@@ 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. Members of the clan include grendel, kwai, pluto, mirkat, eris, subsemifourth, septendesemi, gaster, subsedia, hemiseptisix, browser, and grazer considered below, as well as these considered elsewhere:
+{{Technical data page}}
-* ''[[Octokaidecal]]'' (+28/27 or 50/49) → [[Trienstonic clan #Octokaidecal|Trienstonic clan]]
+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.
-* ''[[Meantritone]]'' (+81/80) → [[Meantone family #Meantritone|Meantone family]]
-* ''[[Nusecond]]'' (+126/125) → [[Starling temperaments #Nusecond|Starling temperaments]]
-* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle|Gamelismic clan]]
-* ''[[Bohpier]]'' (+245/243) → [[Sensamagic clan #Bohpier|Sensamagic clan]]
-* ''[[Semisept]]'' (+1728/1715 or 3136/3125) → [[Hemimean clan #Semisept|Hemimean clan]]
-* ''[[Octoid]]'' (+4375/4374) → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]
-* [[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]]
 == Canopus ==
@@ Line 19: / Line 9: @@
 [[Comma list]]: 16875/16807
-{{Mapping|legend=2| 1 3 3 | 0 -5 -4 }}
+{{Mapping|legend=3| 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}}
-[[Optimal tuning]] ([[POTE]]): ~3 = 1\1edt, ~7/5 = 583.9584
+: [[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 ET sequence]]: [[13edt|b13]], [[62edt|b62]], [[75edt|b75]], [[88edt|b88]], [[101edt|b101]], [[114edt|b114]], [[355edt|b355]], [[469edt|b469]], [[583edt|b583]], [[697edt|b697]]
-== Grendel ==
+[[Badness]] (Sintel): 0.0996
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 6144/6125, 16875/16807
+=== 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. These temperaments are distributed into different temperament clan and collection pages.
+* ''[[Nusecond]]'' (+126/125) → [[Starling temperaments #Nusecond|Starling temperaments]]
+* [[Octoid]] (+4375/4374) → [[Stearnsmic clan #Octoid|Stearnsmic clan]]
-{{Mapping|legend=1| 1 9 2 7 | 0 -23 1 -13 }}
+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.
-: mapping generators: ~2, ~5/4
+Members of the clan discussed elsewhere are:
+* ''[[Kwai]]'' (+5120/5103) → [[Aberschismic temperaments #Kwai|Aberschismic temperaments]]
+* ''[[Octokaidecal]]'' (+28/27 or 50/49) → [[Trienstonic clan #Octokaidecal|Trienstonic clan]]
+* ''[[Meantritone]]'' (+81/80) → [[Meantone family #Meantritone|Meantone family]]
+* ''[[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]]
+* ''[[Familia]]'' (+1600000/1594323) → [[Amity family #Familia|Amity family]]
+* [[Sqrtphi]] (+15625/15552) → [[Kleismic family #Sqrtphi|Kleismic family]]
+* ''[[Rainwell]]'' (+2100875/2097152) → [[Semicomma family #Rainwell|Semicomma family]]
+* ''[[Browser]]'' (+78732/78125) → [[Sensipent family #Browser|Sensipent family]]
+* ''[[Quintiquart]]'' (+390625000/387420489) → [[Quartonic family #Quintiquart|Quartonic family]]
-{{Multival|legend=1| 23 -1 13 -55 -44 33 }}
+For ''no-2's'' extensions, see [[No-twos subgroup temperaments #Canopus]].
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 386.863
+Considered below are mirkat, eris, subsemifourth, septendesemi, gaster, hemiseptisix, and grazer, in the order of increasing [[badness]].
-{{Optimal ET sequence|legend=1| 31, 90, 121, 152, 335d }}
+== 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.
-[[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 324: / Line 59: @@
 {{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 338: / Line 76: @@
 Comma list: 540/539, 1375/1372, 8019/8000
-Mapping: {{mapping| 3 2 1 2 9 | 0 6 13 14 3 }}
+{{Mapping|legend=0| 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 351: / Line 91: @@
 Comma list: 351/350, 540/539, 676/675, 1375/1372
-Mapping: {{mapping| 3 2 1 2 9 1 | 0 6 13 14 3 22 }}
+{{Mapping|legend=0| 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 364: / Line 106: @@
 Comma list: 351/350, 442/441, 540/539, 561/560, 715/714
-Mapping: {{mapping| 3 2 1 2 9 1 4 | 0 6 13 14 3 22 18 }}
+{{Mapping|legend=0| 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]]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 tuning]] ([[POTE]]): ~2 = 1\1, ~60/49 = 348.216
+{{Optimal ET sequence|legend=1| 31, 131, 162, 193, 224 }}
-{{Optimal ET sequence|legend=1| 31, 131, 162, 193, 224, 1823cd, 2271cd }}
+[[Badness]] (Sintel): 1.89
-[[Badness]]: 0.074719
 === 11-limit ===
@@ Line 392: / Line 141: @@
 Comma list: 540/539, 1375/1372, 65625/65536
-Mapping: {{mapping| 1 10 0 6 20 | 0 -29 8 -11 -57 }}
+{{Mapping|legend=0| 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 405: / Line 156: @@
 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|legend=0| 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 418: / Line 171: @@
 [[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]] ([[POTE]]): ~2 = 1\1, ~144/125 = 244.719
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9182{{c}}, ~144/125 = 244.7020{{c}}
+: [[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 435: / Line 189: @@
 Comma list: 540/539, 1375/1372, 234375/234256
-Mapping: {{mapping| 1 39 27 45 56 | 0 -47 -31 -53 -66 }}
+{{Mapping|legend=0| 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 448: / Line 204: @@
 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|legend=0| 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 463: / Line 221: @@
 [[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
-{{Multival|legend=1| 41 38 55 -35 -28 21 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~343/324 = 104.916
+[[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 ET sequence|legend=1| 80, 103, 183 }}
+{{Optimal ET sequence|legend=0| 80, 103, 183 }}
-[[Badness]]: 0.146795
+[[Badness]] (Sintel): 3.71
 === 11-limit ===
@@ Line 480: / Line 239: @@
 Comma list: 540/539, 1375/1372, 43923/43750
-Mapping: {{mapping| 1 39 37 53 50 | 0 -41 -38 -55 -51 }}
+{{Mapping|legend=0| 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 493: / Line 254: @@
 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|legend=0| 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 506: / Line 269: @@
 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|legend=0| 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 [[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 524: / Line 293: @@
 [[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]]s:
+* [[WE]]: ~2 = 1199.9920{{c}}, ~567/400 = 605.3546{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~800/567 = 594.641
+: [[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 539: / Line 311: @@
 Comma list: 540/539, 1375/1372, 14348907/14336000
-Mapping: {{mapping| 1 11 38 37 -1 | 0 -19 -72 -69 9 }}
+{{Mapping|legend=0| 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 552: / Line 326: @@
 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|legend=0| 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 565: / Line 341: @@
 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|legend=0| 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 578: / Line 356: @@
 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|legend=0| 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 591: / Line 371: @@
 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|legend=0| 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 604: / Line 386: @@
 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|legend=0| 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 617: / Line 401: @@
 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|legend=0| 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 630: / Line 416: @@
 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|legend=0| 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 643: / Line 431: @@
 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|legend=0| 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
+Optimal tunings:
+* WE: ~2 = 1199.9179{{c}}, ~17/12 = 605.3156{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3567{{c}}
-Mapping: {{mapping| 1 0 5 4 -1 4 3 | 0 16 -27 -12 45 -3 11 }}
+{{Optimal ET sequence|legend=0| 111, 113, 224 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 118.968
+Badness (Sintel): 1.57
-{{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 448: @@
 [[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]]s:
+* [[WE]]: ~2 = 1199.2693{{c}}, ~98/75 = 466.0801{{c}}
-{{Multival|legend=1| 53 24 51 -85 -68 51 }}
+: [[error map]]: {{val| +0.023 -0.149 -0.553 +0.866 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~98/75 = 466.0715{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~98/75 = 466.071
+: 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 744: / Line 466: @@
 Comma list: 540/539, 1375/1372, 2734375/2725888
-Mapping: {{mapping| 1 34 17 34 53 | 0 -53 -24 -51 -81 }}
+{{Mapping|legend=0| 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 757: / Line 481: @@
 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|legend=0| 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 770: / Line 496: @@
 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|legend=0| 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 ==
+== Grazer ==
-{{See also| Sensipent family }}
+Named by [[Xenllium]] in 2022, grazer may be described as the {{nowrap| 113 & 121 }} temperament.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 16875/16807, 78732/78125
-{{Mapping|legend=1| 1 6 8 10 | 0 -35 -45 -57 }}
-{{Multival|legend=1| 35 45 57 -10 -8 6 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/45 = 151.399
-{{Optimal ET sequence|legend=1| 103, 111, 214 }}
-[[Badness]]: 0.180645
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 540/539, 1375/1372, 78732/78125
-Mapping: {{mapping| 1 6 8 10 8 | 0 -35 -45 -57 -36 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 151.405
-{{Optimal ET sequence|legend=1| 103, 214 }}
-Badness: 0.057634
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 351/350, 540/539, 847/845, 1375/1372
-Mapping: {{mapping| 1 6 8 10 8 9 | 0 -35 -45 -57 -36 -42 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 151.403
-{{Optimal ET sequence|legend=1| 103, 111, 214 }}
-Badness: 0.028822
-=== 17-limit ===
-Subgroup: 2.3.5.7.11.13.17
-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 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 151.397
-{{Optimal ET sequence|legend=1| 103, 111, 214 }}
-Badness: 0.020384
-=== 19-limit ===
-Subgroup: 2.3.5.7.11.13.17.19
-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 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 151.396
-{{Optimal ET sequence|legend=1| 103h, 111, 214 }}
-Badness: 0.017570
-== Grazer ==
 [[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 869: / Line 531: @@
 Comma list: 540/539, 1375/1372, 218750/216513
-Mapping: {{mapping| 1 34 47 58 35 | 0 -37 -51 -63 -36 }}
+{{Mapping|legend=0| 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 882: / Line 546: @@
 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|legend=0| 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 895: / Line 561: @@
 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|legend=0| 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 908: / Line 576: @@
 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|legend=0| 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:Canopic clan| ]] <!-- main article -->
+[[Category:Canopic| ]] <!-- key article -->
 [[Category:Temperament clans]]
-[[Category:Mirkwai clan| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Mirkwai| ]] <!-- key article -->
-[[Category:Rank 2]]

Canopic clan: Difference between revisions

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