@@ 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)
+* ''[[Quintapole]]'' (+7812500/7411887) → [[Quintaleap family #Quintapole|Quintaleap family]]
-* ''[[Qintosec]]'' → [[Quintosec family #Qintosec|Quintosec family]] (+2560000/2470629, generated by the classical minor second with a 1/5-octave period)
+* ''[[Houborizic]]'' (+1250000/1240029) → [[Amity family #Houborizic|Amity family]]
-* [[Miracle]] → [[Gamelismic clan #Miracle|Gamelismic clan]] (+1029/1024, fifth sliced in six)
+* ''[[Qintosec]]'' (+2560000/2470629) → [[Quintosec family #Qintosec|Quintosec family]]
-* [[Catakleismic]] → [[Kleismic family #Catakleismic|Kleismic family]] (+4375/4374, twelfth sliced in six)
+* [[Miracle]] (+1029/1024) → [[Gamelismic clan #Miracle|Gamelismic clan]]
-* ''[[Marvo]]'' → [[Gravity family #Marvo|Gravity family]] (+78125000/78121827, two octaves and a fifth sliced in six)
+* [[Catakleismic]] (+4375/4374) → [[Kleismic family #Catakleismic|Kleismic family]]
-* [[Orwell]] → [[Semicomma family #Orwell|Semicomma family]] (+1728/1715, eleventh sliced in seven)
+* ''[[Marvo]]'' (+78125000/78121827) → [[Gravity family #Marvo|Gravity family]]
-* ''[[Snipes]]''  → [[Wesley family #Snipes|Wesley family]] (+6125/5832, two octaves and a fourth sliced in seven)
+* [[Orwell]] (+1728/1715) → [[Semicomma family #Orwell|Semicomma family]]
-* ''[[Escapade]]'' → [[Escapade family #Escapade|Escapade family]] (+65625/65536, fourth sliced in nine)
+* ''[[Snipes]]'' (+6125/5832)  → [[Wesley family #Snipes|Wesley family]]
-* ''[[Decic]]'' → [[Cloudy clan #Decic|Cloudy clan]] (+16807/16384, generated by the fifth with a 1/10-octave period)
+* ''[[Demibuzzard]]'' (+65536/64827) → [[Buzzardsmic clan #Demibuzzard|Buzzardsmic clan]]
-* ''[[Amavil]]'' → [[Mabila family #Amavil|Mabila family]] (+17496/16807, four octaves and a fourth sliced in ten)
+* ''[[Escapist]]'' (+65625/65536) → [[Escapade family #Escapist|Escapade family]]
-* ''[[Betic]]'' → [[Sycamore family #Betic|Sycamore family]] (+1071875/1062882, fifth sliced in eleven)
+* ''[[Decic]]'' (+16807/16384) → [[Cloudy clan #Decic|Cloudy clan]]
-* ''[[Compton]]'' → [[Compton family #Compton|Compton family]] (+250047/250000, generated by the classical major third with a 1/12-octave period)
+* ''[[Amavil]]'' (+17496/16807) → [[Mabila family #Amavil|Mabila family]]
-* ''[[Maquila]]'' → [[Maquila family #Septimal maquila|Maquila family]] (+30233088/28824005, seven octaves and a fifth sliced in seventeen)
+* ''[[Betic]]'' (+1071875/1062882) → [[Sycamore family #Betic|Sycamore family]]
-* ''[[Gammy]]'' → [[Gammic family #Gammy|Gammic family]] (+94143178827/91913281250, fifth sliced in twenty)
+* ''[[Hendeca]]'' (+122880/117649) → [[11th-octave temperaments #Hendeca|11th-octave temperaments]]
+* [[Compton]] (+250047/250000) → [[Compton family #Compton|Compton family]]
+* ''[[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 46: / Line 53: @@
 {{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 66: / Line 72: @@
 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 81: / Line 87: @@
 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 94: / Line 102: @@
 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 107: / Line 117: @@
 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 120: / Line 132: @@
 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 133: / Line 147: @@
 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 146: / Line 162: @@
 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 159: / Line 177: @@
 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 172: / Line 194: @@
 [[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 187: / Line 212: @@
 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 200: / Line 227: @@
 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 466: / Line 528: @@
 {{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 482: / Line 547: @@
 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 495: / Line 562: @@
 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 508: / Line 577: @@
 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 519: / Line 592: @@
 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 529: / Line 606: @@
 {{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 545: / Line 625: @@
 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 558: / Line 640: @@
 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 572: / Line 656: @@
 {{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 588: / Line 675: @@
 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 601: / Line 690: @@
 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 614: / Line 705: @@
 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 627: / Line 720: @@
 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 640: / Line 735: @@
 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 653: / Line 750: @@
 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 666: / Line 765: @@
 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 679: / Line 780: @@
 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 692: / Line 795: @@
 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 705: / Line 810: @@
 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 718: / Line 825: @@
 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 729: / Line 838: @@
 [[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 744: / Line 856: @@
 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 759: / Line 873: @@
 [[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 774: / Line 891: @@
 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 787: / Line 906: @@
 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 802: / Line 923: @@
 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 815: / Line 940: @@
 [[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 830: / Line 958: @@
 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 843: / Line 973: @@
 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 857: / Line 1,056: @@
 {{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 873: / Line 1,075: @@
 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 886: / Line 1,090: @@
 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 899: / Line 1,105: @@
 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 913: / Line 1,123: @@
 {{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 929: / Line 1,142: @@
 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 942: / Line 1,159: @@
 [[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 957: / Line 1,177: @@
 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