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Temperaments discussed elsewhere are:  
Temperaments discussed elsewhere are:  
* ''[[Armodue (temperament)|Armodue]]'' (+36/35) → [[Mavila family #Armodue|Mavila family]]
* ''[[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]]
* [[Porcupine]] (+64/63) → [[Porcupine family #Porcupine|Porcupine family]]
* [[Mohajira]] (+81/80) → [[Meantone family #Mohajira|Meantone family]]
* ''[[Alphatrident]]'' (+14348907/14336000) → [[Alphatricot family #Alphatrident|Alphatricot family]]
* [[Valentine]] (+126/125) → [[Starling temperaments #Valentine|Starling temperaments]]
* [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]]
* [[Shrutar]] (+245/243) → [[Diaschismic family #Shrutar|Diaschismic family]]
* [[Shrutar]] (+245/243) → [[Diaschismic family #Shrutar|Diaschismic family]]
* ''[[Quinkee]]'' (+1029/1000) → [[Cloudy clan #Quinkee|Cloudy clan]]
* ''[[Hemiwürschmidt]]'' (+2401/2400 or 3136/3125) → [[Hemimean clan #Hemiwürschmidt|Hemimean clan]]
* ''[[Hemikleismic]]'' (+4000/3969) → [[Kleismic family #Hemikleismic|Kleismic family]]
* [[Amity]] (+4375/4374 or 5120/5103) → [[Amity family #Septimal amity|Amity 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]]
* ''[[Freivald]]'' (+6272/6075) → [[Passion family #Freivald|Passion family]]
* ''[[Grendel]]'' (+16875/16807) → [[Mirkwai clan #Grendel|Mirkwai clan]]
* ''[[Decimaleap]]'' (+{{monzo| 15 -18 1 4 }}) → [[Quintaleap family #Decimaleap|Quintaleap family]]
* ''[[Hemischis]]'' (+19683/19600) → [[Schismatic family #Hemischis|Schismatic family]]
* ''[[Hemikleismic]]'' (+4000/3969) → [[Kleismic family #Hemikleismic|Kleismic family]]
* ''[[Bison]]'' (+78732/78125) → [[Sensipent family #Bison|Sensipent 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]]
* ''[[Hemimabila]]'' (+117649/116640) → [[Mabila family #Hemimabila|Mabila family]]
* ''[[Septisuperfourth]]'' (+118098/117649) → [[Escapade family #Septisuperfourth|Escapade family]]
* ''[[Grendel]]'' (+16875/16807) → [[Mirkwai clan #Grendel|Mirkwai clan]]
* ''[[Alphatrident]]'' (+14348907/14336000) → [[Alphatricot family #Alphatrident|Alphatricot family]]
* ''[[Countermiracle]]'' (+823543/819200) → [[Quince clan #Countermiracle|Quince clan]]
* ''[[Hemimaquila]]'' (+{{monzo| -5 10 5 -8 }}) → [[Maquila family #Hemimaquila|Maquila family]]
* ''[[Hemimaquila]]'' (+{{monzo| -5 10 5 -8 }}) → [[Maquila family #Hemimaquila|Maquila family]]
* ''[[Decimaleap]]'' (+{{monzo| 15 -18 1 4 }}) → [[Quintaleap family #Decimaleap|Quintaleap family]]
* ''[[Twilight]]'' (+{{monzo| 19 -22 2 4 }}) → [[Undim family #Twilight|Undim family]]
* ''[[Countermiracle]]'' (+823543/819200) → [[Quince clan #Countermiracle|Quince clan]]


Considered below are hendecatonic, twothirdtonic, nessafof, aufo, whoops, polypyth, icositritonic, absurdity, and dodifo.  
Considered below are hendecatonic, nessafof, twothirdtonic, aufo, absurdity, polypyth, whoops, dodifo, and icositritonic, in the order of increasing [[badness]].  


== Hendecatonic ==
== Hendecatonic ==
Line 154: Line 154:


Badness (Sintel): 1.84
Badness (Sintel): 1.84
== Nessafof ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #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"/>.
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 6144/6125, 250047/250000
{{Mapping|legend=1| 3 2 5 10 | 0 7 5 -4 }}
: mapping generators: ~63/50, ~35/32
[[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 }}
{{Optimal ET sequence|legend=1| 15, 54b, 69, 84, 99, 282, 381 }}
[[Badness]] (Sintel): 1.14
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 250047/250000
Mapping: {{mapping| 3 2 5 10 8 | 0 7 5 -4 6 }}
Optimal tunings:
* WE: ~63/50 = 400.0266{{c}}, ~12/11 = 157.5301{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~12/11 = 157.5240{{c}}
{{Optimal ET sequence|legend=0| 15, 69e, 84e, 99 }}
Badness (Sintel): 2.26
=== Nessa ===
Subgroup: 2.3.5.7.11
Comma list: 441/440, 1344/1331, 4375/4356
Mapping: {{mapping| 3 2 5 10 10 | 0 7 5 -4 1 }}
Optimal tunings:
* WE: ~44/35 = 399.7815{{c}}, ~35/32 = 157.4527{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~35/32 = 157.5109{{c}}
{{Optimal ET sequence|legend=0| 15, 69, 84, 99e }}
Badness (Sintel): 1.61
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 364/363, 441/440, 625/624
Mapping: {{mapping| 3 2 5 10 10 6 | 0 7 5 -4 1 13 }}
Optimal tunings:
* WE: ~44/35 = 399.7595{{c}}, ~35/32 = 157.3348{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~35/32 = 157.3955{{c}}
{{Optimal ET sequence|legend=0| 15, 54bf, 69, 84, 99ef, 183ef, 282eeff }}
Badness (Sintel): 1.55


== Twothirdtonic ==
== Twothirdtonic ==
Line 254: Line 321:


Badness (Sintel): 1.35
Badness (Sintel): 1.35
== Nessafof ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #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"/>.
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 6144/6125, 250047/250000
{{Mapping|legend=1| 3 2 5 10 | 0 7 5 -4 }}
: mapping generators: ~63/50, ~35/32
[[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 }}
{{Optimal ET sequence|legend=1| 15, 54b, 69, 84, 99, 282, 381 }}
[[Badness]] (Sintel): 1.14
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 250047/250000
Mapping: {{mapping| 3 2 5 10 8 | 0 7 5 -4 6 }}
Optimal tunings:
* WE: ~63/50 = 400.0266{{c}}, ~12/11 = 157.5301{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~12/11 = 157.5240{{c}}
{{Optimal ET sequence|legend=0| 15, 69e, 84e, 99 }}
Badness (Sintel): 2.26
=== Nessa ===
Subgroup: 2.3.5.7.11
Comma list: 441/440, 1344/1331, 4375/4356
Mapping: {{mapping| 3 2 5 10 10 | 0 7 5 -4 1 }}
Optimal tunings:
* WE: ~44/35 = 399.7815{{c}}, ~35/32 = 157.4527{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~35/32 = 157.5109{{c}}
{{Optimal ET sequence|legend=0| 15, 69, 84, 99e }}
Badness (Sintel): 1.61
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 364/363, 441/440, 625/624
Mapping: {{mapping| 3 2 5 10 10 6 | 0 7 5 -4 1 13 }}
Optimal tunings:
* WE: ~44/35 = 399.7595{{c}}, ~35/32 = 157.3348{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~35/32 = 157.3955{{c}}
{{Optimal ET sequence|legend=0| 15, 54bf, 69, 84, 99ef, 183ef, 282eeff }}
Badness (Sintel): 1.55


== Aufo ==
== Aufo ==
Line 404: Line 404:
Badness (Sintel): 1.61
Badness (Sintel): 1.61


== Whoops ==
== Absurdity ==
: ''For the 5-limit version, see [[Very high accuracy temperaments #Whoosh]].''  
: ''For the 5-limit version, see [[Syntonic–chromatic equivalence continuum #Absurdity (5-limit)]].''
 
{{See also| Fifth-chroma temperaments }}
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
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 6144/6125, 244140625/243045684
[[Comma list]]: 6144/6125, 177147/175000


{{Mapping|legend=1| 1 -16 -11 14 | 0 33 25 -21 }}
{{Mapping|legend=1| 7 0 -17 64 | 0 1 3 -4 }}
: mapping generators: ~2, ~640/441
: mapping generators: ~972/875, ~3


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.5944{{c}}, ~640/441 = 639.2648{{c}}
* [[WE]]: ~972/875 = 171.4382{{c}}, ~3/2 = 700.6247{{c}}
: [[error map]]: {{val| -0.406 +0.272 -0.233 +0.936 }}
: [[error map]]: {{val| +0.067 -1.263 +1.313 +0.450 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~640/441 = 639.4769{{c}}
* [[CWE]]: ~972/875 = 171.4286{{c}}, ~3/2 = 700.5871{{c}}
: error map: {{val| 0.000 +0.783 +0.609 +2.159 }}
: error map: {{val| 0.000 -1.368 +1.162 +0.254 }}


{{Optimal ET sequence|legend=1| 15, 122d, 137, 152, 623bdd, 775bcdd, 927bcddd, 1079bcddd }}
{{Optimal ET sequence|legend=1| 77, 84, 161 }}


[[Badness]] (Sintel): 4.45
[[Badness]] (Sintel): 3.38


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 3025/3024, 4000/3993, 6144/6125
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| 1 -16 -11 14 -4 | 0 33 25 -21 14 }}
Mapping: {{mapping| 7 0 -17 64 124 37 -49 63 76 34 | 0 1 3 -4 -9 -1 7 -3 -4 0 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.5936{{c}}, ~175/121 = 639.264{{c}}
* WE: ~21/19 = 171.4348{{c}}, ~3/2 = 700.6612{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~175/121 = 639.4770{{c}}
* CWE: ~21/19 = 171.4286{{c}}, ~3/2 = 700.6351{{c}}


{{Optimal ET sequence|legend=0| 15, 122d, 137, 152, 623bdde, 775bcdde, 927bcdddee, 1079bcdddee }}
{{Optimal ET sequence|legend=0| 77, 84, 161 }}


Badness (Sintel): 1.45
Badness (Sintel): 1.25


== Polypyth ==
== Polypyth ==
Line 507: Line 581:


Badness (Sintel): 0.971
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 ==
== Icositritonic ==
Line 604: Line 767:


Badness (Sintel): 1.27
Badness (Sintel): 1.27
== 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
== 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


== References ==
== References ==
Retrieved from "https://en.xen.wiki/w/Porwell_temperaments"