@@ Line 1: / Line 1: @@
 {{Technical data page}}
-[[Temperament]]s of the '''mirkwai clan''' [[Tempering out|temper out]] the [[mirkwai comma]], {{monzo| 0 3 4 -5 }} = 16875/16807, a no-twos comma.
+The '''canopic clan''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[canopic comma]] ({{monzo|legend=1| 0 3 4 -5 }}, [[ratio]]: 16875/16807), a no-twos comma.
 == Canopus ==
@@ Line 9: / Line 9: @@
 [[Comma list]]: 16875/16807
-{{Mapping|legend=2| 1 3 3 | 0 -5 -4 }}
+{{Mapping|legend=2| 1 -2 -1 | 0 5 4 }}
+: mapping generators: ~3, ~15/7
-: sval mapping generators: ~3, ~7/5
+[[Optimal tuning]]s:
+* [[WE]]: ~3 = 1901.7826{{c}}, ~15/7 = 1317.8771{{c}}
+: [[error map]]: {{val| +1.785 -0.771 -2.248 }}
+* [[CWE]]: ~3 = 1901.9550{{c}}, ~15/7 = 1317.9686{{c}}
+: error map: {{val| 0.000 -0.381 +1.093 }}
-[[Optimal tuning]] ([[POTE]]): ~3 = 1\1edt, ~7/5 = 583.9584
+[[Optimal ET sequence]]: [[13edt|b13]], [[62edt|b62]], [[75edt|b75]], [[88edt|b88]], [[101edt|b101]], [[114edt|b114]], [[355edt|b355]], [[469edt|b469]], [[583edt|b583]], [[697edt|b697]]
-[[Optimal ET sequence]]: [[13edt|b13]], [[62edt|b62]], [[75edt|b75]], [[88edt|b88]], [[101edt|b101]], [[114edt|b114]], [[355edt|b355]], [[469edt|b469]], [[583edt|b583]], [[697edt|b697]]
+[[Badness]] (Sintel): 0.0996
 === Overview to extensions ===
-The full 7-limit extensions' relation to canopus is clearer if the mapping is normalized in terms of 3.5.7.2. In fact, the strong extensions are nusecond and octoid.
+The full 7-limit extensions' relation to canopus is clearer if the mapping is normalized in terms of 3.5.7.2. In fact, the strong extensions are nusecond and octoid. These temperaments are distributed into different temperament collection pages.
+* ''[[Nusecond]]'' (+126/125) → [[Starling temperaments #Nusecond|Starling temperaments]]
+* ''[[Octoid]]'' (+4375/4374) → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]
-The others are weak extensions. Mirkat tempers out [[19683/19600]], splitting the generator in two with a semitwelfth period. Sqrtphi tempers out [[15625/15552]], splitting the period in six. Miracle tempers out [[225/224]]. Pluto tempers out [[4000/3969]]. These split the generator in five. Quanharuk tempers out [[32805/32768]], splitting the generator in three with a 1/5-twelfth period. Semisept tempers out [[1728/1715]] and [[3136/3125]], splitting the generator in six. Kwai tempers out [[5120/5103]], splitting the generator in ten. Grendel tempers out [[6144/6125]], splitting the generator in eleven. Finally, eris tempers out [[65625/65536]], splitting the generator in sixteen.
+The others are weak extensions. Mirkat tempers out [[19683/19600]], splitting the generator in two with a semitwelfth period. Sqrtphi tempers out [[15625/15552]], splitting the period in six. Semisept tempers out [[1728/1715]] and [[3136/3125]], splitting the generator in six. Miracle tempers out [[225/224]]. Pluto tempers out [[4000/3969]]. These split the generator in five. Kwai tempers out [[5120/5103]], splitting the generator in ten. Quanharuk tempers out [[32805/32768]], splitting the generator in three with a 1/5-twelfth period. Grendel tempers out [[6144/6125]], splitting the generator in eleven. Finally, eris tempers out [[65625/65536]], splitting the generator in sixteen.
-Members of the clan considered below are grendel, kwai, pluto, mirkat, eris, subsemifourth, septendesemi, gaster, subsedia, hemiseptisix, browser, and grazer. Discussed elsewhere are:
+Members of the clan discussed elsewhere are:
+* ''[[Kwai]]'' (+5120/5103) → [[Hemifamity temperaments #Kwai|Hemifamity temperaments]]
 * ''[[Octokaidecal]]'' (+28/27 or 50/49) → [[Trienstonic clan #Octokaidecal|Trienstonic clan]]
 * ''[[Meantritone]]'' (+81/80) → [[Meantone family #Meantritone|Meantone family]]
-* ''[[Nusecond]]'' (+126/125) → [[Starling temperaments #Nusecond|Starling temperaments]]
+* ''[[Quanharuk]]'' (+32805/32768) → [[Schismatic family #Quanharuk|Schismatic family]]
 * [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle|Gamelismic clan]]
+* ''[[Pluto]]'' (+4000/3969) → [[Octagar temperaments #Pluto|Octagar temperaments]]
 * ''[[Bohpier]]'' (+245/243) → [[Sensamagic clan #Bohpier|Sensamagic clan]]
+* ''[[Subsedia]]'' (+65536/64827) → [[Buzzardsmic clan #Subsedia|Buzzardsmic clan]]
 * ''[[Semisept]]'' (+1728/1715 or 3136/3125) → [[Hemimean clan #Semisept|Hemimean clan]]
+* ''[[Grendel]]'' (+6144/6125) → [[Porwell temperaments #Grendel|Porwell temperaments]]
 * ''[[Quinmage]]'' (+3125/3072) → [[Magic family #Quinmage|Magic family]]
-* ''[[Octoid]]'' (+4375/4374) → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]
+* ''[[Familia]]'' (+1600000/1594323) → [[Amity family #Familia|Amity family]]
 * [[Sqrtphi]] (+15625/15552) → [[Kleismic family #Sqrtphi|Kleismic family]]
-* ''[[Quanharuk]]'' (+32805/32768) → [[Schismatic family #Quanharuk|Schismatic family]]
-* ''[[Familia]]'' (+1600000/1594323) → [[Amity family #Familia|Amity family]]
 * ''[[Rainwell]]'' (+2100875/2097152) → [[Semicomma family #Rainwell|Semicomma family]]
 * ''[[Quintiquart]]'' (+390625000/387420489) → [[Quartonic family #Quintiquart|Quartonic family]]
-For ''no-twos'' extensions, see [[No-twos subgroup temperaments#Canopus]].
+For ''no-twos'' extensions, see [[No-twos subgroup temperaments #Canopus]].
-== Grendel ==
+Considered below are mirkat, eris, subsemifourth, septendesemi, gaster, hemiseptisix, browser, and grazer, in the order of increasing [[badness]].
-: ''For the 5-limit version of this temperament, see [[Syntonic–31 equivalence continuum #Counterwürschmidt]].''
-[[Subgroup]]: 2.3.5.7
+== Mirkat ==
+Mirkat tempers out 19683/19600, the [[cataharry comma]], as well as 250047/250000, the [[landscape comma]], and may be described as the {{nowrap| 72 & 111 }} temperament with a [[ploidacot]] signature of triploid alpha-hexacot.
-[[Comma list]]: 6144/6125, 16875/16807
-{{Mapping|legend=1| 1 9 2 7 | 0 -23 1 -13 }}
-: mapping generators: ~2, ~5/4
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 386.863
-{{Optimal ET sequence|legend=1| 31, 90, 121, 152, 335d }}
-[[Badness]]: 0.051834
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 540/539, 1375/1372, 5632/5625
-Mapping: {{mapping| 1 9 2 7 17 | 0 -23 1 -13 -42 }}
-Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 386.856
-{{Optimal ET sequence|legend=1| 31, 90e, 121, 152, 335d, 487d }}
-Badness: 0.019845
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 352/351, 540/539, 625/624, 1375/1372
-Mapping: {{mapping| 1 9 2 7 17 -5 | 0 -23 1 -13 -42 27 }}
-Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 386.826
-{{Optimal ET sequence|legend=1| 31, 121, 152f, 425deff }}
-Badness: 0.024839
-=== 17-limit ===
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 256/255, 352/351, 625/624, 715/714, 1275/1274
-Mapping: {{mapping| 1 9 2 7 17 -5 -3 | 0 -23 1 -13 -42 27 22 }}
-Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 386.812
-{{Optimal ET sequence|legend=1| 31, 121, 273defgg }}
-Badness: 0.021400
-=== 19-limit ===
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 256/255, 352/351, 375/374, 400/399, 456/455, 715/714
-Mapping: {{mapping| 1 9 2 7 17 -5 -3 -8 | 0 -23 1 -13 -42 27 22 38 }}
-Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 386.819
-{{Optimal ET sequence|legend=1| 31, 121, 152fg, 273defgg }}
-Badness: 0.018413
-== Kwai ==
-: ''For the 5-limit version of this temperament, see [[High badness temperaments #Kwai]].''
-Named by [[Gene Ward Smith]] in 2004 for its "bridgeability"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10766.html Yahoo! Tuning Group | ''Kwai'']</ref>, kwai is generated by a fifth, and can be described as 41 & 70.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 5120/5103, 16875/16807
-{{Mapping|legend=1| 1 0 -50 -40 | 0 1 33 27 }}
-: mapping generators: ~2, ~3
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.616
-{{Optimal ET sequence|legend=1| 41, 111, 152, 345, 497d }}
-[[Badness]]: 0.054476
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 540/539, 1375/1372, 5120/5103
-Mapping: {{mapping| 1 0 -50 -40 32 | 0 1 33 27 -18 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.623
-{{Optimal ET sequence|legend=1| 29cd, 41, 111, 152 }}
-Badness: 0.026219
-==== 13-limit ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 352/351, 540/539, 729/728, 1375/1372
-Mapping: {{mapping| 1 0 -50 -40 32 27 | 0 1 33 27 -18 -21 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.644
-{{Optimal ET sequence|legend=1| 29cd, 41, 111, 152f }}
-Badness: 0.024555
-===== 17-limit =====
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 256/255, 352/351, 540/539, 715/714, 1089/1088
-Mapping: {{mapping| 1 0 -50 -40 32 27 58 | 0 1 33 27 -18 -21 -34 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.660
-{{Optimal ET sequence|legend=1| 29cdg, 41, 111, 152fg, 263dfg }}
-Badness: 0.021950
-===== 19-limit =====
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 256/255, 352/351, 400/399, 456/455, 715/714, 847/845
-Mapping: {{mapping| 1 0 -50 -40 32 27 58 -56 | 0 1 33 27 -18 -21 -34 38 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.657
-{{Optimal ET sequence|legend=1| 29cdgh, 41, 111, 152fg, 263dfgh }}
-Badness: 0.016957
-==== Hemikwai ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 540/539, 676/675, 1375/1372, 5120/5103
-Mapping: {{mapping| 1 0 -50 -40 32 -51 | 0 2 66 54 -36 69 }}
-: mapping generators: ~2, ~26/15
-Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 951.314
-{{Optimal ET sequence|legend=1| 82, 111, 193, 304d }}
-Badness: 0.044108
-===== 17-limit =====
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 442/441, 540/539, 676/675, 715/714, 5120/5103
-Mapping: {{mapping| 1 0 -50 -40 32 -51 -30 | 0 2 66 54 -36 69 43 }}
-Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 951.314
-{{Optimal ET sequence|legend=1| 82, 111, 193, 304d }}
-Badness: 0.025806
-===== 19-limit =====
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 400/399, 442/441, 540/539, 676/675, 715/714, 1445/1444
-Mapping: {{mapping| 1 0 -50 -40 32 -51 -30 -56 | 0 2 66 54 -36 69 43 76 }}
-Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 951.313
-{{Optimal ET sequence|legend=1| 82, 111, 193, 304dh }}
-Badness: 0.019146
-== Pluto ==
-{{Distinguish| plutus }}
-Pluto, named by [[Gene Ward Smith]] in 2010<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_18465.html Yahoo! Tuning Group | ''19-limit Pluto temperament'']</ref>, can be described as the 41 & 80 temperament. It is generated by a sharpened [[7/5]], and [[121edo|59\121]] is about perfect as a tuning.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 4000/3969, 10976/10935
-{{Mapping|legend=1| 1 5 15 15 | 0 -7 -26 -25 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 585.147
-{{Optimal ET sequence|legend=1| 39d, 41, 80, 121, 404bd }}
-[[Badness]]: 0.057514
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 540/539, 896/891, 1375/1372
-Mapping: {{mapping| 1 5 15 15 2 | 0 -7 -26 -25 3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.114
-{{Optimal ET sequence|legend=1| 39d, 41, 80, 121 }}
-Badness: 0.029844
-==== 13-limit ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 325/324, 352/351, 364/363, 540/539
-Mapping: {{mapping| 1 5 15 15 2 -8 | 0 -7 -26 -25 3 24 }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.123
-{{Optimal ET sequence|legend=1| 39d, 41, 80, 121 }}
-Badness: 0.025717
-===== 17-limit =====
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 256/255, 325/324, 352/351, 364/363, 540/539
-Mapping: {{mapping| 1 5 15 15 2 -8 -12 | 0 -7 -26 -25 3 24 33 }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.116
-{{Optimal ET sequence|legend=1| 39d, 41, 80, 121 }}
-Badness: 0.021463
-===== 19-limit =====
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 190/189, 256/255, 325/324, 352/351, 361/360, 595/594
-Mapping: {{mapping| 1 5 15 15 2 -8 -12 14 | 0 -7 -26 -25 3 24 33 -20 }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.109
-{{Optimal ET sequence|legend=1| 39d, 41, 80, 121 }}
-Badness: 0.017650
-==== Orcus ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 144/143, 196/195, 275/273, 896/891
-Mapping: {{mapping| 1 5 15 15 2 12 | 0 -7 -26 -25 3 -17 }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.111
-{{Optimal ET sequence|legend=1| 39df, 41, 80f, 121ff }}
-Badness: 0.033441
-=== Plutino ===
-Subgroup: 2.3.5.7.11
-Comma list: 100/99, 245/242, 10976/10935
-Mapping: {{mapping| 1 5 15 15 22 | 0 -7 -26 -25 -38 }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.283
-{{Optimal ET sequence|legend=1| 39dee, 41 }}
-Badness: 0.057966
-==== 13-limit ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 100/99, 196/195, 245/242, 729/728
-Mapping: {{mapping| 1 5 15 15 22 12 | 0 -7 -26 -25 -38 -17 }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.232
-{{Optimal ET sequence|legend=1| 39deef, 41 }}
-Badness: 0.040182
-== Mirkat ==
 [[Subgroup]]: 2.3.5.7
@@ Line 334: / Line 58: @@
 {{Mapping|legend=1| 3 2 1 2 | 0 6 13 14 }}
+: mapping generators: ~63/50, ~10/9
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 183.539
+[[Optimal tuning]]s:
+* [[WE]]: ~63/50 = 400.0277{{c}}, ~10/9 = 183.5515{{c}}
+: [[error map]]: {{val| +0.083 -0.591 -0.117 +0.950 }}
+* [[CWE]]: ~63/50 = 400.0000{{c}}, ~10/9 = 183.5470{{c}}
+: error map: {{val| 0.000 -0.673 -0.203 +0.831 }}
 {{Optimal ET sequence|legend=1| 39d, 72, 111, 183, 255 }}
-[[Badness]]: 0.059376
+[[Badness]] (Sintel): 1.50
 === 11-limit ===
@@ Line 348: / Line 77: @@
 Mapping: {{mapping| 3 2 1 2 9 | 0 6 13 14 3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 183.528
+Optimal tunings:
+* WE: ~63/50 = 400.0463{{c}}, ~10/9 = 183.5496{{c}}
+* CWE: ~63/50 = 400.0000{{c}}, ~10/9 = 183.5391{{c}}
-{{Optimal ET sequence|legend=1| 39d, 72, 111, 183, 255 }}
+{{Optimal ET sequence|legend=0| 39d, 72, 111, 183, 255 }}
-Badness: 0.022126
+Badness (Sintel): 0.731
 === 13-limit ===
@@ Line 361: / Line 92: @@
 Mapping: {{mapping| 3 2 1 2 9 1 | 0 6 13 14 3 22 }}
-Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 183.577
+Optimal tunings:
+* WE: ~63/50 = 400.0245{{c}}, ~10/9 = 183.5885{{c}}
+* CWE: ~63/50 = 400.0000{{c}}, ~10/9 = 183.5825{{c}}
-{{Optimal ET sequence|legend=1| 39df, 72, 111, 183 }}
+{{Optimal ET sequence|legend=0| 39df, 72, 111, 183 }}
-Badness: 0.018632
+Badness (Sintel): 0.770
 === 17-limit ===
@@ Line 374: / Line 107: @@
 Mapping: {{mapping| 3 2 1 2 9 1 4 | 0 6 13 14 3 22 18 }}
-Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 183.579
+Optimal tunings:
+* WE: ~34/27 = 400.0257{{c}}, ~10/9 = 183.5906{{c}}
+* CWE: ~34/27 = 400.0000{{c}}, ~10/9 = 183.5843{{c}}
-{{Optimal ET sequence|legend=1| 39dfg, 72, 111, 183 }}
+{{Optimal ET sequence|legend=0| 39dfg, 72, 111, 183 }}
-Badness: 0.011775
+Badness (Sintel): 0.600
 == Eris ==
-The [[2.5.7 subgroup]] restriction of this temperament is [[exodia]].
+Eris tempers out 65625/65536, the [[horwell comma]], and may be described as the {{nowrap| 31 & 224 }} temperament. The [[2.5.7-subgroup|2.5.7 subgroup]] restriction of this temperament is [[exodia]].
 [[Subgroup]]: 2.3.5.7
@@ Line 387: / Line 122: @@
 [[Comma list]]: 16875/16807, 65625/65536
-{{Mapping|legend=1| 1 10 0 6 | 0 -29 8 -11 }}
+{{Mapping|legend=1| 1 -19 8 -5 | 0 29 -8 11 }}
+: mapping generators: ~2, ~49/30
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~60/49 = 348.216
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0256{{c}}, ~49/30 = 851.8023{{c}}
+: [[error map]]: {{val| +0.026 -0.173 -0.528 +0.872 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/30 = 851.7845{{c}}
+: error map: {{val| 0.000 -0.204 -0.590 +0.804 }}
-{{Optimal ET sequence|legend=1| 31, 131, 162, 193, 224, 1823cd, 2271cd }}
+{{Optimal ET sequence|legend=1| 31, 131, 162, 193, 224 }}
-[[Badness]]: 0.074719
+[[Badness]] (Sintel): 1.89
 === 11-limit ===
@@ Line 400: / Line 140: @@
 Comma list: 540/539, 1375/1372, 65625/65536
-Mapping: {{mapping| 1 10 0 6 20 | 0 -29 8 -11 -57 }}
+Mapping: {{mapping| 1 -19 8 -5 -37 | 0 29 -8 11 57 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 348.219
+Optimal tunings:
+* WE: ~2 = 1200.0218{{c}}, ~18/11 = 851.7963{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~18/11 = 851.7812{{c}}
-{{Optimal ET sequence|legend=1| 31, 193, 224, 703, 927d, 1151cd }}
+{{Optimal ET sequence|legend=0| 31, …, 193, 224, 703, 927d }}
-Badness: 0.027621
+Badness (Sintel): 0.913
 === 13-limit ===
@@ Line 413: / Line 155: @@
 Comma list: 540/539, 625/624, 1375/1372, 4096/4095
-Mapping: {{mapping| 1 10 0 6 20 -14 | 0 -29 8 -11 -57 61 }}
+Mapping: {{mapping| 1 -19 8 -5 -37 47 | 0 29 -8 11 57 -61 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 348.213
+Optimal tuning:
+* WE ~2 = 1199.9623{{c}}, ~18/11 = 851.7598{{c}}
+* CWE ~2 = 1200.0000{{c}}, ~18/11 = 851.7865{{c}}
-{{Optimal ET sequence|legend=1| 31, 193, 224 }}
+{{Optimal ET sequence|legend=0| 31, 193, 224 }}
-Badness: 0.025137
+Badness (Sintel): 1.04
 == Subsemifourth ==
@@ Line 426: / Line 170: @@
 [[Comma list]]: 16875/16807, 26873856/26796875
-{{Mapping|legend=1| 1 39 27 45 | 0 -47 -31 -53 }}
+{{Mapping|legend=1| 1 -8 -4 -8 | 0 47 31 53 }}
+: mapping generators: ~2, ~144/125
-: mapping generators: ~2, ~125/72
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9182{{c}}, ~144/125 = 244.7020{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~144/125 = 244.719
+: [[error map]]: {{val| -0.082 -0.305 -0.223 +1.037 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~144/125 = 244.7172{{c}}
+: error map: {{val| 0.000 -0.248 -0.082 +1.184 }}
 {{Optimal ET sequence|legend=1| 49, 103, 152, 255, 407 }}
-[[Badness]]: 0.135173
+[[Badness]] (Sintel): 3.42
 === 11-limit ===
@@ Line 441: / Line 188: @@
 Comma list: 540/539, 1375/1372, 234375/234256
-Mapping: {{mapping| 1 39 27 45 56 | 0 -47 -31 -53 -66 }}
+Mapping: {{mapping| 1 -8 -4 -8 -10 | 0 47 31 53 66 }}
-Optimal tuning (POTE): ~2 = 1\1, ~121/105 = 244.719
+Optimal tunings:
+* WE: ~2 = 1199.9229{{c}}, ~121/105 = 244.7033{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~121/105 = 244.7175{{c}}
-{{Optimal ET sequence|legend=1| 49, 103, 152, 255, 407, 966d }}
+{{Optimal ET sequence|legend=0| 49, 103, 152, 255, 407 }}
-Badness: 0.034276
+Badness (Sintel): 1.13
 === 13-limit ===
@@ Line 454: / Line 203: @@
 Comma list: 540/539, 847/845, 1375/1372, 1575/1573
-Mapping: {{mapping| 1 39 27 45 56 65 | 0 -47 -31 -53 -66 -77 }}
+Mapping: {{mapping| 1 -8 -4 -8 -10 -12 | 0 0 47 31 53 66 77 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/13 = 244.714
+Optimal tunings:
+* WE: ~2 = 1199.9003{{c}}, ~15/13 = 244.6932{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/13 = 244.7116{{c}}
-{{Optimal ET sequence|legend=1| 49f, 103, 152f, 255, 407f, 662df }}
+{{Optimal ET sequence|legend=0| 49f, 103, 152f, 255, 407f }}
-Badness: 0.028387
+Badness (Sintel): 1.17
 == Septendesemi ==
-The name ''septendesemi'' means a septendecimal semitone ([[17/16]]). The septendesemi temperament (80 &amp; 103) tempers out the mirkwai comma and 1959552/1953125 (''parkleiness'' comma, zotritrigu) in the 7-limit. [[183edo]] provides an excellent tuning for 7, 11, 13, and 17-limit septendesemi.
+Septendesemi tempers out the mirkwai comma and 1959552/1953125 (parkleiness comma) in the 7-limit, and may be described as the {{nowrap| 80 & 103 }} temperament. [[183edo]] provides an excellent tuning for 7-, 11-, 13-, and 17-limit septendesemi. Septendesemi was named by [[Xenllium]] in 2021; the name ''septendesemi'' refers to a septendecimal semitone ([[17/16]]).
 [[Subgroup]]: 2.3.5.7
@@ Line 469: / Line 220: @@
 [[Comma list]]: 16875/16807, 1959552/1953125
-{{Mapping|legend=1| 1 39 37 53 | 0 -41 -38 -55 }}
+{{Mapping|legend=1| 1 -2 -1 -2 | 0 41 38 55 }}
+: mapping generators: ~2, ~343/324
-: mapping generators: ~2, ~648/343
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.8649{{c}}, ~343/324 = 104.9046{{c}}
+: [[error map]]: {{val| -0.135 -0.597 +0.195 +1.196 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~343/324 = 104.9134{{c}}
+: error map: {{val| 0.000 -0.506 +0.395 +1.410 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~343/324 = 104.916
+{{Optimal ET sequence|legend=0| 80, 103, 183 }}
-{{Optimal ET sequence|legend=1| 80, 103, 183 }}
+[[Badness]] (Sintel): 3.71
-[[Badness]]: 0.146795
 === 11-limit ===
@@ Line 484: / Line 238: @@
 Comma list: 540/539, 1375/1372, 43923/43750
-Mapping: {{mapping| 1 39 37 53 50 | 0 -41 -38 -55 -51 }}
+Mapping: {{mapping| 1 -2 -1 -2 -1 | 0 41 38 55 51 }}
-Optimal tuning (POTE): ~2 = 1\1, ~35/33 = 104.916
+Optimal tunings:
+* WE: ~2 = 1199.9327{{c}}, ~35/33 = 104.9100{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~35/33 = 104.9144{{c}}
-{{Optimal ET sequence|legend=1| 80, 103, 183 }}
+{{Optimal ET sequence|legend=0| 80, 103, 183 }}
-Badness: 0.041554
+Badness (Sintel): 1.37
 === 13-limit ===
@@ Line 497: / Line 253: @@
 Comma list: 351/350, 540/539, 1375/1372, 4225/4224
-Mapping: {{mapping| 1 39 37 53 50 11 | 0 -41 -38 -55 -51 -8 }}
+Mapping: {{mapping| 1 -2 -1 -2 -1 3 | 0 41 38 55 51 8 }}
-Optimal tuning (POTE): ~2 = 1\1, ~35/33 = 104.908
+Optimal tunings:
+* WE: ~2 = 1200.1082{{c}}, ~35/33 = 104.9170{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~35/33 = 104.9094{{c}}
-{{Optimal ET sequence|legend=1| 80, 103, 183, 469f, 652def }}
+{{Optimal ET sequence|legend=0| 80, 103, 183, 469f }}
-Badness: 0.027908
+Badness (Sintel): 1.15
 === 17-limit ===
@@ Line 510: / Line 268: @@
 Comma list: 351/350, 540/539, 561/560, 715/714, 4225/4224
-Mapping: {{mapping| 1 39 37 53 50 11 5 | 0 -41 -38 -55 -51 -8 -1 }}
+Mapping: {{mapping| 1 -2 -1 -2 -1 3 4 | 0 41 38 55 51 8 1 }}
-Optimal tuning (POTE): ~2 = 1\1, ~17/16 = 104.909
+Optimal tunings:
+* WE: ~2 = 1200.0758{{c}}, ~17/16 = 104.9158{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/16 = 104.9101{{c}}
-{{Optimal ET sequence|legend=1| 80, 103, 183, 469f, 652def }}
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~17/16 = 104.909{{c}}
-Badness: 0.020128
+{{Optimal ET sequence|legend=0| 80, 103, 183, 469f }}
+Badness (Sintel): 1.03
 == Gaster ==
-: ''For the 5-limit version of this temperament, see [[Very high accuracy temperaments #Gaster]].''
+: ''For the 5-limit version, see [[Very high accuracy temperaments #Gaster]].''
 {{Main| Gaster temperament }}
-The ''gaster'' temperament (111 &amp; 113) tempers out {{monzo| -70 72 -19 }} (quadbila-negu) in the 5-limit; mirkwai comma (16875/16807) and [[scheme comma]] (14348907/14336000) in the 7-limit. The word "[[Wiktionary: gaster|gaster]]" means [[Wiktionary: abdomen|abdomen]] or [[Wiktionary: stomach|stomach]], but also a restructuring of the words "gassormic tritone", which is a generator of this temperament. This temperament is sufficient to obtain high prime limit harmonics like a stomach, so that patent vals [[111edo|111]], [[113edo|113]] and [[224edo|224]] support it even in the 41-limit.
+Gaster tempers out {{monzo| -70 72 -19 }} in the 5-limit, mirkwai comma (16875/16807) and [[scheme comma]] (14348907/14336000) in the 7-limit, and may be described as the {{nowrap| 111 & 113 }} temperament.
+It was named by [[Xenllium]] in 2022; the word "[[Wiktionary: gaster|gaster]]" means [[Wiktionary: abdomen|abdomen]] or [[Wiktionary: stomach|stomach]], but also a restructuring of the words "gassormic tritone", which is a generator of this temperament. This temperament is sufficient to obtain high prime limit harmonics like a stomach, so that patent vals [[111edo|111]], [[113edo|113]] and [[224edo|224]] support it even in the 41-limit.
 [[Subgroup]]: 2.3.5.7
@@ Line 528: / Line 292: @@
 [[Comma list]]: 16875/16807, 14348907/14336000
-{{Mapping|legend=1| 1 11 38 37 | 0 -19 -72 -69 }}
+{{Mapping|legend=1| 1 -8 -34 -32 | 0 19 72 69 }}
+: mapping generators: ~2, ~567/400
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~800/567 = 594.641
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9920{{c}}, ~567/400 = 605.3546{{c}}
+: [[error map]]: {{val| -0.008 -0.152 -0.506 +0.902 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~567/400 = 605.3586{{c}}
+: error map: {{val| 0.000 -0.142 -0.497 +0.915 }}
 {{Optimal ET sequence|legend=1| 111, 224 }}
-[[Badness]]: 0.154521
+[[Badness]] (Sintel): 3.91
 === 11-limit ===
@@ Line 541: / Line 310: @@
 Comma list: 540/539, 1375/1372, 14348907/14336000
-Mapping: {{mapping| 1 11 38 37 -1 | 0 -19 -72 -69 9 }}
+Mapping: {{mapping| 1 -8 -34 -32 8 | 0 19 72 69 -9 }}
-Optimal tuning (POTE): ~2 = 1\1, ~512/363 = 594.639
+Optimal tunings:
+* WE: ~2 = 1199.9387{{c}}, ~363/256 = 605.3300{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~363/256 = 605.3603{{c}}
-{{Optimal ET sequence|legend=1| 111, 224, 783d, 1007d, 1231dd }}
+{{Optimal ET sequence|legend=0| 111, 224, 783d }}
-Badness: 0.054060
+Badness (Sintel): 1.79
 === 13-limit ===
@@ Line 554: / Line 325: @@
 Comma list: 540/539, 729/728, 1375/1372, 2200/2197
-Mapping: {{mapping| 1 11 38 37 -1 26 | 0 -19 -72 -69 9 -45 }}
+Mapping: {{mapping| 1 -8 -34 -32 8 -19 | 0 19 72 69 -9 45 }}
-Optimal tuning (POTE): ~2 = 1\1, ~55/39 = 594.639
+Optimal tunings:
+* WE: ~2 = 1199.9154{{c}}, ~78/55 = 605.3183{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~78/55 = 605.3601{{c}}
-{{Optimal ET sequence|legend=1| 111, 224, 783df, 1007df, 1231ddf }}
+{{Optimal ET sequence|legend=0| 111, 224, 783df }}
-Badness: 0.024882
+Badness (Sintel): 1.03
 === 17-limit ===
@@ Line 567: / Line 340: @@
 Comma list: 540/539, 715/714, 729/728, 936/935, 2200/2197
-Mapping: {{mapping| 1 11 38 37 -1 26 14 | 0 -19 -72 -69 9 -45 -20 }}
+Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 | 0 19 72 69 -9 45 20 }}
-Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.636
+Optimal tunings:
+* WE: ~2 = 1199.8076{{c}}, ~17/12 = 605.2674{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3626{{c}}
-{{Optimal ET sequence|legend=1| 111, 224, 559dgg }}
+{{Optimal ET sequence|legend=0| 111, 224, 559dgg }}
-Badness: 0.021436
+Badness (Sintel): 1.09
 === 19-limit ===
@@ Line 580: / Line 355: @@
 Comma list: 324/323, 400/399, 495/494, 540/539, 715/714, 1445/1444
-Mapping: {{mapping| 1 11 38 37 -1 26 14 32 | 0 -19 -72 -69 9 -45 -20 -56 }}
+Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 | 0 19 72 69 -9 45 20 56 }}
-Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.636
+Optimal tunings:
+* WE: ~2 = 1199.7542{{c}}, ~17/12 = 605.2674{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3613{{c}}
-{{Optimal ET sequence|legend=1| 111, 224 }}
+{{Optimal ET sequence|legend=0| 111, 224 }}
-Badness: 0.018370
+Badness (Sintel): 1.12
 === 23-limit ===
@@ Line 593: / Line 370: @@
 Comma list: 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714
-Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 | 0 -19 -72 -69 9 -45 -20 -56 -5 }}
+Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 | 0 19 72 69 -9 45 20 56 5 }}
-Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.641
+Optimal tunings:
+* WE: ~2 = 1199.8733{{c}}, ~17/12 = 605.2946{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3575{{c}}
-{{Optimal ET sequence|legend=1| 111, 224 }}
+{{Optimal ET sequence|legend=0| 111, 224 }}
-Badness: 0.017619
+Badness (Sintel): 1.26
 === 29-limit ===
@@ Line 606: / Line 385: @@
 Comma list: 290/289, 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714
-Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 -11 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 }}
+Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 21 | 0 19 72 69 -9 45 20 56 5 -32 }}
-Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.646
+Optimal tunings:
+* WE: ~2 = 1199.9442{{c}}, ~17/12 = 605.3263{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3541{{c}}
-{{Optimal ET sequence|legend=1| 111, 113, 224 }}
+{{Optimal ET sequence|legend=0| 111, 113, 224 }}
-Badness: 0.016815
+Badness (Sintel): 1.41
 === 31-limit ===
@@ Line 619: / Line 400: @@
 Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 715/714
-Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 -11 0 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 10 }}
+Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 | 0 19 72 69 -9 45 20 56 5 -32 -10 }}
-Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.644
+Optimal tunings:
+* WE: ~2 = 1199.9100{{c}}, ~17/12 = 605.3107{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3556{{c}}
-{{Optimal ET sequence|legend=1| 111, 113, 224 }}
+{{Optimal ET sequence|legend=0| 111, 113, 224 }}
-Badness: 0.014790
+Badness (Sintel): 1.42
 === 37-limit ===
@@ Line 632: / Line 415: @@
 Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 667/666, 715/714
-Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 -11 0 -27 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65 }}
+Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 38 | 0 19 72 69 -9 45 20 56 5 -32 -10 -65 }}
-Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.644
+Optimal tunings:
+* WE: ~2 = 1199.9087{{c}}, ~17/12 = 605.3101{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3559{{c}}
-{{Optimal ET sequence|legend=1| 111, 113, 224 }}
+{{Optimal ET sequence|legend=0| 111, 113, 224 }}
-Badness: 0.014377
+Badness (Sintel): 1.56
 === 41-limit ===
@@ Line 645: / Line 430: @@
 Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 533/532, 540/539, 575/574, 667/666
-Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 -11 0 -27 45 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65 -80 }}
+Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 38 -35 | 0 19 72 69 -9 45 20 56 5 -32 -10 -65 80 }}
-Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.643
-{{Optimal ET sequence|legend=1| 111, 113, 224 }}
-Badness: 0.012858
-== Subsedia ==
+Optimal tunings:
-The generator for ''subsedia'' (10 &amp; 111) is 0.5 cents flat of [[15/14]]-wide semitone and tempers out the mirkwai comma and 65536/64827 (''buzzardisma'', saquadru comma). In this temperament, three generators makes ~[[16/13]], five of them equals ~[[24/17]], twelve of them equals ~[[16/7]], sixteen of them equals ~[[3/1]], and 45 of them equals ~22/1.
+* WE: ~2 = 1199.9179{{c}}, ~17/12 = 605.3156{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3567{{c}}
-[[Subgroup]]: 2.3.5.7
+{{Optimal ET sequence|legend=0| 111, 113, 224 }}
-[[Comma list]]: 16875/16807, 65536/64827
+Badness (Sintel): 1.57
-{{Mapping|legend=1| 1 0 5 4 | 0 16 -27 -12 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~15/14 = 118.965
-{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d }}
-[[Badness]]: 0.157658
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 540/539, 1375/1372, 65536/64827
-Mapping: {{mapping| 1 0 5 4 -1 | 0 16 -27 -12 45 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 118.968
-{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d }}
-Badness: 0.066838
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 352/351, 540/539, 676/675, 1375/1372
-Mapping: {{mapping| 1 0 5 4 -1 4 | 0 16 -27 -12 45 -3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 118.968
-{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d }}
-Badness: 0.031635
-=== 17-limit ===
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 256/255, 352/351, 442/441, 540/539, 715/714
-Mapping: {{mapping| 1 0 5 4 -1 4 3 | 0 16 -27 -12 45 -3 11 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 118.968
-{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232dg }}
-Badness: 0.019707
-=== 19-limit ===
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 256/255, 352/351, 400/399, 442/441, 456/455, 715/714
-Mapping: {{mapping| 1 0 5 4 -1 4 3 10 | 0 16 -27 -12 45 -3 11 -58 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 118.964
-{{Optimal ET sequence|legend=1| 10, 101h, 111, 121, 232dg }}
-Badness: 0.017935
 == Hemiseptisix ==
-The name ''hemiseptisix'' means a half of septimal major sixth ([[12/7]]). The hemiseptisix temperament (103 &amp; 121) tempers out the mirkwai comma and 95703125/95551488 (''pontiqak'' comma, lazozotritriyo) in the 7-limit. [[224edo]] provides an excellent tuning for 7-, 11-, and 13-limit hemiseptisix.
+Hemiseptisix tempers out the mirkwai comma and 95703125/95551488 (pontiqak comma) in the 7-limit, and may be described as the {{nowrap| 103 & 121 }} temperament. [[224edo]] provides an excellent tuning for 7-, 11-, and 13-limit hemiseptisix. Hemiseptisix was named by [[Xenllium]] in 2021; the name ''hemiseptisix'' refers to a half of septimal major sixth ([[12/7]]).
 [[Subgroup]]: 2.3.5.7
@@ Line 727: / Line 447: @@
 [[Comma list]]: 16875/16807, 95703125/95551488
-{{Mapping|legend=1| 1 34 17 34 | 0 -53 -24 -51 }}
+{{Mapping|legend=1| 1 -19 -7 -17 | 0 53 24 51 }}
+: mapping generators: ~2, ~98/75
-: mapping generators: ~2, ~75/49
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~98/75 = 466.071
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.2693{{c}}, ~98/75 = 466.0801{{c}}
+: [[error map]]: {{val| +0.023 -0.149 -0.553 +0.866 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~98/75 = 466.0715{{c}}
+: error map: {{val| 0.000 -0.167 -0.598 +0.819 }}
 {{Optimal ET sequence|legend=1| 103, 121, 224 }}
-[[Badness]]: 0.162826
+[[Badness]] (Sintel): 4.12
 === 11-limit ===
@@ Line 742: / Line 465: @@
 Comma list: 540/539, 1375/1372, 2734375/2725888
-Mapping: {{mapping| 1 34 17 34 53 | 0 -53 -24 -51 -81 }}
+Mapping: {{mapping| 1 -19 -7 -17 -28 | 0 53 24 51 81 }}
-Optimal tuning (POTE): ~2 = 1\1, ~55/42 = 466.070
+Optimal tunings:
+* WE: ~2 = 1200.0183{{c}}, ~55/42 = 466.0767{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~55/42 = 466.0699{{c}}
-{{Optimal ET sequence|legend=1| 103, 121, 224 }}
+{{Optimal ET sequence|legend=0| 103, 121, 224 }}
-Badness: 0.043381
+Badness (Sintel): 1.43
 === 13-limit ===
@@ Line 755: / Line 480: @@
 Comma list: 540/539, 625/624, 1375/1372, 2200/2197
-Mapping: {{mapping| 1 34 17 34 53 30 | 0 -53 -24 -51 -81 -43 }}
+Mapping: {{mapping| 1 -19 -7 -17 -28 -13 | 0 53 24 51 81 43 }}
-Optimal tuning (POTE): ~2 = 1\1, ~55/42 = 466.071
+Optimal tunings:
+* WE: ~2 = 1199.9784{{c}}, ~55/42 = 466.0622{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~55/42 = 466.0703{{c}}
-{{Optimal ET sequence|legend=1| 103, 121, 224 }}
+{{Optimal ET sequence|legend=0| 103, 121, 224 }}
-Badness: 0.021127
+Badness (Sintel): 0.873
 === 17-limit ===
@@ Line 768: / Line 495: @@
 Comma list: 375/374, 540/539, 625/624, 715/714, 2200/2197
-Mapping: {{mapping| 1 34 17 34 53 30 31 | 0 -53 -24 -51 -81 -43 -44 }}
+Mapping: {{mapping| 1 -19 -7 -17 -28 -13 -13 | 0 53 24 51 81 43 44 }}
-Optimal tuning (POTE): ~2 = 1\1, ~17/13 = 466.074
+Optimal tunings:
+* WE: ~2 = 1199.8544{{c}}, ~17/13 = 466.0174{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/13 = 466.0718{{c}}
-{{Optimal ET sequence|legend=1| 103, 121, 224 }}
+{{Optimal ET sequence|legend=0| 103, 121, 224 }}
-Badness: 0.018611
+Badness (Sintel): 0.948
 == Browser ==
 {{See also| Sensipent family }}
+Named by [[Xenllium]] in 2022, browser may be described as the {{nowrap| 103 & 111 }} temperament.
+This can also be considered a [[non-over-1 temperament]], with considerable scope for harmony in the 2.5/3.7/3.11/3.13/3.17/3 subgroup with mos scales of 8, 15, 23, and 31 notes despite no harmonics from the root. It can be considered a detemperament of 8d-et, with a generator very slightly flat of 7\8.
 [[Subgroup]]: 2.3.5.7
@@ Line 783: / Line 516: @@
 [[Comma list]]: 16875/16807, 78732/78125
-{{Mapping|legend=1| 1 6 8 10 | 0 -35 -45 -57 }}
+{{Mapping|legend=1| 1 -29 -37 -47 | 0 35 45 57 }}
+: mapping generators: ~2, ~90/49
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/45 = 151.399
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9313{{c}}, ~90/49 = 1048.5414{{c}}
+: [[error map]]: {{val| -0.069 -1.013 +0.592 +1.264 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~90/49 = 1048.5998{{c}}
+: error map: {{val| 0.000 -0.962 +0.677 +1.362 }}
 {{Optimal ET sequence|legend=1| 103, 111, 214 }}
-[[Badness]]: 0.180645
+[[Badness]] (Sintel): 4.57
 === 11-limit ===
@@ Line 796: / Line 534: @@
 Comma list: 540/539, 1375/1372, 78732/78125
-Mapping: {{mapping| 1 6 8 10 8 | 0 -35 -45 -57 -36 }}
+Mapping: {{mapping| 1 -29 -37 -47 -28 | 0 35 45 57 36 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 151.405
+Optimal tunings:
+* WE: ~2 = 1200.1344{{c}}, ~11/6 = 1048.7124{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1048.5981{{c}}
-{{Optimal ET sequence|legend=1| 103, 214 }}
+{{Optimal ET sequence|legend=0| 103, 214 }}
-Badness: 0.057634
+Badness (Sintel): 1.91
 === 13-limit ===
@@ Line 809: / Line 549: @@
 Comma list: 351/350, 540/539, 847/845, 1375/1372
-Mapping: {{mapping| 1 6 8 10 8 9 | 0 -35 -45 -57 -36 -42 }}
+Mapping: {{mapping| 1 -29 -37 -47 -28 -33 | 0 35 45 57 36 42 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 151.403
+Optimal tunings:
+* WE: ~2 = 1200.1344{{c}}, ~11/6 = 1048.7124{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1048.5984{{c}}
-{{Optimal ET sequence|legend=1| 103, 111, 214 }}
+{{Optimal ET sequence|legend=0| 103, 111, 214 }}
-Badness: 0.028822
+Badness (Sintel): 1.19
 === 17-limit ===
@@ Line 822: / Line 564: @@
 Comma list: 351/350, 540/539, 561/560, 715/714, 847/845
-Mapping: {{mapping| 1 6 8 10 8 9 8 | 0 -35 -45 -57 -36 -42 -31 }}
+Mapping: {{mapping| 1 -29 -37 -47 -28 -33 -23 | 0 35 45 57 36 42 31 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 151.397
+Optimal tunings:
+* WE: ~2 = 1199.9191{{c}}, ~11/6 = 1048.5324{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1048.6014{{c}}
-{{Optimal ET sequence|legend=1| 103, 111, 214 }}
+{{Optimal ET sequence|legend=0| 103, 111, 214 }}
-Badness: 0.020384
+Badness (Sintel): 1.04
 === 19-limit ===
@@ Line 835: / Line 579: @@
 Comma list: 324/323, 351/350, 456/455, 495/494, 540/539, 715/714
-Mapping: {{mapping| 1 6 8 10 8 9 8 18 | 0 -35 -45 -57 -36 -42 -31 -109 }}
+Mapping: {{mapping| 1 -29 -37 -47 -28 -33 -23 -91 | 0 35 45 57 36 42 31 109 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 151.396
+Optimal tunings:
+* WE: ~2 = 1199.9145{{c}}, ~11/6 = 1048.5290{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1048.6021{{c}}
-{{Optimal ET sequence|legend=1| 103h, 111, 214 }}
+{{Optimal ET sequence|legend=0| 103h, 111, 214 }}
-Badness: 0.017570
+Badness (Sintel): 1.07
 == Grazer ==
+Named by [[Xenllium]] in 2022, grazer may be described as the {{nowrap| 113 & 121 }} temperament.
 [[Subgroup]]: 2.3.5.7
 [[Comma list]]: 16875/16807, 1071875/1062882
-{{Mapping|legend=1| 1 34 47 58 | 0 -37 -51 -63 }}
+{{Mapping|legend=1| 1 -3 -4 -5 | 0 37 51 63 }}
+: mapping generators: ~2, ~49/45
-: mapping generators: ~2, ~90/49
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0310{{c}}, ~49/45 = 148.7229{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/45 = 148.719
+: [[error map]]: {{val| +0.031 +0.700 -1.561 +0.563 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/45 = 148.7198{{c}}
+: error map: {{val| 0.000 +0.676 -1.606 +0.519 }}
 {{Optimal ET sequence|legend=1| 113, 121, 234 }}
-[[Badness]]: 0.217166
+[[Badness]] (Sintel): 5.50
 === 11-limit ===
@@ Line 863: / Line 614: @@
 Comma list: 540/539, 1375/1372, 218750/216513
-Mapping: {{mapping| 1 34 47 58 35 | 0 -37 -51 -63 -36 }}
+Mapping: {{mapping| 1 -3 -4 -5 -1 | 0 37 51 63 36 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 148.729
+Optimal tunings:
+* WE: ~2 = 1199.7242{{c}}, ~12/11 = 148.6946{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 148.7230{{c}}
-{{Optimal ET sequence|legend=1| 113, 121, 234, 355e, 589cee }}
+{{Optimal ET sequence|legend=0| 113, 121, 234 }}
-Badness: 0.076062
+Badness (Sintel): 2.51
 === 13-limit ===
@@ Line 876: / Line 629: @@
 Comma list: 325/324, 364/363, 540/539, 2200/2197
-Mapping: {{mapping| 1 34 47 58 35 44 | 0 -37 -51 -63 -36 -46 }}
+Mapping: {{mapping| 1 -3 -4 -5 -1 -2 | 0 37 51 63 36 46 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 148.729
+Optimal tunings:
+* WE: ~2 = 1199.7257{{c}}, ~12/11 = 148.6947{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 148.7230{{c}}
-{{Optimal ET sequence|legend=1| 113, 121, 234, 355e, 589cee }}
+{{Optimal ET sequence|legend=0| 113, 121, 234 }}
-Badness: 0.036248
+Badness (Sintel): 1.50
 === 17-limit ===
@@ Line 889: / Line 644: @@
 Comma list: 325/324, 364/363, 540/539, 595/594, 2000/1989
-Mapping: {{mapping| 1 34 47 58 35 44 33 | 0 -37 -51 -63 -36 -46 -33 }}
+Mapping: {{mapping| 1 -3 -4 -5 -1 -2 0 | 0 37 51 63 36 46 33 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 148.735
+Optimal tunings:
+* WE: ~2 = 1199.5690{{c}}, ~12/11 = 148.6815{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 148.7267{{c}}
-{{Optimal ET sequence|legend=1| 113, 121, 234g, 355eg }}
+{{Optimal ET sequence|legend=0| 113, 121, 234g }}
-Badness: 0.025410
+Badness (Sintel): 1.29
 === 19-limit ===
@@ Line 902: / Line 659: @@
 Comma list: 325/324, 364/363, 400/399, 540/539, 595/594, 665/663
-Mapping: {{mapping| 1 34 47 58 35 44 33 6 | 0 -37 -51 -63 -36 -46 -33 -2 }}
+Mapping: {{mapping| 1 -3 -4 -5 -1 -2 0 4 | 0 37 51 63 36 46 33 2 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 148.727
-{{Optimal ET sequence|legend=1| 113, 121, 234g, 355eg, 589ceegg }}
+Optimal tunings:
+* WE: ~2 = 1199.7269{{c}}, ~12/11 = 148.6928{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 148.7227{{c}}
-Badness: 0.022574
+{{Optimal ET sequence|legend=0| 113, 121, 234g }}
-== Notes ==
+Badness (Sintel): 1.37
 [[Category:Temperament clans]]
-[[Category:Pages with mostly numerical content]]
 [[Category:Mirkwai clan| ]] <!-- main article -->
-[[Category:Mirkwai| ]] <!-- key article -->
 [[Category:Rank 2]]

Canopic clan: Difference between revisions