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-__FORCETOC__
+{{Technical data page}}
------
+This is a collection of [[regular temperament|temperaments]] that [[tempering out|temper out]] the [[porwell comma]] ({{monzo|legend=1| 11 1 -3 -2 }}, [[ratio]]: [[6144/6125]]).
-This family of temperaments tempers out the ''porwell comma'', |11 1 -3 -2&gt; = 6144/6125, and includes hemiwuerschmidt, orwell, amity, valentine, porcupine, hendecatonic, shrutar, hexadecimal, grendel, hemikleismic, mohajira, twothirdtonic and nessafof.
-=Hendecatonic=
+Temperaments discussed elsewhere are:
-Commas: 6144/6125, 10976/10935
+* ''[[Armodue (temperament)|Armodue]]'' (+36/35) → [[Mavila family #Armodue|Mavila family]]
+* [[Mohajira]] (+81/80) → [[Meantone family #Mohajira|Meantone family]]
+* ''[[Hemischis]]'' (+19683/19600) → [[Schismatic family #Hemischis|Schismatic family]]
+* [[Porcupine]] (+64/63) → [[Porcupine family #Porcupine|Porcupine family]]
+* ''[[Alphatrident]]'' (+14348907/14336000) → [[Alphatricot family #Alphatrident|Alphatricot family]]
+* ''[[Shrutar]]'' (+245/243) → [[Diaschismic family #Shrutar|Diaschismic family]]
+* [[Amity]] (+4375/4374 or 5120/5103) → [[Amity family #Septimal amity|Amity family]]
+* [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]]
+* ''[[Twilight]]'' (+{{monzo| 19 -22 2 4 }}) → [[Undim family #Twilight|Undim family]]
+* [[Valentine]] (+126/125) → [[Starling temperaments #Valentine|Starling temperaments]]
+* ''[[Freivald]]'' (+6272/6075) → [[Passion family #Freivald|Passion family]]
+* ''[[Decimaleap]]'' (+{{monzo| 15 -18 1 4 }}) → [[Quintaleap family #Decimaleap|Quintaleap family]]
+* ''[[Hemikleismic]]'' (+4000/3969) → [[Kleismic family #Hemikleismic|Kleismic family]]
+* ''[[Bison]]'' (+78732/78125) → [[Sensipent family #Bison|Sensipent family]]
+* ''[[Quinkee]]'' (+1029/1000) → [[Cloudy clan #Quinkee|Cloudy clan]]
+* ''[[Hemiwürschmidt]]'' (+2401/2400 or 3136/3125) → [[Hemimean clan #Hemiwürschmidt|Hemimean clan]]
+* ''[[Septisuperfourth]]'' (+118098/117649) → [[Escapade family #Septisuperfourth|Escapade family]]
+* ''[[Hemimabila]]'' (+117649/116640) → [[Mabila family #Hemimabila|Mabila family]]
+* ''[[Countermiracle]]'' (+823543/819200) → [[Quince clan #Countermiracle|Quince clan]]
+* ''[[Hemimaquila]]'' (+{{monzo| -5 10 5 -8 }}) → [[Maquila family #Hemimaquila|Maquila family]]
-[[POTE_tuning|POTE generator]]: ~3/2 = 703.054
+Considered below are hendecatonic, nessafof, grendel, twothirdtonic, aufo, absurdity, polypyth, whoops, dodifo, and icositritonic, in the order of increasing [[badness]].
-Map: [&lt;11 0 43 -4], &lt;0 1 -1 2|]
+== Hendecatonic ==
+: ''For the 5-limit version, see [[11th-octave temperaments #Hendecapent]].''
-Wedgie: &lt;&lt;11 -11 22 -43 4 82||
+The hendecatonic temperament has a period of 1/11 octave, which represents [[16/15]] and four times of which represent [[9/7]]. It tempers out 10976/10935, the [[hemimage comma]], and may be described as the {{nowrap| 22 & 99 }} temperament, with [[99edo]] giving an almost perfect tuning.
-EDOs: 22, 55, 77, [[99edo|99]]
+[[Subgroup]]: 2.3.5.7
-Badness: 0.0411
+[[Comma list]]: 6144/6125, 10976/10935
-==11-limit==
+{{Mapping|legend=1| 11 0 43 -4 | 0 1 -1 2 }}
-Commas: 121/120, 176/175, 10976/10935
+: mapping generators: ~16/15, ~3
-[[POTE_tuning|POTE generator]]: ~3/2 = 702.636
+[[Optimal tuning]]s:
+* [[WE]]: ~16/15 = 109.0526{{c}}, ~3/2 = 702.8069{{c}}
+: [[error map]]: {{val| -0.421 +0.431 +0.563 -0.265 }}
+* [[CWE]]: ~16/15 = 109.0909{{c}}, ~3/2 = 702.9705{{c}}
+: error map: {{val| 0.000 +1.015 +1.625 +0.751 }}
-Map: [&lt;11 0 43 -4 38], &lt;0 1 -1 2 0|]
+{{Optimal ET sequence|legend=1| 22, 55, 77, 99 }}
-EDOs: 22, 55, 77, 99, 176e, 275e
+[[Badness]] (Sintel): 1.04
-Badness: 0.0461
+=== Hendecaton ===
+Subgroup: 2.3.5.7.11
-==Icosidillic==
+Comma list: 121/120, 176/175, 10976/10935
-Commas: 3388/3375, 6144/6125, 9801/9800
-[[POTE_tuning|POTE generator]]: 702.914
+Mapping: {{mapping| 11 0 43 -4 38 | 0 1 -1 2 0 }}
-Map: [&lt;22 0 86 -8 111|, &lt;0 1 -1 2 -1|]
+Optimal tunings:
+* WE: ~16/15 = 109.0977{{c}}, ~3/2 = 702.6801{{c}}
+* CWE: ~16/15 = 109.0909{{c}}, ~3/2 = 702.6484{{c}}
-EDOs: 22, 154, 176, 198, 968, 1166
+{{Optimal ET sequence|legend=0| 22, 55, 77, 99 }}
-Badness: 0.0577
+Badness (Sintel): 1.52
-=Hemischis=
+==== 13-limit ====
-Commas: 6144/6125, 19683/19600
+Subgroup: 2.3.5.7.11.13
-POTE generator: ~81/70 = 249.203
+Comma list: 121/120, 176/175, 351/350, 4459/4455
-Map: [&lt;1 0 15 -17|, &lt;0 2 -16 25|]
+Mapping: {{mapping| 11 0 43 -4 38 93 | 0 1 -1 2 0 -3 }}
-Wedgie: &lt;&lt;2 -16 25 -30 34 103||
+Optimal tunings:
+* WE: ~16/15 = 109.1092{{c}}, ~3/2 = 702.4093{{c}}
+* CWE: ~16/15 = 109.0909{{c}}, ~3/2 = 702.2930{{c}}
-EDOs: 5, 9, 14, 19, 24, 29, 53, 130, 183, 313
+{{Optimal ET sequence|legend=0| 22, 55, 77, 99 }}
-Badness: 0.0458
+Badness (Sintel): 1.66
-==11-limit==
+==== 17-limit ====
-Commas: 540/539, 8019/8000, 5632/5625
+Subgroup: 2.3.5.7.11.13.17
-POTE generator: ~81/70 = 249.199
+Comma list: 121/120, 154/153, 176/175, 273/272, 2025/2023
-Map: [&lt;1 0 15 -17 51|, &lt;0 2 -16 25 -60|]
+Mapping: {{mapping| 11 0 43 -4 38 93 45 | 0 1 -1 2 0 -3 0 }}
-EDOs: 5, 9, 14, 19, 24, 29, 53, 130, 183, 313
+Optimal tunings:
+* WE: ~16/15 = 109.0933{{c}}, ~3/2 = 702.3170{{c}}
+* CWE: ~16/15 = 109.0909{{c}}, ~3/2 = 702.3017{{c}}
-Badness: 0.0363
+{{Optimal ET sequence|legend=0| 22, 55, 77, 99, 176eg }}
-==13-limit==
+Badness (Sintel): 1.48
-Commas: 351/350, 540/539, 676/675, 4096/4095
-POTE generator: ~15/13 = 249.199
+=== Cohendecatonic ===
+Subgroup: 2.3.5.7.11
-Map: [&lt;1 0 15 -17 51 14|, &lt;0 2 -16 25 -60 -13|]
+Comma list: 540/539, 896/891, 4375/4356
-EDOs: 5, 9, 14, 19, 24, 29, 53, 130, 183, 313
+Mapping: {{mapping| 11 0 43 -4 73 | 0 1 -1 2 -2 }}
-Badness: 0.0208
+Optimal tunings:
+* WE: ~16/15 = 109.0237{{c}}, ~3/2 = 703.2522{{c}}
+* CWE: ~16/15 = 109.0909{{c}}, ~3/2 = 703.6563{{c}}
-==17-limit==
+{{Optimal ET sequence|legend=0| 22, 77e, 99e, 121, 220e }}
-Commas: 351/350, 442/441, 561/560, 676/675, 4096/4095
-POTE generator: ~15/13 = 249.190
+Badness (Sintel): 1.26
-Map: [&lt;1 0 15 -17 51 14|, &lt;0 2 -16 25 -60 -13|]
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
-EDOs: 5, 9, 14, 19, 24, 29, 53, 130, 183, 679
+Comma list: 352/351, 364/363, 540/539, 625/624
-Badness: 0.0211
+Mapping: {{mapping| 11 0 43 -4 73 128 | 0 1 -1 2 -2 -5 }}
-=Twothirdtonic=
+Optimal tunings:
-Commas: 686/675, 6144/6125
+* WE: ~16/15 = 109.0189{{c}}, ~3/2 = 703.4228{{c}}
+* CWE: ~16/15 = 109.0909{{c}}, ~3/2 = 703.9248{{c}}
-POTE generator: ~15/14 = 130.401
+{{Optimal ET sequence|legend=0| 22, 99ef, 121, 341bdeeff }}
-Map: [&lt;1 3 2 4|, &lt;0 -13 3 -11|]
+Badness (Sintel): 1.49
-Wedgie: &lt;&lt;13 -3 11 -35 -19 34||
+==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
-EDOs: 9, 10, 19, 28, 37, 46
+Comma list: 256/255, 352/351, 364/363, 375/374, 540/539
-Badness: 0.0996
+Mapping: {{mapping| 11 0 43 -4 73 128 45 | 0 1 -1 2 -2 -5 0 }}
-==11-limit==
+Optimal tunings:
-Commas: 121/120, 176/175, 686/675
+* WE: ~16/15 = 109.0159{{c}}, ~3/2 = 703.3932{{c}}
+* CWE: ~16/15 = 109.0909{{c}}, ~3/2 = 703.9110{{c}}
-POTE generator: ~15/14 = 130.430
+{{Optimal ET sequence|legend=0| 22, 99ef, 121, 220efg, 341bdeeffgg }}
-Map: [&lt;1 3 2 4 4|, &lt;0 -13 3 -11 -5|]
+Badness (Sintel): 1.15
-EDOs: 9, 10, 19, 28, 37, 46
+=== Icosidillic ===
+Subgroup: 2.3.5.7.11
-Badness: 0.0408
+Comma list: 3388/3375, 6144/6125, 9801/9800
-==13-limit==
+Mapping: {{mapping| 22 0 86 -8 111 | 0 1 -1 2 -1 }}
-Commas: 91/90, 121/120, 169/168, 176/175
+: mapping generators: ~33/32, ~3
-POTE generator: ~15/14 = 130.409
+Optimal tunings:
+* WE: ~33/32 = 54.5305{{c}}, ~3/2 = 702.7206{{c}}
+* CWE: ~33/32 = 54.5455{{c}}, ~3/2 = 702.8829{{c}}
-Map: [&lt;1 3 2 4 4 5|, &lt;0 -13 3 -11 -5 -12|]
+{{Optimal ET sequence|legend=0| 22, 154, 176, 198 }}
-EDOs: 9, 10, 19, 28, 37, 46
+Badness (Sintel): 1.84
-Badness: 0.0259
+== Nessafof ==
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Nessafof]].''
-=Nessafof=
+Cryptically named by [[Petr Pařízek]] in 2011<ref name="petr's short post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101089.html Yahoo! Tuning Group | ''Some more unclassified temperaments'']</ref>, nessafof adds the [[landscape comma]] and has a third-octave period. The name actually refers to the fact that it has a neutral-second generator, and that a semi-augmented fourth, stacked five times, makes 5/1<ref name="petr's long post"/>.
-Commas: 6144/6125, 250047/250000
-POTE generator: ~35/32 = 157.420
+[[Subgroup]]: 2.3.5.7
-Map: [&lt;3 2 5 10|, &lt;0 7 5 -4|]
+[[Comma list]]: 6144/6125, 250047/250000
-Wedgie: &lt;&lt;21 15 -12 -25 -78 -70||
+{{Mapping|legend=1| 3 2 5 10 | 0 7 5 -4 }}
+: mapping generators: ~63/50, ~35/32
-EDOs: 15, 69, 84, 99, 282, 381
+[[Optimal tuning]]s:
+* [[WE]]: ~63/50 = 399.9023{{c}}, ~35/32 = 157.4418{{c}}
+: [[error map]]: {{val| -0.293 -0.057 +0.407 +0.430 }}
+* [[CWE]]: ~63/50 = 400.0000{{c}}, ~35/32 = 157.4658{{c}}
+: error map: {{val| 0.000 +0.306 1.016 +1.311 }}
-Badness: 0.0450
+{{Optimal ET sequence|legend=1| 15, 54b, 69, 84, 99, 282, 381 }}
-=Septisuperfourth=
+[[Badness]] (Sintel): 1.14
-Commas: 6144/6125, 118098/117649
-POTE generator: ~48/35 = 544.680
+=== Nessa ===
+Subgroup: 2.3.5.7.11
-Map: [&lt;2 4 4 7|, &lt;0 -9 7 -15|]
+Comma list: 441/440, 1344/1331, 4375/4356
-Wedgie: &lt;&lt;18 -14 30 -64 -3 109||
+Mapping: {{mapping| 3 2 5 10 10 | 0 7 5 -4 1 }}
-EDOs: 22, 86, 108, 130, 152, 282
+Optimal tunings:
+* WE: ~44/35 = 399.7815{{c}}, ~35/32 = 157.4527{{c}}
+* CWE: ~44/35 = 400.0000{{c}}, ~35/32 = 157.5109{{c}}
-Badness: 0.0592
+{{Optimal ET sequence|legend=0| 15, 69, 84, 99e }}
-==11-limit==
+Badness (Sintel): 1.61
-Commas: 540/539, 4000/3993, 5632/5625
-POTE generator: ~48/35 = 544.696
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
-Map: [&lt;2 4 4 7 6|, &lt;0 -9 7 -15 10|]
+Comma list: 144/143, 364/363, 441/440, 625/624
-EDOs: 22, 86, 108, 130, 152, 282, 434de, 716de
+Mapping: {{mapping| 3 2 5 10 10 6 | 0 7 5 -4 1 13 }}
-Badness: 0.0246
+Optimal tunings:
+* WE: ~44/35 = 399.7595{{c}}, ~35/32 = 157.3348{{c}}
+* CWE: ~44/35 = 400.0000{{c}}, ~35/32 = 157.3955{{c}}
-==13-limit==
+{{Optimal ET sequence|legend=0| 15, 69, 84, 99ef, 183ef, 282eeff }}
-Commas: 540/539 729/728 4000/3993 21168/21125
-POTE generator: ~48/35 = 544.675
+Badness (Sintel): 1.55
-Map: [&lt;2 4 4 7 6 11|, &lt;0 -9 7 -15 10 -39|]
+=== Fof ===
+Subgroup: 2.3.5.7.11
-EDOs: 130, 282
+Comma list: 121/120, 176/175, 250047/250000
-Badness: 0.0229
+Mapping: {{mapping| 3 2 5 10 8 | 0 7 5 -4 6 }}
-==Septisuperquad==
+Optimal tunings:
-Commas: 351/350, 364/363, 540/539, 5632/5625
+* WE: ~63/50 = 400.0266{{c}}, ~12/11 = 157.5301{{c}}
+* CWE: ~63/50 = 400.0000{{c}}, ~12/11 = 157.5240{{c}}
-POTE generator: ~48/35 = 544.641
+{{Optimal ET sequence|legend=0| 15, 69e, 84e, 99 }}
-Map: [&lt;2 4 4 7 6 5|, &lt;0 -9 7 -15 10 26|]
+Badness (Sintel): 2.26
-EDOs: 22, 108, 130
+== Grendel ==
+: ''For the 5-limit version, see [[Syntonic–31 equivalence continuum #Counterwürschmidt]].''
-Badness: 0.0330
+Grendel tempers out 16875/16807, the [[mirkwai comma]], and may be described as the {{nowrap| 31 & 152 }} temperament. [[152edo]], [[183edo]] and especially [[335edo]] serve as good tunings.
-=Whoops=
+[[Subgroup]]: 2.3.5.7
-Commas: 6144/6125, 244140625/243045684
-POTE generator: ~441/320 = 560.519
+[[Comma list]]: 6144/6125, 16875/16807
-Map: [&lt;1 17 14 -7|, &lt;0 -33 -25 21|]
+{{Mapping|legend=1| 1 -14 3 -6 | 0 23 -1 13 }}
+: mapping generators: ~2, ~8/5
-Wedgie: &lt;&lt;33 25 -21 -37 -126 -119||
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.7348{{c}}, ~8/5 = 812.9574{{c}}
+: [[error map]]: {{val| -0.265 -0.220 -0.067 +1.212 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/5 = 813.1311{{c}}
+: error map: {{val| 0.000 +0.059 +0.555 +1.878 }}
-EDOs: 15, 122d, 137, 152, 608d, 623bd, 775bcd
+{{Optimal ET sequence|legend=1| 31, 90, 121, 152, 335d, 822dd }}
-Badness: 0.1758
+[[Badness]] (Sintel): 1.31
-==11-limit==
+=== 11-limit ===
-Commas: 6144/6125, 3025/3024, 4000/3993
+Subgroup: 2.3.5.7.11
-POTE generator: ~242/175 = 560.519
+Comma list: 540/539, 1375/1372, 5632/5625
-Map: [&lt;1 17 14 -7 10|, &lt;0 -33 -25 21 -14|]
+Mapping: {{mapping| 1 -14 3 -6 -25 | 0 23 -1 13 42 }}
-EDOs: 15, 122d, 137, 152, 608de, 623bde, 775bcde
+Optimal tunings:
+* WE: ~2 = 1199.7355{{c}}, ~8/5 = 812.9622{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~8/5 = 813.1353{{c}}
-Badness: 0.0437
+{{Optimal ET sequence|legend=0| 31, 90e, 121, 152, 335d, 487d }}
-=Polypyth=
+Badness (Sintel): 0.656
-Commas: 6144/6125, 179200/177147
-POTE generator: ~3/2 = 704.174
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-Map: [&lt;1 0 -31 52|, &lt;0 1 21 -31|]
+Comma list: 352/351, 540/539, 625/624, 1375/1372
-EDOs: 46, 121, 167, 288b, 455bcd, 743bcd
+Mapping: {{mapping| 1 -14 3 -6 -25 22 | 0 23 -1 13 42 -27 }}
-Badness: 0.13800
+Optimal tunings:
+* WE: ~2 = 1199.4412{{c}}, ~8/5 = 812.7956{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~8/5 = 813.1209{{c}}
-==11-limit==
+{{Optimal ET sequence|legend=0| 31, 90e, 121, 152f, 273def, 425deff }}
-Commas: 896/891, 2200/2187, 6144/6125
-POTE generator: ~3/2 = 704.177
+Badness (Sintel): 1.03
-Map: [&lt;1 0 -31 52 59|, &lt;0 1 21 -31 -35|]
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
-EDOs: 46, 121, 167, 288be, 455bcde
+Comma list: 256/255, 352/351, 625/624, 715/714, 1275/1274
-Badness: 0.0511
+Mapping: {{mapping| 1 -14 3 -6 -25 22 19 | 0 23 -1 13 42 -27 -22 }}
-==13-limit==
+Optimal tunings:
-Commas: 325/324, 352/351, 364/363, 1716/1715
+* WE: ~2 = 1199.3029{{c}}, ~8/5 = 812.7156{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~8/5 = 813.1843{{c}}
-POTE generator: ~3/2 = 704.168
+{{Optimal ET sequence|legend=0| 31, 90e, 121, 152fg, 273defgg }}
-Map: [&lt;1 0 -31 52 59 64|, &lt;0 1 21 -31 -35 -38|]
+Badness (Sintel): 1.09
-EDOs: 46, 121, 167, 288be
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
-Badness: 0.0303
+Comma list: 256/255, 352/351, 375/374, 400/399, 456/455, 715/714
-==17-limit==
+Mapping: {{mapping| 1 -14 3 -6 -25 22 19 30 | 0 23 -1 13 42 -27 -22 -38 }}
-Commas: 256/255, 325/324, 352/351, 364/363, 1716/1715
-POTE generator: ~3/2 = 704.168
+Optimal tunings:
+* WE: ~2 = 1199.3587{{c}}, ~8/5 = 812.7462{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~8/5 = 813.1796{{c}}
-Map: [&lt;1 0 -31 52 59 64 39|, &lt;0 1 21 -31 -35 -38 -22|]
+{{Optimal ET sequence|legend=0| 31, 90e, 121, 152fg, 273defgg }}
-EDOs: 46, 121, 167, 288beg
+Badness (Sintel): 1.12
-Badness: 0.0191
+== Twothirdtonic ==
-[[Category:hemischis]]
+Twothirdtonic tempers out 686/675, the [[senga]], in addition to the porwell comma, and may be described as the {{nowrap| 37 & 46 }} temperament, generated by one third of a [[5/4|classical major third]] that represents [[15/14]], [[14/13]], and [[13/12]] in the [[13-limit]] interpretation. Note that in the data below, the generator is taken to be its [[octave complement]], thirteen of which [[octave reduction|octave reduced]] make the [[3/2|perfect fifth]]; it follows that the [[ploidacot]] for this temperament is 11-sheared 13-cot. [[46edo]] may be recommended as a tuning.
-[[Category:hendecatonic]]
-[[Category:porwell]]
+[[Subgroup]]: 2.3.5.7
-[[Category:rank_2]]
-[[Category:temperament]]
+[[Comma list]]: 686/675, 6144/6125
+{{Mapping|legend=1| 1 -10 5 -7 | 0 13 -3 11 }}
+: mapping generators: ~2, ~28/15
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.3074{{c}}, ~28/15 = 1068.9820{{c}}
+: [[error map]]: {{val| -0.693 +1.736 +3.278 -5.176 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~28/15 = 1069.5746{{c}}
+: error map: {{val| 0.000 +2.515 +4.962 -3.505 }}
+{{Optimal ET sequence|legend=1| 9, 28b, 37, 46 }}
+[[Badness]] (Sintel): 2.52
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 121/120, 176/175, 686/675
+Mapping: {{mapping| 1 -10 5 -7 -1 | 0 13 -3 11 5 }}
+Optimal tunings:
+* WE: ~2 = 1199.7068{{c}}, ~28/15 = 1069.3084{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~28/15 = 1069.5600{{c}}
+{{Optimal ET sequence|legend=0| 9, 28b, 37, 46 }}
+Badness (Sintel): 1.35
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 91/90, 121/120, 169/168, 176/175
+Mapping: {{mapping| 1 -10 5 -7 -1 -7 | 0 13 -3 11 5 12 }}
+Optimal tunings:
+* WE: ~2 = 1199.9531{{c}}, ~13/7 = 1069.5492{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~13/7 = 1069.5893{{c}}
+{{Optimal ET sequence|legend=0| 9, 28b, 37, 46 }}
+Badness (Sintel): 1.07
+== Semaja ==
+{{See also| Llywelynsmic clan }}
+Cryptically named by [[Petr Pařízek]] in 2011, semaja adds the [[gariboh comma]] to the comma list, and may be described as the {{nowrap| 37 & 53 }} temperament. Its [[ploidacot]] is gamma-19-cot (or alpha-heptaseph due to a much simpler [[2.5.7 subgroup|2.5.7-subgroup]] [[restriction]]). The name actually refers to the fact that two of its ~[[8/7]] generator steps reach a ~[[13/10]]<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 3125/3087, 6144/6125
+{{Mapping|legend=1| 1 -2 1 3 | 0 19 7 -1 }}
+: mapping generators: ~2, ~8/7
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.4860{{c}}, ~8/7 = 226.3864{{c}}
+: [[error map]]: {{val| -0.514 +0.415 -2.123 +3.246 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 226.4697{{c}}
+: error map: {{val| 0.000 +0.970 -1.026 +4.704 }}
+{{Optimal ET sequence|legend=1| 16, 37, 53, 196d }}
+[[Badness]] (Sintel): 2.71
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 121/120, 176/175, 3125/3087
+Mapping: {{mapping| 1 -2 1 3 1 | 0 19 7 -1 13 }}
+Optimal tunings:
+* WE: ~2 = 1199.9818{{c}}, ~8/7 = 226.4821{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 226.4851{{c}}
+{{Optimal ET sequence|legend=0| 16, 37, 53 }}
+Badness (Sintel): 1.98
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 121/120, 169/168, 176/175, 275/273
+Mapping: {{mapping| 1 -2 1 3 1 2 | 0 19 7 -1 13 9 }}
+Optimal tunings:
+* WE: ~2 = 1200.1020{{c}}, ~8/7 = 226.4987{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 226.4822{{c}}
+{{Optimal ET sequence|legend=0| 16, 37, 53 }}
+Badness (Sintel): 1.35
+== Aufo ==
+:''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Untriton]].''
+Also named by [[Petr Pařízek]] in 2011, ''aufo'' refers to the augmented fourth, which is a generator of this temperament<ref name="petr's long post"/>. The functional generator however is the [[64/45]] diminished fifth, and like its [[untriton]] variant, nine generator steps give the [[interval class]] of [[3/1|3]]. The [[ploidacot]] for this temperament is delta-enneacot.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 6144/6125, 177147/175616
+{{Mapping|legend=1| 1 -3 12 -14 | 0 9 -19 33 }}
+: mapping generators: ~2, ~64/45
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9758{{c}}, ~64/45 = 611.2055{{c}}
+: [[error map]]: {{val| -0.024 -1.303 +0.491 +1.295 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~64/45 = 611.2177{{c}}
+: error map: {{val| 0.000 -0.996 +0.551 +1.357 }}
+{{Optimal ET sequence|legend=1| 53, 161, 214 }}
+[[Badness]] (Sintel): 3.07
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 121/120, 176/175, 177147/175616
+Mapping: {{mapping| 1 -3 12 -14 6 | 0 9 -19 33 -5 }}
+Optimal tunings:
+* WE: ~2 = 1200.4500{{c}}, ~64/45 = 611.4185{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~64/45 = 611.1918{{c}}
+{{Optimal ET sequence|legend=0| 53, 108e, 161e }}
+Badness (Sintel): 2.93
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 121/120, 176/175, 351/350, 58806/57967
+Mapping: {{mapping| 1 -3 12 -14 6 20 | 0 9 -19 33 -5 -32 }}
+Optimal tunings:
+* WE: ~2 = 1200.3134{{c}}, ~64/45 = 611.3715{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~64/45 = 611.2118{{c}}
+{{Optimal ET sequence|legend=0| 53, 108e }}
+Badness (Sintel): 2.42
+=== Aufic ===
+Subgroup: 2.3.5.7.11
+Comma list: 540/539, 5632/5625, 72171/71680
+Mapping: {{mapping| 1 -3 12 -14 33 | 0 9 -19 33 -58 }}
+Optimal tunings:
+* WE: ~2 = 1200.0668{{c}}, ~64/45 = 611.2342{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~64/45 = 611.2000{{c}}
+{{Optimal ET sequence|legend=0| 53, 108, 161, 214, 375 }}
+Badness (Sintel): 2.48
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 351/350, 540/539, 847/845, 4096/4095
+Mapping: {{mapping| 1 -3 12 -14 33 20 | 0 9 -19 33 -58 -32 }}
+Optimal tunings:
+* WE: ~2 = 1200.0177{{c}}, ~64/45 = 611.2130{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~64/45 = 611.2039{{c}}
+{{Optimal ET sequence|legend=0| 53, 108, 161, 214, 375 }}
+Badness (Sintel): 1.61
+== Absurdity ==
+: ''For the 5-limit version, see [[Syntonic–chromatic equivalence continuum #Absurdity (5-limit)]].''
+{{See also| Fifth-chroma temperaments }}
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 6144/6125, 177147/175000
+{{Mapping|legend=1| 7 0 -17 64 | 0 1 3 -4 }}
+: mapping generators: ~972/875, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~972/875 = 171.4382{{c}}, ~3/2 = 700.6247{{c}}
+: [[error map]]: {{val| +0.067 -1.263 +1.313 +0.450 }}
+* [[CWE]]: ~972/875 = 171.4286{{c}}, ~3/2 = 700.5871{{c}}
+: error map: {{val| 0.000 -1.368 +1.162 +0.254 }}
+{{Optimal ET sequence|legend=1| 77, 84, 161 }}
+[[Badness]] (Sintel): 3.38
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 441/440, 6144/6125, 72171/71680
+Mapping: {{mapping| 7 0 -17 64 124 | 0 1 3 -4 -9 }}
+Optimal tunings:
+* WE: ~495/448 = 171.4346{{c}}, ~3/2 = 700.6602{{c}}
+* CWE: ~495/448 = 171.4286{{c}}, ~3/2 = 700.6339{{c}}
+{{Optimal ET sequence|legend=0| 77, 84, 161 }}
+Badness (Sintel): 2.70
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 351/350, 441/440, 1188/1183, 3584/3575
+Mapping: {{mapping| 7 0 -17 64 124 37 | 0 1 3 -4 -9 -1 }}
+Optimal tunings:
+* WE: ~72/65 = 171.4223{{c}}, ~3/2 = 700.6036{{c}}
+* CWE: ~72/65 = 171.4286{{c}}, ~3/2 = 700.6306{{c}}
+{{Optimal ET sequence|legend=0| 77, 84, 161 }}
+Badness (Sintel): 1.72
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 351/350, 441/440, 561/560, 1188/1183, 1632/1625
+Mapping: {{mapping| 7 0 -17 64 124 37 -49 | 0 1 3 -4 -9 -1 7 }}
+Optimal tunings:
+* WE: ~72/65 = 171.4263{{c}}, ~3/2 = 700.6429{{c}}
+* CWE: ~72/65 = 171.4286{{c}}, ~3/2 = 700.6525{{c}}
+{{Optimal ET sequence|legend=0| 77, 161 }}
+Badness (Sintel): 1.62
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 324/323, 351/350, 441/440, 456/455, 476/475, 495/494
+Mapping: {{mapping| 7 0 -17 64 124 37 -49 63 | 0 1 3 -4 -9 -1 7 -3 }}
+Optimal tunings:
+* WE: ~21/19 = 171.4244{{c}}, ~3/2 = 700.6395{{c}}
+* CWE: ~21/19 = 171.4286{{c}}, ~3/2 = 700.6568{{c}}
+{{Optimal ET sequence|legend=0| 77, 161 }}
+Badness (Sintel): 1.36
+=== 23-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23
+Comma list: 276/275, 324/323, 351/350, 441/440, 456/455, 476/475, 495/494
+Mapping: {{mapping| 7 0 -17 64 124 37 -49 63 76 | 0 1 3 -4 -9 -1 7 -3 -4 }}
+Optimal tunings:
+* WE: ~21/19 = 171.4321{{c}}, ~3/2 = 700.6475{{c}}
+* CWE: ~21/19 = 171.4286{{c}}, ~3/2 = 700.6325{{c}}
+{{Optimal ET sequence|legend=0| 77, 84, 161 }}
+Badness (Sintel): 1.34
+=== 29-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23.29
+Comma list: 261/260, 276/275, 324/323, 351/350, 441/440, 456/455, 476/475, 495/494
+Mapping: {{mapping| 7 0 -17 64 124 37 -49 63 76 34 | 0 1 3 -4 -9 -1 7 -3 -4 0 }}
+Optimal tunings:
+* WE: ~21/19 = 171.4348{{c}}, ~3/2 = 700.6612{{c}}
+* CWE: ~21/19 = 171.4286{{c}}, ~3/2 = 700.6351{{c}}
+{{Optimal ET sequence|legend=0| 77, 84, 161 }}
+Badness (Sintel): 1.25
+== Polypyth ==
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Leapday]].''
+Polypyth tempers out the same 5-limit comma as [[leapday]], with which it shares the similarly sharp [[3/2|perfect-fifth]] generator, but the porwell comma (6144/6125) rather than the hemifamity comma (5120/5103) is tempered out here. It may be described as the {{nowrap| 46 & 121 }} temperament, and [[121edo]] and [[167edo]] make for good tunings.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 6144/6125, 179200/177147
+{{Mapping|legend=1| 1 0 -31 52 | 0 1 21 -31 }}
+: mapping generators: ~2, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.3465{{c}}, ~3/2 = 703.7905{{c}}
+: [[error map]]: {{val| -0.654 +1.182 -0.177 -0.056 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.1749{{c}}
+: error map: {{val| 0.000 +2.220 +1.359 +1.752 }}
+{{Optimal ET sequence|legend=1| 46, 121, 167, 288b, 455bcd }}
+[[Badness]] (Sintel): 3.49
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 896/891, 2200/2187, 6144/6125
+Mapping: {{mapping| 1 0 -31 52 59 | 0 1 21 -31 -35 }}
+Optimal tunings:
+* WE: ~2 = 1199.3335{{c}}, ~3/2 = 703.7856{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1812{{c}}
+{{Optimal ET sequence|legend=0| 46, 121, 167, 288be, 455bcde }}
+Badness (Sintel): 1.69
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 325/324, 352/351, 364/363, 1716/1715
+Mapping: {{mapping| 1 0 -31 52 59 64 | 0 1 21 -31 -35 -38 }}
+Optimal tunings:
+* WE: ~2 = 1199.3768{{c}}, ~3/2 = 703.8018{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1731{{c}}
+{{Optimal ET sequence|legend=0| 46, 75e, 121, 167, 288be }}
+Badness (Sintel): 1.25
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 256/255, 325/324, 352/351, 364/363, 1716/1715
+Mapping: {{mapping| 1 0 -31 52 59 64 39 | 0 1 21 -31 -35 -38 -22 }}
+Optimal tunings:
+* WE: ~2 = 1199.3518{{c}}, ~3/2 = 703.7880{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1747{{c}}
+{{Optimal ET sequence|legend=0| 46, 75e, 121, 167, 288beg }}
+Badness (Sintel): 0.971
+== Whoops ==
+: ''For the 5-limit version, see [[Very high accuracy temperaments #Whoosh]].''
+Also named by [[Petr Pařízek]] in 2011, whoops is a relatively simple extension to the otherwise very accurate microtemperament known as ''whoosh''<ref name="petr's long post"/>.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 6144/6125, 244140625/243045684
+{{Mapping|legend=1| 1 -16 -11 14 | 0 33 25 -21 }}
+: mapping generators: ~2, ~640/441
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.5944{{c}}, ~640/441 = 639.2648{{c}}
+: [[error map]]: {{val| -0.406 +0.272 -0.233 +0.936 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~640/441 = 639.4769{{c}}
+: error map: {{val| 0.000 +0.783 +0.609 +2.159 }}
+{{Optimal ET sequence|legend=1| 15, 122d, 137, 152, 623bdd, 775bcdd, 927bcddd, 1079bcddd }}
+[[Badness]] (Sintel): 4.45
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 3025/3024, 4000/3993, 6144/6125
+Mapping: {{mapping| 1 -16 -11 14 -4 | 0 33 25 -21 14 }}
+Optimal tunings:
+* WE: ~2 = 1199.5936{{c}}, ~175/121 = 639.264{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~175/121 = 639.4770{{c}}
+{{Optimal ET sequence|legend=0| 15, 122d, 137, 152, 623bdde, 775bcdde, 927bcdddee, 1079bcdddee }}
+Badness (Sintel): 1.45
+== Dodifo ==
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Dodifo]].''
+Also named by [[Petr Pařízek]] in 2011, ''dodifo'' refers to the (tetraptolemaic) double-diminished fourth, which is a generator of this temperament<ref name="petr's long post"/>. The extension here is a less accurate 7-limit interpretation.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 6144/6125, 2500000/2470629
+{{Mapping|legend=1| 1 -23 -4 0 | 0 35 9 4 }}
+: mapping generators: ~2, ~80/49
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.6429{{c}}, ~80/49 = 842.6790{{c}}
+: [[error map]]: {{val| -0.357 +0.228 -0.774 +1.890 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~80/49 = 842.9243{{c}}
+: error map: {{val| 0.000 +0.396 +0.005 +2.871 }}
+{{Optimal ET sequence|legend=1| 37, 84, 121, 205 }}
+[[Badness]] (Sintel): 4.55
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 1375/1372, 2560/2541, 4375/4356
+Mapping: {{mapping| 1 -23 -4 0 14 | 0 35 9 4 -15 }}
+Optimal tunings:
+* WE: ~2 = 1199.3401{{c}}, ~80/49 = 842.4880{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~80/49 = 842.9457{{c}}
+{{Optimal ET sequence|legend=0| 37, 84, 121, 326dee }}
+Badness (Sintel): 2.71
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 364/363, 625/624, 640/637, 1375/1372
+Mapping: {{mapping| 1 12 5 4 -1 4 | 0 -35 -9 -4 15 -1 }}
+Optimal tunings:
+* WE: ~2 = 1199.3410{{c}}, ~13/8 = 842.4885{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~13/8 = 842.9466{{c}}
+{{Optimal ET sequence|legend=0| 37, 84, 121, 326deef }}
+Badness (Sintel): 1.63
+== Icositritonic ==
+{{See also| 23rd-octave temperaments }}
+Icositritonic has a period of 1/23 octave, so six period represents [[6/5]] and nine period represents [[21/16]]. It may be described as {{nowrap| 46 & 161 }}. It was named by [[Xenllium]] in 2019 for its number of periods per octave.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 6144/6125, 9920232/9765625
+{{Mapping|legend=1| 23 0 17 101 | 0 1 1 -1 }}
+: mapping generators: ~1323/1280, ~3
+[[Optimal tuning]]s:
+* [[WE]]: ~1323/1280 = 52.1732{{c}}, ~3/2 = 701.0660{{c}}
+: [[error map]]: {{val| -0.017 -0.906 +1.679 -0.386 }}
+* [[CWE]]: ~1323/1280 = 52.1739{{c}}, ~3/2 = 701.0722{{c}}
+: error map: {{val| 0.000 -0.883 +1.715 -0.333 }}
+{{Optimal ET sequence|legend=1| 46, 115, 161, 207, 368c }}
+[[Badness]] (Sintel): 4.98
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 441/440, 6144/6125, 35937/35840
+Mapping: {{mapping| 23 0 17 101 116 | 0 1 1 -1 -1 }}
+Optimal tunings:
+* WE: ~33/32 = 52.1740{{c}}, ~3/2 = 701.0379{{c}}
+* CWE: ~33/32 = 52.1739{{c}}, ~3/2 = 701.0370{{c}}
+{{Optimal ET sequence|legend=0| 46, 115, 161, 207, 368c }}
+Badness (Sintel): 2.14
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 351/350, 441/440, 847/845, 3584/3575
+Mapping: {{mapping| 23 0 17 101 116 158 | 0 1 1 -1 -1 -2 }}
+Optimal tunings:
+* WE: ~33/32 = 52.1724{{c}}, ~3/2 = 701.1310{{c}}
+* CWE: ~33/32 = 52.1739{{c}}, ~3/2 = 701.1524{{c}}
+{{Optimal ET sequence|legend=0| 46, 115, 161, 207, 368c }}
+Badness (Sintel): 1.67
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 351/350, 441/440, 561/560, 847/845, 1089/1088
+Mapping: {{mapping| 23 0 17 101 116 158 94 | 0 1 1 -1 -1 -2 0 }}
+Optimal tunings:
+* WE: ~33/32 = 52.1735{{c}}, ~3/2 = 701.1493{{c}}
+* CWE: ~33/32 = 52.1739{{c}}, ~3/2 = 701.1549{{c}}
+{{Optimal ET sequence|legend=0| 46, 115, 161, 207, 368c }}
+Badness (Sintel): 1.26
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 351/350, 441/440, 456/455, 476/475, 513/512, 847/845
+Mapping: {{mapping| 23 0 17 101 116 158 94 207 | 0 1 1 -1 -1 -2 0 -3 }}
+Optimal tunings:
+* WE: ~33/32 = 52.1744{{c}}, ~3/2 = 701.0649{{c}}
+* CWE: ~33/32 = 52.1739{{c}}, ~3/2 = 701.0582{{c}}
+{{Optimal ET sequence|legend=0| 46, 115, 161, 207, 368c }}
+Badness (Sintel): 1.31
+=== 23-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23
+Comma list: 276/275, 351/350, 391/390, 441/440, 456/455, 476/475, 847/845
+Mapping: {{mapping| 23 0 17 101 116 158 94 207 104 | 0 1 1 -1 -1 -2 0 -3 0 }}
+Optimal tunings:
+* WE: ~33/32 = 52.1768{{c}}, ~3/2 = 701.1259{{c}}
+* CWE: ~33/32 = 52.1739{{c}}, ~3/2 = 701.0841{{c}}
+{{Optimal ET sequence|legend=0| 46, 115, 161, 207 }}
+Badness (Sintel): 1.27
+== References ==
+[[Category:Temperament collections]]
+[[Category:Porwell temperaments| ]] <!-- main article -->
+[[Category:Rank 2]]

Porwell temperaments: Difference between revisions