=0| 22, 55d }}
+Badness (Sintel): 2.46
 == Gwazy ==
-{{See also| Very high accuracy temperaments #Kwazy }}
+: ''For the 5-limit version, see [[Very high accuracy temperaments #Kwazy]].''
+Named by [[Petr Pařízek]] in 2011<ref name="petr's long post"/>, gwazy may be described as the {{nowrap| 22 & 74 }} temperament.
 [[Subgroup]]: 2.3.5.7
@@ Line 874: / Line 1,321: @@
 {{Mapping|legend=1| 2 1 6 4 | 0 8 -5 6 }}
+: mapping generators: ~2401/1728, ~35/32
-[[Optimal tuning]] ([[POTE]]): ~2401/1728 = 600.000, ~35/32 = 162.658
+[[Optimal tuning]]s:
+* [[WE]]: ~2401/1728 = 599.7132{{c}}, ~35/32 = 162.5806{{c}}
+: [[error map]]: {{val| -0.574 -1.597 -0.937 +5.510 }}
+* [[CWE]]: ~2401/1728 = 600.0000{{c}}, ~35/32 = 162.6388{{c}}
+: error map: {{val| 0.000 -0.844 +0.492 +7.007 }}
 {{Optimal ET sequence|legend=1| 22, 74, 96, 118d }}
-[[Badness]]: 0.178826
+[[Badness]] (Sintel): 4.53
 === 11-limit ===
@@ Line 888: / Line 1,340: @@
 Mapping: {{mapping| 2 1 6 4 8 | 0 8 -5 6 -4 }}
-Optimal tuning (POTE): ~363/256 = 600.000, ~11/10 = 162.592
+Optimal tunings:
+* WE: ~363/256 = 599.8517{{c}}, ~11/10 = 162.5518{{c}}
+* CWE: ~363/256 = 600.0000{{c}}, ~11/10 = 162.5863{{c}}
-{{Optimal ET sequence|legend=1| 22, 74, 96, 118d }}
+{{Optimal ET sequence|legend=0| 22, 74, 96 }}
-Badness: 0.068410
+Badness (Sintel): 2.26
 == Tertiosec ==
-: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Tertiosec]].''
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Tertiosec]].''
+Tertiosec may be described as the {{nowrap| 21 & 75 }} temperament. It was initially named ''tertiomar'' by [[Petr Pařízek]] in 2011<ref name="petr's long post"/>, but was changed to ''tertiosec'' in 2012<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104268.html Yahoo! Tuning Group | ''2D temperament names, part I -- reclassified temperaments from message #101780'']</ref>.
 [[Subgroup]]: 2.3.5.7
@@ Line 901: / Line 1,357: @@
 [[Comma list]]: 225/224, 14495514624/13841287201
-{{Mapping|legend=1| 3 7 5 9 | 0 -8 7 -2 }}
+{{Mapping|legend=1| 3 -1 12 7 | 0 8 -7 2 }}
+: mapping generators: ~3072/2401, ~2048/1715
-[[Optimal tuning]] ([[POTE]]): ~3072/2401 = 400.000, ~15/14 = 112.283
+[[Optimal tuning]]s:
+* [[WE]]: ~3072/2401 = 399.8257{{c}}, ~2048/1715 = 287.5920{{c}}
+: [[error map]]: {{val| -0.523 -1.044 -1.549 +5.138 }}
+* [[CWE]]: ~3072/2401 = 400.0000{{c}}, ~2048/1715 = 287.7088{{c}}
+: error map: {{val| 0.000 -0.284 -0.276 +6.592 }}
 {{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171d }}
-[[Badness]]: 0.431636
+[[Badness]] (Sintel): 10.9
 === 11-limit ===
@@ Line 914: / Line 1,375: @@
 Comma list: 225/224, 3840/3773, 12005/11979
-Mapping: {{mapping| 3 7 5 9 9 | 0 -8 7 -2 5 }}
+Mapping: {{mapping| 3 -1 12 7 14 | 0 8 -7 2 -5 }}
+Optimal tunings:
+* WE: ~44/35 = 399.6550{{c}}, ~33/28 = 287.5803{{c}}
+* CWE: ~44/35 = 400.0000{{c}}, ~33/28 = 287.8224{{c}}
-Optimal tuning (POTE): ~44/35 = 400.000, ~15/14 = 112.171
+{{Optimal ET sequence|legend=0| 21, 54, 75e }}
-{{Optimal ET sequence|legend=1| 21, 54, 75e }}
+Badness (Sintel): 5.74
-Badness: 0.173485
+== References ==
 [[Category:Temperament collections]]
 [[Category:Marvel temperaments| ]] <!-- main article -->
-[[Category:Marvel| ]] <!-- key article -->
 [[Category:Rank 2]]

Marvel temperaments: Difference between revisions