@@ Line 1: / Line 1: @@
-This page discusses miscellaneous rank-2 temperaments tempering out {{monzo|-5 2 2 -1}} = [[225/224]], the marvel comma or septimal kleisma.
+{{Technical data page}}
+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]]'' → [[Pelogic family #Pelogic|Pelogic 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 temperament|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]]
-* ''[[Sharp]]'' → [[Dicot family #Sharp|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, eleventh 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]]
-* ''[[Escapade]]'' → [[Escapade family #Escapade|Escapade family]] (+65625/65536, fourth sliced in nine)
+* ''[[Demibuzzard]]'' (+65536/64827) → [[Buzzardsmic clan #Demibuzzard|Buzzardsmic clan]]
-* ''[[Decic]]'' → [[Cloudy clan #Decic|Cloudy clan]] (+16807/16384, generated by the fifth with a 1/10-octave period)
+* ''[[Escapist]]'' (+65625/65536) → [[Escapade family #Escapist|Escapade family]]
-* ''[[Amavil]]'' → [[Mabila family #Amavil|Mabila family]] (+17496/16807, four octaves and a fourth sliced in ten)
+* ''[[Decic]]'' (+16807/16384) → [[Cloudy clan #Decic|Cloudy clan]]
-* ''[[Betic]]'' → [[Sycamore family #Betic|Sycamore family]] (+1071875/1062882, fifth sliced in eleven)
+* ''[[Amavil]]'' (+17496/16807) → [[Mabila family #Amavil|Mabila family]]
-* ''[[Compton]]'' → [[Compton family #Compton|Compton family]] (+250047/250000, generated by the classical major third with a 1/12-octave period)
+* ''[[Betic]]'' (+1071875/1062882) → [[Sycamore family #Betic|Sycamore family]]
-* ''[[Raccoon]]'' → [[Vavoom family #Raccoon|Vavoom family]] (+41943040/40353607, twelfth sliced in seventeen)
+* ''[[Hendeca]]'' (+122880/117649) → [[11th-octave temperaments #Hendeca|11th-octave temperaments]]
-* ''[[Maquila]]'' → [[Maquila family #Septimal maquila|Maquila family]] (+30233088/28824005, seven octaves and a fifth sliced in seventeen)
+* [[Compton]] (+250047/250000) → [[Compton family #Compton|Compton family]]
-* ''[[Gammy]]'' → [[Gammic family #Gammy|Gammic family]] (+94143178827/91913281250, fifth sliced in twenty)
+* ''[[Raccoon]]'' (+41943040/40353607) → [[Vavoom family #Raccoon|Vavoom family]]
+* ''[[Maquila]]'' (+30233088/28824005) → [[Maquila family #Septimal maquila|Maquila family]]
+* ''[[Gammy]]'' (+94143178827/91913281250) → [[Gammic family #Gammy|Gammic family]]
-Considered below are wizard, tritonic, septimin, slender, triton, merman, marvolo, amavil, enneaportent, submajor, alphorn, tertiosec, gwazy, and gracecordial.
+Considered below are wizard, tritonic, septimin, merman, slender, triton, marvolo, enneaportent, gracecordial, alphorn, misneb, untriton, naiadical, quintannic, gwazy, and tertiosec, in the order of increasing [[badness]].
-Since (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.
-Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is (16/9)/(5/4) = 64/45. Setting this equal to 10/7 gives (10/7)/(64/45) = 225/224.)
+Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is {{nowrap|(16/9)/(5/4) {{=}} 64/45}}. Setting this equal to 10/7 gives {{nowrap|(10/7)/(64/45) {{=}} 225/224}}.)
 == Wizard ==
 {{Main| Wizard }}
-: ''For the 5-limit version of this temperament, see [[High badness 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 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 47: / Line 52: @@
 {{Mapping|legend=1| 2 1 5 2 | 0 6 -1 10 }}
 : mapping generators: ~1225/864, ~245/216
-[[Optimal tuning]] ([[POTE]]): ~1225/864 = 1\2, ~5/4 = 383.256 (~245/216 = 216.744)
+[[Optimal tuning]]s:
+* [[WE]]: ~1225/864 = 600.3438{{c}}, ~245/216 = 216.8680{{c}}
+: [[error map]]: {{val| +0.688 -0.403 -1.463 +0.541 }}
+* [[CWE]]: ~1225/864 = 600.0000{{c}}, ~245/216 = 216.7977{{c}}
+: error map: {{val| 0.000 -1.169 -3.111 -0.849 }}
-{{Multival|legend=1| 12 -2 20 -31 -2 52 }}
+{{Optimal ET sequence|legend=1| 22, 50, 72, 238c, 310c, 382c, 454bccd }}
-{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 382c }}
+[[Badness]] (Sintel): 1.03
-[[Badness]]: 0.040846
-Scales: [[wizard22]]
 === 11-limit ===
@@ Line 67: / Line 71: @@
 Mapping: {{mapping| 2 1 5 2 8 | 0 6 -1 10 -3 }}
-Optimal tuning (POTE): ~99/70 = 1\2, ~5/4 = 383.232 (~25/22 = 216.768)
+Optimal tunings:
+* WE: ~99/70 = 600.3051{{c}}, ~25/22 = 216.8782{{c}}
-{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c }}
+* CWE: ~99/70 = 600.0000{{c}}, ~25/22 = 216.7961{{c}}
-Badness: 0.018539
+{{Optimal ET sequence|legend=0| 22, 50, 72, 166, 238c, 310c }}
-Scales: [[wizard22]]
+Badness (Sintel): 0.613
 ==== Lizard ====
@@ Line 82: / Line 86: @@
 Mapping: {{mapping| 2 1 5 2 8 11 | 0 6 -1 10 -3 -10 }}
-Optimal tuning (POTE): ~55/39 = 1\2, ~5/4 = 383.389 (~25/22 = 216.711)
+Optimal tunings:
+* WE: ~55/39 = 600.4824{{c}}, ~25/22 = 216.7852{{c}}
+* CWE: ~55/39 = 600.0000{{c}}, ~25/22 = 216.6247{{c}}
-{{Optimal ET sequence|legend=1| 22, 50, 72, 122, 194df }}
+{{Optimal ET sequence|legend=0| 22, 50, 72 }}
-Badness: 0.021781
+Badness (Sintel): 0.900
 ===== 17-limit =====
@@ Line 95: / Line 101: @@
 Mapping: {{mapping| 2 1 5 2 8 11 6 | 0 6 -1 10 -3 -10 6 }}
-Optimal tuning (POTE): ~17/12 = 1\2, ~5/4 = 383.381 (~17/15 = 216.619)
+Optimal tunings:
+* WE: ~17/12 = 600.5032{{c}}, ~17/15 = 216.8002{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.6361{{c}}
-{{Optimal ET sequence|legend=1| 22, 50, 72, 122g, 194dfg }}
+{{Optimal ET sequence|legend=0| 22, 50, 72 }}
-Badness: 0.014536
+Badness (Sintel): 0.741
 ===== 19-limit =====
@@ Line 108: / Line 116: @@
 Mapping: {{mapping| 2 1 5 2 8 11 6 2 | 0 6 -1 10 -3 -10 6 18 }}
-Optimal tuning (POTE): ~17/12 = 1\2, ~5/4 = 383.477 (~17/15 = 216.523)
+Optimal tunings:
+* WE: ~17/12 = 600.4698{{c}}, ~17/15 = 216.6925{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.5434{{c}}
-{{Optimal ET sequence|legend=1| 22h, 50, 72, 122g, 194dfg }}
+{{Optimal ET sequence|legend=0| 22h, 50, 72, 122g, 194dfg }}
-Badness: 0.015702
+Badness (Sintel): 0.955
 ==== Gizzard ====
@@ Line 121: / Line 131: @@
 Mapping: {{mapping| 2 1 5 2 8 -2 | 0 6 -1 10 -3 26 }}
-Optimal tuning (POTE): ~99/70 = 1\2, ~5/4 = 383.170 (~25/22 = 216.830)
+Optimal tunings:
+* WE: ~99/70 = 600.2896{{c}}, ~25/22 = 216.9343{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~25/22 = 216.8501{{c}}
-{{Optimal ET sequence|legend=1| 72, 166, 238cf }}
+{{Optimal ET sequence|legend=0| 22f, 72, 166, 238cf }}
-Badness: 0.020252
+Badness (Sintel): 0.837
 ===== 17-limit =====
@@ Line 134: / Line 146: @@
 Mapping: {{mapping| 2 1 5 2 8 -2 6 | 0 6 -1 10 -3 26 6 }}
-Optimal tuning (POTE): ~17/12 = 1\2, ~5/4 = 383.175 (~25/22 = 216.825)
+Optimal tunings:
+* WE: ~17/12 = 600.3227{{c}}, ~17/15 = 216.9414{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.8469{{c}}
-{{Optimal ET sequence|legend=1| 72, 166g, 238cfg }}
+{{Optimal ET sequence|legend=0| 22f, 72, 166g, 238cfg }}
-Badness: 0.013624
+Badness (Sintel): 0.694
 ===== 19-limit =====
@@ Line 147: / Line 161: @@
 Mapping: {{mapping| 2 1 5 2 8 -2 6 15 | 0 6 -1 10 -3 26 6 -18 }}
-Optimal tuning (POTE): ~17/12 = 1\2, ~5/4 = 383.138 (~17/15 = 216.862)
+Optimal tunings:
+* WE: ~17/12 = 600.2637{{c}}, ~17/15 = 216.9570{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.8687{{c}}
-{{Optimal ET sequence|legend=1| 72, 94, 166g }}
+{{Optimal ET sequence|legend=0| 72, 94, 166g }}
-Badness: 0.014810
+Badness (Sintel): 0.901
 === Mage ===
@@ Line 160: / Line 176: @@
 Mapping: {{mapping| 2 1 5 2 4 | 0 6 -1 10 8 }}
-Optimal tuning (POTE): ~77/54 = 1\2, ~5/4 = 383.124 (~55/48 = 216.876)
+Optimal tunings:
+* WE: ~77/54 = 600.6486{{c}}, ~55/48 = 217.1099{{c}}
+* CWE: ~77/54 = 600.0000{{c}}, ~55/48 = 216.9841{{c}}
-{{Optimal ET sequence|legend=1| 22, 50e, 72ee, 94ee }}
+{{Optimal ET sequence|legend=0| 22, 50e, 72ee }}
-Badness: 0.057799
+Badness (Sintel): 1.91
 == Tritonic ==
-: ''For the 5-limit version of this temperament, see [[High badness 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 173: / Line 193: @@
 [[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
-{{Multival|legend=1| 5 -11 -12 -29 -33 3 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1201.3539{{c}}, ~10/7 = 620.4131{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 580.286
+: [[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 188: / Line 211: @@
 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 = 1\1, ~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 201: / Line 226: @@
 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 = 1\1, ~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, 151cde }}
+{{Optimal ET sequence|legend=0| 29, 31, 60e }}
-Badness: 0.022993
+Badness (Sintel): 0.950
-=== Tritoni ===
+==== 17-limit ====
-Subgroup: 2.3.5.7.11
+Subgroup: 2.3.5.7.11.13.17
-Comma list: 225/224, 385/384, 27783/27500
+Comma list: 105/104, 121/120, 154/153, 196/195, 273/272
-Mapping: {{mapping| 1 4 -3 -3 17 | 0 -5 11 12 -28 }}
+Mapping: {{mapping| 1 -1 8 9 5 13 17 | 0 5 -11 -12 -3 -18 -25 }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 580.389
+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| 31, 91, 122, 153d }}
+{{Optimal ET sequence|legend=0| 29g, 31, 60e }}
-Badness: 0.045456
+Badness (Sintel): 0.973
-== Septimin ==
+==== 19-limit ====
-: ''For the 5-limit version of this temperament, see [[High badness temperaments #Septimin]].''
+Subgroup: 2.3.5.7.11.13.17.19
-[[Subgroup]]: 2.3.5.7
+Comma list: 77/76, 105/104, 121/120, 153/152, 196/195, 273/272
-[[Comma list]]: 225/224, 84035/82944
+Mapping: {{mapping| 1 -1 8 9 5 13 17 12 | 0 5 -11 -12 -3 -18 -25 -15 }}
-{{Mapping|legend=1| 1 4 1 5 | 0 -11 6 -10 }}
+Optimal tunings:
+* WE: ~2 = 1201.3100{{c}}, ~10/7 = 620.6509{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.9328{{c}}
-{{Multival|legend=1| 11 -6 10 -35 -15 40 }}
+{{Optimal ET sequence|legend=0| 29g, 31, 60e }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 263.632
+Badness (Sintel): 1.03
-{{Optimal ET sequence|legend=1| 41, 91, 132d }}
+==== 23-limit ====
+Subgroup: 2.3.5.7.11.13.17.19.23
-[[Badness]]: 0.054502
+Comma list: 77/76, 105/104, 115/114, 121/120, 153/152, 161/160, 196/195
-=== 11-limit ===
+Mapping: {{mapping| 1 -1 8 9 5 13 17 12 4 | 0 5 -11 -12 -3 -18 -25 -15 1 }}
-Subgroup: 2.3.5.7.11
-Comma list: 225/224, 385/384, 2401/2376
+Optimal tunings:
+* WE: ~2 = 1201.4074{{c}}, ~10/7 = 620.7185{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.9548{{c}}
-Mapping: {{mapping| 1 4 1 5 5 | 0 -11 6 -10 -7 }}
+{{Optimal ET sequence|legend=0| 29g, 31, 60e }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 263.634
+Badness (Sintel): 1.04
-{{Optimal ET sequence|legend=1| 41, 91, 223cdef }}
+=== Tritoni ===
+Subgroup: 2.3.5.7.11
-Badness: 0.031309
+Comma list: 225/224, 385/384, 27783/27500
-=== 13-limit ===
+Mapping: {{mapping| 1 -1 8 9 -11 | 0 5 -11 -12 28 }}
-Subgroup: 2.3.5.7.11.13
-Comma list: 105/104, 144/143, 196/195, 245/242
+Optimal tunings:
+* WE: ~2 = 1201.0888{{c}}, ~10/7 = 620.1733{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6146{{c}}
-Mapping: {{mapping| 1 4 1 5 5 7 | 0 -11 6 -10 -7 -15 }}
+{{Optimal ET sequence|legend=0| 31, 91, 122, 153d }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 263.700
+Badness (Sintel): 1.50
-{{Optimal ET sequence|legend=1| 41, 91 }}
+== Septimin ==
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Septimin]].''
-Badness: 0.023117
+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.
-== Merman ==
-: ''For the 5-limit version of this temperament, see [[High badness temperaments #Merman]].''
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 225/224, 2500000/2470629
+[[Comma list]]: 225/224, 84035/82944
-{{Mapping|legend=1| 1 5 -5 -5 | 0 -7 15 16 }}
+{{Mapping|legend=1| 1 -7 7 -5 | 0 11 -6 10 }}
+: mapping generators: ~2, ~12/7
-{{Multival|legend=1| 7 -15 -16 -40 -45 5 }}
+[[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 tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 585.585
+{{Optimal ET sequence|legend=1| 41, 91, 132d }}
-{{Optimal ET sequence|legend=1| 41, 84, 125 }}
+[[Badness]] (Sintel): 1.38
-[[Badness]]: 0.055078
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 225/224, 441/440, 1344/1331
+Comma list: 225/224, 245/242, 385/384
-Mapping: {{mapping| 1 5 -5 -5 2 | 0 -7 15 16 3 }}
+Mapping: {{mapping| 1 -7 7 -5 -2 | 0 11 -6 10 7 }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.606
+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, 84, 125e }}
+{{Optimal ET sequence|legend=0| 41, 91, 223cdef }}
-Badness: 0.036383
+Badness (Sintel): 1.04
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 144/143, 225/224, 364/363, 441/440
+Comma list: 105/104, 144/143, 196/195, 245/242
-Mapping: {{mapping| 1 5 -5 -5 2 12 | 0 -7 15 16 3 -17 }}
+Mapping: {{mapping| 1 -7 7 -5 -2 -8 | 0 11 -6 10 7 15 }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.657
+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, 84, 125e, 209ef, 293ef }}
+{{Optimal ET sequence|legend=0| 41, 91 }}
-Badness: 0.027544
+Badness (Sintel): 0.955
-== Slender ==
+== Merman ==
-Slender (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.
+: ''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
-[[Comma list]]: 225/224, 589824/588245
+[[Comma list]]: 225/224, 2500000/2470629
-{{Mapping|legend=1| 1 2 2 3 | 0 -13 10 -6 }}
+{{Mapping|legend=1| 1 -2 10 11 | 0 7 -15 -16 }}
+: mapping generators: ~2, ~10/7
-{{Multival|legend=1| 13 -10 6 -46 -27 42 }}
+[[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 tuning]] ([[POTE]]): ~2 = 1\1, ~49/48 = 38.413
+{{Optimal ET sequence|legend=1| 41, 84, 125 }}
-{{Optimal ET sequence|legend=1| 31, 94, 125 }}
+[[Badness]] (Sintel): 1.39
-[[Badness]]: 0.056934
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 225/224, 385/384, 1331/1323
+Comma list: 225/224, 441/440, 1344/1331
-Mapping: {{mapping| 1 2 2 3 4 | 0 -13 10 -6 -17 }}
+Mapping: {{mapping| 1 -2 10 11 5 | 0 7 -15 -16 -3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~49/48 = 38.387
+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| 31, 63, 94, 125 }}
+{{Optimal ET sequence|legend=0| 41, 84, 125e }}
-Badness: 0.025342
+Badness (Sintel): 1.20
-=== 13-limit ===
+==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 225/224, 275/273, 385/384, 1331/1323
+Comma list: 144/143, 225/224, 364/363, 441/440
-Mapping: {{mapping| 1 2 2 3 4 3 | 0 -13 10 -6 -17 22 }}
+Mapping: {{mapping| 1 -2 10 11 5 -5 | 0 7 -15 -16 -3 17 }}
-Optimal tuning (POTE): ~2 = 1\1, ~49/48 = 38.314
+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=1| 31, 63, 94 }}
+{{Optimal ET sequence|legend=0| 41, 84, 125e, 209ef, 293ef }}
-Badness: 0.025913
+Badness (Sintel): 1.14
-== Triton ==
+=== Mermaid ===
-: ''For the 5-limit version of this temperament, see [[High badness temperaments #Stump]].''
+Subgroup: 2.3.5.7.11
-[[Subgroup]]: 2.3.5.7
+Comma list: 225/224, 385/384, 532400/531441
-[[Comma list]]: 225/224, 1029/1000
+Mapping: {{mapping| 1 -2 10 11 -16 | 0 7 -15 -16 38 }}
-{{Mapping|legend=1| 1 0 6 7 | 0 3 -7 -8 }}
+Optimal tunings:
+* WE: ~2 = 1199.4973{{c}}, ~10/7 = 614.7004{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.4470{{c}}
-{{Multival|legend=1| 3 -7 -8 -18 -21 1 }}
+{{Optimal ET sequence|legend=0| 41, 84e, 125, 166 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 568.865
+Badness (Sintel): 1.46
-{{Optimal ET sequence|legend=1| 2, 17d, 19, 78bd, 97bd }}
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
-[[Badness]]: 0.059245
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 45/44, 56/55, 1029/1000
+Comma list: 225/224, 325/324, 385/384, 10648/10647
-Mapping: {{mapping| 1 0 6 7 4 | 0 3 -7 -8 -1 }}
+Mapping: {{mapping| 1 -2 10 11 22 32 | 0 7 -15 -16 38 58 }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 569.144
+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| 2, 17d, 19, 59bde, 78bde, 97bde }}
+{{Optimal ET sequence|legend=0| 41, 84ef, 125f, 166 }}
-Badness: 0.045675
+Badness (Sintel): 1.47
-== Submajor ==
+== Slender ==
-[[Subgroup]]: 2.3.5
+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.
-[[Comma list]]: 69198046875/68719476736
+The name was likely derived from ''slendro diesis'', one of the names for the interval 49/48.
-{{Mapping|legend=1| 1 4 -1 | 0 -8 11 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10125/8192 = 362.321
-{{Optimal ET sequence|legend=1| 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc }}
-[[Badness]]: 0.130236
-=== 7-limit ===
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 225/224, 51200/50421
+[[Comma list]]: 225/224, 589824/588245
-{{Mapping|legend=1| 1 4 -1 1 | 0 -8 11 6 }}
+{{Mapping|legend=1| 1 2 2 3 | 0 -13 10 -6 }}
+: mapping generators: ~2, ~49/48
-{{Multival|legend=1| 8 -11 -6 -36 -32 17 }}
+[[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 tuning]] ([[POTE]]): ~2 = 1\1, ~49/40 = 362.255
+{{Optimal ET sequence|legend=1| 31, 94, 125, 406c }}
-{{Optimal ET sequence|legend=1| 10, 33, 43, 53 }}
+[[Badness]] (Sintel): 1.44
-[[Badness]]: 0.060533
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 225/224, 385/384, 6655/6561
+Comma list: 225/224, 385/384, 1331/1323
-Mapping: {{mapping| 1 4 -1 1 11 | 0 -8 11 6 -25 }}
+Mapping: {{mapping| 1 2 2 3 4 | 0 -13 10 -6 -17 }}
-Optimal tuning (POTE): ~2 = 1\1, ~27/22 = 362.101
+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| 10, 43e, 53, 116, 169de, 285cde }}
+{{Optimal ET sequence|legend=0| 31, 63, 94, 125 }}
-Badness: 0.050582
+Badness (Sintel): 0.838
-==== 13-limit ====
+=== 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 169/168, 225/224, 275/273, 385/384
+Comma list: 225/224, 275/273, 385/384, 1331/1323
-Mapping: {{mapping| 1 4 -1 1 11 4 | 0 -8 11 6 -25 -1 }}
+Mapping: {{mapping| 1 2 2 3 4 3 | 0 -13 10 -6 -17 22 }}
-Optimal tuning (POTE): ~2 = 1\1, ~16/13 = 362.105
+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| 10, 43e, 53, 116, 169de, 285cdef }}
+{{Optimal ET sequence|legend=0| 31, 63, 94 }}
-Badness: 0.027689
+Badness (Sintel): 1.07
-=== Interpental ===
+== Triton ==
-Subgroup: 2.3.5.7.11
+: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Stump]].''
-Comma list: 99/98, 176/175, 51200/50421
+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.
-Mapping: {{mapping| 1 4 -1 1 -5 | 0 -8 11 6 28 }}
+[[Subgroup]]: 2.3.5.7
-Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 362.418
+[[Comma list]]: 225/224, 1029/1000
-{{Optimal ET sequence|legend=1| 43, 53, 96, 149d }}
+{{Mapping|legend=1| 1 0 6 7 | 0 3 -7 -8 }}
+: mapping generators: ~2, ~10/7
-Badness: 0.051806
+[[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 }}
-==== 13-limit ====
+{{Optimal ET sequence|legend=1| 2, 17d, 19, 78bd, 97bd }}
-Subgroup: 2.3.5.7.11.13
+[[Badness]] (Sintel): 1.50
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-Comma list: 99/98, 169/168, 176/175, 640/637
+Comma list: 45/44, 56/55, 1029/1000
-Mapping: {{mapping| 1 4 -1 1 -5 4 | 0 -8 11 6 28 -1 }}
+Mapping: {{mapping| 1 0 6 7 4 | 0 3 -7 -8 -1 }}
-Optimal tuning (POTE): ~2 = 1\1, ~16/13 = 362.402
+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| 43, 53, 96, 149d }}
+{{Optimal ET sequence|legend=0| 2, 17d, 19 }}
-Badness: 0.029680
+Badness (Sintel): 1.51
 == Marvolo ==
@@ Line 467: / Line 527: @@
 {{Mapping|legend=1| 1 2 1 1 | 0 -6 19 26 }}
+: mapping generators: ~2, ~21/20
-{{Multival|legend=1| 6 -19 -26 -44 -58 -7 }}
+[[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 tuning]] ([[POTE]]): ~2 = 1\1, ~21/20 = 83.348
+{{Optimal ET sequence|legend=1| 29, 43, 72, 619bbccd, 691bbccd }}
-{{Optimal ET sequence|legend=1| 29, 43, 72, 619bcd, 691bcd }}
+[[Badness]] (Sintel): 2.11
-[[Badness]]: 0.083338
 === 11-limit ===
@@ Line 483: / Line 546: @@
 Mapping: {{mapping| 1 2 1 1 2 | 0 -6 19 26 21 }}
-Optimal tuning (POTE): ~2 = 1\1, ~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 496: / Line 561: @@
 Mapping: {{mapping| 1 2 1 1 2 3 | 0 -6 19 26 21 10 }}
-Optimal tuning (POTE): ~2 = 1\1, ~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 509: / Line 576: @@
 Mapping: {{mapping| 1 2 1 1 2 3 2 | 0 -6 19 26 21 10 30 }}
-Optimal tuning (POTE): ~2 = 1\1, ~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 (Sintel): 0.760
 === 19-limit ===
@@ Line 520: / Line 591: @@
 Mapping: {{mapping| 1 2 1 1 2 3 2 3 | 0 -6 19 26 21 10 30 18 }}
-Optimal tuning (POTE): ~2 = 1\1, ~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 }}
-{{Optimal ET sequence|legend=1| 29g, 43, 72 }}
+Badness (Sintel): 0.895
 == Enneaportent ==
@@ Line 530: / Line 605: @@
 {{Mapping|legend=1| 9 0 28 11 | 0 2 -1 2 }}
+: mapping generators: ~2592/2401, ~12005/6912
-{{Multival|legend=1| 18 -9 18 -56 -22 67 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2592/2401 = 133.4174{{c}}, ~12005/6912 = 950.7667{{c}} (~1728/1715 = 16.8452{{c}})
-[[Optimal tuning]] ([[POTE]]): ~2592/2401 = 1\9, ~5/4 = 383.165
+: [[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 ET sequence|legend=1| 9, 63, 72, 495bcd }}
+{{Optimal ET sequence|legend=1| 9, 54, 63, 72, 495bccd, 567bcccd }}
-[[Badness]]: 0.093679
+[[Badness]] (Sintel): 2.37
 === 11-limit ===
@@ Line 546: / Line 624: @@
 Mapping: {{mapping| 9 0 28 11 24 | 0 2 -1 2 1 }}
-Optimal tuning (POTE): ~121/112 = 1\9, ~5/4 = 383.146
+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 559: / Line 639: @@
 Mapping: {{mapping| 9 0 28 11 24 19 | 0 2 -1 2 1 2 }}
-Optimal tuning (POTE): ~14/13 = 1\9, ~5/4 = 383.047
+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 [[High badness temperaments #Gracecordial]].''
+: ''For the 5-limit version, see [[Schismic–Pythagorean equivalence continuum #Gracecordial (5-limit)]].''
 [[Subgroup]]: 2.3.5.7
@@ Line 573: / Line 655: @@
 {{Mapping|legend=1| 1 0 34 63 | 0 1 -20 -38 }}
+: mapping generators: ~2, ~3
-{{Multival|legend=1| 1 -20 -38 -34 -63 -32 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.4904{{c}}, ~3/2 = 701.1103{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 700.824
+: [[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 589: / Line 674: @@
 Mapping: {{mapping| 1 0 34 63 -90 | 0 1 -20 -38 59 }}
-Optimal tuning (POTE): ~2 = 1\1, ~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 602: / Line 689: @@
 Mapping: {{mapping| 1 0 34 63 -90 -66 | 0 1 -20 -38 59 44 }}
-Optimal tuning (POTE): ~2 = 1\1, ~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 615: / Line 704: @@
 Mapping: {{mapping| 1 0 34 63 -90 -66 -7 | 0 1 -20 -38 59 44 7 }}
-Optimal tuning (POTE): ~2 = 1\1, ~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 628: / Line 719: @@
 Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 | 0 1 -20 -38 59 44 7 -3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~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 641: / Line 734: @@
 Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 | 0 1 -20 -38 59 44 7 -3 30 }}
-Optimal tuning (POTE): ~2 = 1\1, ~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 654: / Line 749: @@
 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 = 1\1, ~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 667: / Line 764: @@
 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 = 1\1, ~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 680: / Line 779: @@
 Mapping: {{mapping| 1 0 34 63 89 | 0 1 -20 -38 -54 }}
-Optimal tuning (POTE): ~2 = 1\1, ~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 693: / Line 794: @@
 Mapping: {{mapping| 1 0 34 63 89 113 | 0 1 -20 -38 -54 -69 }}
-Optimal tuning (POTE): ~2 = 1\1, ~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 706: / Line 809: @@
 Mapping: {{mapping| 1 0 34 63 89 113 -7 | 0 1 -20 -38 -54 -69 7 }}
-Optimal tuning (POTE): ~2 = 1\1, ~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 719: / Line 824: @@
 Mapping: {{mapping| 1 0 34 63 89 113 -7 9 | 0 1 -20 -38 -54 -69 7 -3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~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 730: / Line 837: @@
 [[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
-{{Multival|legend=1| 16 -5 22 -45 -10 65 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~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 745: / Line 855: @@
 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 = 1\1, ~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 [[High badness temperaments #Misneb]].''
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Misneb]].''
 [[Subgroup]]: 2.3.5.7
@@ Line 760: / Line 872: @@
 [[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
-{{Multival|legend=1| 15 -14 2 -57 -39 44 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.7642{{c}}, ~15/8 = 1086.5513{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/15 = 113.235
+: [[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 775: / Line 890: @@
 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 = 1\1, ~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 788: / Line 905: @@
 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 = 1\1, ~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 803: / Line 922: @@
 Mapping: {{mapping| 1 3 1 3 6 | 0 -15 14 -2 -27 }}
-Optimal tuning (POTE): ~2 = 1\1, ~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 [[High badness 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 816: / Line 939: @@
 [[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
-{{Multival|legend=1| 9 -19 -20 -51 -57 7 }}
+[[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 tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 588.641
+{{Optimal ET sequence|legend=1| 51, 53 }}
-{{Optimal ET sequence|legend=1| 51, 53, 316cd, 369cdd, 422cdd }}
+[[Badness]] (Sintel): 3.64
-[[Badness]]: 0.143976
 === 11-limit ===
@@ Line 831: / Line 957: @@
 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 = 1\1, ~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 844: / Line 972: @@
 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 (POTE): ~2 = 1\1, ~7/5 = 588.654
+[[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| 51f, 53 }}
+{{Optimal ET sequence|legend=1| 21, 29, 50, 79d, 129cdd, 179bcddd }}
-Badness: 0.047441
+[[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
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 105/104, 170/169, 196/195, 221/220, 245/242
+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 858: / Line 1,055: @@
 {{Mapping|legend=1| 1 1 5 7 | 0 5 -23 -36 }}
+: mapping generators: ~2, ~10000/9261
-{{Multival|legend=1| 5 -23 -36 -48 -71 -19 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.9803{{c}}, ~10000/9261 = 139.9522{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10000/9261 = 139.838
+: [[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 874: / Line 1,074: @@
 Mapping: {{mapping| 1 1 5 7 8 | 0 5 -23 -36 -39 }}
-Optimal tuning (POTE): ~2 = 1\1, ~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 887: / Line 1,089: @@
 Mapping: {{mapping| 1 1 5 7 8 3 | 0 5 -23 -36 -39 6 }}
-Optimal tuning (POTE): ~2 = 1\1, ~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 900: / Line 1,104: @@
 Mapping: {{mapping| 1 1 5 7 8 3 7 | 0 5 -23 -36 -39 6 -25 }}
-Optimal tuning (POTE): ~2 = 1\1, ~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=1| 43, 60e, 103 }}
+{{Optimal ET sequence|legend=0| 43, 60e, 103 }}
-Badness: 0.023038
+Badness (Sintel): 1.17
 == 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 914: / Line 1,122: @@
 {{Mapping|legend=1| 2 1 6 4 | 0 8 -5 6 }}
+: mapping generators: ~2401/1728, ~35/32
-{{Multival|legend=1| 16 -10 12 -53 -26 56 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2401/1728 = 599.7132{{c}}, ~35/32 = 162.5806{{c}}
-[[Optimal tuning]] ([[POTE]]): 1\2, ~35/32 = 162.658
+: [[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 930: / Line 1,141: @@
 Mapping: {{mapping| 2 1 6 4 8 | 0 8 -5 6 -4 }}
-Optimal tuning (POTE): 1\2, ~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 [[High badness 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 943: / Line 1,158: @@
 [[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
-{{Multival|legend=1| 24 -21 6 -89 -58 73 }}
-[[Optimal tuning]] ([[POTE]]): 1\3, ~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 958: / Line 1,176: @@
 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): 1\3, ~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