@@ Line 1: / Line 1: @@
-[[Temperament]]s of the '''mirkwai clan''' [[Tempering out|temper out]] the [[mirkwai comma]], {{monzo| 0 3 4 -5 }} = 16875/16807, a no-twos comma.
+{{Technical data page}}
+The '''canopus clan''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the '''canopus''' or '''[[mirkwai comma]]''' ({{monzo|legend=1| 0 3 4 -5 }}, [[ratio]]: 16875/16807), a no-twos comma.
 == Canopus ==
@@ Line 8: / 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]]
-== Grendel ==
+For ''no-twos'' extensions, see [[No-twos subgroup temperaments #Canopus]].
-: ''For the 5-limit version of this temperament, see [[Syntonic-31 equivalence continuum #Counterwürschmidt]].''
-[[Subgroup]]: 2.3.5.7
+Considered below are mirkat, eris, subsemifourth, septendesemi, gaster, hemiseptisix, browser, and grazer, in the order of increasing [[badness]].
-[[Comma list]]: 6144/6125, 16875/16807
+== 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.
-{{Mapping|legend=1| 1 9 2 7 | 0 -23 1 -13 }}
-: mapping generators: ~2, ~5/4
-{{Multival|legend=1| 23 -1 13 -55 -44 33 }}
-[[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]].''
-[[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
-{{Multival|legend=1| 1 33 27 50 40 -30 }}
-[[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 }}
-{{Multival|legend=1| 7 26 25 25 20 -15 }}
-[[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
-{{Multival|legend=1| 18 39 42 20 16 -12 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~63/50 = 400.0277{{c}}, ~10/9 = 183.5515{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 183.539
+: [[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 350: / 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 363: / 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 376: / 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 ==
+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
 [[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
-{{Multival|legend=1| 29 -8 11 -80 -64 48 }}
-[[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 402: / 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 415: / 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 428: / 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
-{{Multival|legend=1| 47 31 53 -60 -48 36 }}
+[[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 445: / 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 458: / 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 473: / 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 }}
-{{Multival|legend=1| 41 38 55 -35 -28 21 }}
+{{Optimal ET sequence|legend=0| 80, 103, 183 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~343/324 = 104.916
+[[Badness]] (Sintel): 3.71
-{{Optimal ET sequence|legend=1| 80, 103, 183 }}
-[[Badness]]: 0.146795
 === 11-limit ===
@@ Line 490: / 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 503: / 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 516: / 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 tunings:
+* WE: ~2 = 1200.0758{{c}}, ~17/16 = 104.9158{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/16 = 104.9101{{c}}
-Optimal tuning (POTE): ~2 = 1\1, ~17/16 = 104.909
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~17/16 = 104.909{{c}}
-{{Optimal ET sequence|legend=1| 80, 103, 183, 469f, 652def }}
+{{Optimal ET sequence|legend=0| 80, 103, 183, 469f }}
-Badness: 0.020128
+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 [[skeetsma]] (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 534: / 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
-{{Multival|legend=1| 19 72 69 70 56 -42 }}
-[[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 549: / 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 562: / 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 575: / 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 588: / 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 601: / 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 614: / 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 627: / 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 640: / 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 653: / 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 ==
-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.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 16875/16807, 65536/64827
-{{Mapping|legend=1| 1 0 5 4 | 0 16 -27 -12 }}
-{{Multival|legend=1| 16 -27 -12 -80 -64 48 }}
-[[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 tunings:
+* WE: ~2 = 1199.9179{{c}}, ~17/12 = 605.3156{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3567{{c}}
-{{Optimal ET sequence|legend=1| 10, 101h, 111, 121, 232dg }}
+{{Optimal ET sequence|legend=0| 111, 113, 224 }}
-Badness: 0.017935
+Badness (Sintel): 1.57
 == 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 737: / 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
-{{Multival|legend=1| 53 24 51 -85 -68 51 }}
-[[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 754: / 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 767: / 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 780: / 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 795: / 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
-{{Multival|legend=1| 35 45 57 -10 -8 6 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9313{{c}}, ~90/49 = 1048.5414{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/45 = 151.399
+: [[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 810: / 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 823: / 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 836: / 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 849: / 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
-{{Multival|legend=1| 37 51 63 -5 -4 3 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/45 = 148.719
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0310{{c}}, ~49/45 = 148.7229{{c}}
+: [[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 879: / 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 892: / 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 905: / 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 918: / 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 tunings:
+* WE: ~2 = 1199.7269{{c}}, ~12/11 = 148.6928{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 148.7227{{c}}
-{{Optimal ET sequence|legend=1| 113, 121, 234g, 355eg, 589ceegg }}
+{{Optimal ET sequence|legend=0| 113, 121, 234g }}
-Badness: 0.022574
+Badness (Sintel): 1.37
 [[Category:Temperament clans]]
 [[Category:Mirkwai clan| ]] <!-- main article -->
-[[Category:Mirkwai| ]] <!-- key article -->
 [[Category:Rank 2]]

Canopus clan: Difference between revisions