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Porwell temperaments: Difference between revisions

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This family of temperaments tempers out the ''porwell comma'', {{monzo| 11 1 -3 -2 }} = [[6144/6125]], and includes hendecatonic, hemischis, twothirdtonic, nessafof, septisuperfourth, whoops, and polypyth.  
This family of temperaments tempers out the ''porwell comma'', {{monzo| 11 1 -3 -2 }} = [[6144/6125]], and includes hendecatonic, hemischis, twothirdtonic, nessafof, septisuperfourth, whoops, and polypyth.  


Discussed elsewhere are [[Würschmidt family #Hemiwürschmidt|hemiwürschmidt]], [[Semicomma family #Orwell|orwell]], [[Amity family #Amity|amity]], [[Starling temperaments #Valentine|valentine]], [[Porcupine family #Porcupine|porcupine]], [[Diaschismic family #Shrutar|shrutar]], [[Pelogic family #Armodue|hexadecimal]], [[Mirkwai clan #Grendel|grendel]], [[Kleismic family #Hemikleismic|hemikleismic]], and [[Meantone family #Mohajira|mohajira]].  
Discussed elsewhere are [[Würschmidt family #Hemiwürschmidt|hemiwürschmidt]], [[Semicomma family #Orwell|orwell]], [[Amity family #Amity|amity]], [[Starling temperaments #Valentine|valentine]], [[Porcupine family #Porcupine|porcupine]], [[Diaschismic family #Shrutar|shrutar]], [[Pelogic family #Armodue|hexadecimal]], [[Mirkwai clan #Grendel|grendel]], [[Tricot family|trident]], [[Kleismic family #Hemikleismic|hemikleismic]], and [[Meantone family #Mohajira|mohajira]].  


= Hendecatonic =
= Hendecatonic =
Line 43: Line 43:
{{see also| Schismatic family }}
{{see also| Schismatic family }}


Commas: 6144/6125, 19683/19600
[[Comma list]]: 6144/6125, 19683/19600


POTE generator: ~81/70 = 249.203
[[Mapping]]: [<1 0 15 -17|, <0 2 -16 25|]


Map: [<1 0 15 -17|, <0 2 -16 25|]
[[Wedgie]]: <<2 -16 25 -30 34 103||


Wedgie: <<2 -16 25 -30 34 103||
[[POTE tuning|POTE generator]]: ~81/70 = 249.203


EDOs: {{EDOs| 24, 53, 130, 183, 313 }}
[[EDO|Vals]]: {{Val list| 24, 53, 130, 183, 313 }}


Badness: 0.0458
[[Badness]]: 0.045817


== 11-limit ==
== 11-limit ==
Commas: 540/539, 8019/8000, 5632/5625
Comma list: 540/539, 8019/8000, 5632/5625
 
Mapping: [<1 0 15 -17 51|, <0 2 -16 25 -60|]


POTE generator: ~81/70 = 249.199
POTE generator: ~81/70 = 249.199


Map: [<1 0 15 -17 51|, <0 2 -16 25 -60|]
Vals: {{Val list| 24e, 53, 130, 183, 313 }}


EDOs: {{EDOs| 24e, 53, 130, 183, 313 }}
Badness: 0.036289


Badness: 0.0363
== 13-limit ==
Comma list: 351/350, 540/539, 676/675, 4096/4095


== 13-limit ==
Mapping: [<1 0 15 -17 51 14|, <0 2 -16 25 -60 -13|]
Commas: 351/350, 540/539, 676/675, 4096/4095


POTE generator: ~15/13 = 249.199
POTE generator: ~15/13 = 249.199


Map: [<1 0 15 -17 51 14|, <0 2 -16 25 -60 -13|]
Vals: {{Val list| 24e, 53, 130, 183, 313 }}


EDOs: {{EDOs| 24e, 53, 130, 183, 313 }}
Badness: 0.020816


Badness: 0.0208
== 17-limit ==
Comma list: 351/350, 442/441, 561/560, 676/675, 4096/4095


== 17-limit ==
Map: [<1 0 15 -17 51 14 -49|, <0 2 -16 25 -60 -13 67|]
Commas: 351/350, 442/441, 561/560, 676/675, 4096/4095


POTE generator: ~15/13 = 249.190
POTE generator: ~15/13 = 249.190


Map: [<1 0 15 -17 51 14 -49|, <0 2 -16 25 -60 -13 67|]
Vals: {{Val list| 53, 130, 183, 679df }}
 
EDOs: {{EDOs| 24egg, 53, 130, 183, 679df }}


Badness: 0.0211
Badness: 0.021073


= Twothirdtonic =
= Twothirdtonic =
Commas: 686/675, 6144/6125
[[Comma list]]: 686/675, 6144/6125


POTE generator: ~15/14 = 130.401
[[Mapping]]: [<1 3 2 4|, <0 -13 3 -11|]


Map: [<1 3 2 4|, <0 -13 3 -11|]
[[Wedgie]]: <<13 -3 11 -35 -19 34||


Wedgie: <<13 -3 11 -35 -19 34||
[[POTE tuning|POTE generator]]: ~15/14 = 130.401


EDOs: {{EDOs| 9, 28b, 37, 46 }}
[[EDO|Vals]]: {{Val list| 9, 28b, 37, 46 }}


Badness: 0.0996
[[Badness]]: 0.099601


== 11-limit ==
== 11-limit ==
Commas: 121/120, 176/175, 686/675
Comma list: 121/120, 176/175, 686/675
 
Mapping: [<1 3 2 4 4|, <0 -13 3 -11 -5|]


POTE generator: ~15/14 = 130.430
POTE generator: ~15/14 = 130.430


Map: [<1 3 2 4 4|, <0 -13 3 -11 -5|]
Vals: {{Val list| 9, 28b, 37, 46 }}


EDOs: {{EDOs| 9, 28b, 37, 46 }}
Badness: 0.040768


Badness: 0.0408
== 13-limit ==
Comma list: 91/90, 121/120, 169/168, 176/175


== 13-limit ==
Mapping: [<1 3 2 4 4 5|, <0 -13 3 -11 -5 -12|]
Commas: 91/90, 121/120, 169/168, 176/175


POTE generator: ~15/14 = 130.409
POTE generator: ~15/14 = 130.409


Map: [<1 3 2 4 4 5|, <0 -13 3 -11 -5 -12|]
Vals: {{Val list| 9, 28b, 37, 46 }}


EDOs: {{EDOs| 9, 28b, 37, 46 }}
Badness: 0.025941
 
Badness: 0.0259


= Nessafof =
= Nessafof =
Commas: 6144/6125, 250047/250000
[[Comma list]]: 6144/6125, 250047/250000


POTE generator: ~35/32 = 157.420
[[Mapping]]: [<3 2 5 10|, <0 7 5 -4|]


Map: [<3 2 5 10|, <0 7 5 -4|]
[[Wedgie]]: <<21 15 -12 -25 -78 -70||


Wedgie: <<21 15 -12 -25 -78 -70||
[[POTE tuning|POTE generator]]: ~35/32 = 157.480


EDOs: {{EDOs| 15, 54b, 69, 84, 99, 282, 381 }}
[[EDO|Vals]]: {{Val list| 15, 54b, 69, 84, 99, 282, 381 }}


Badness: 0.0450
[[Badness]]: 0.045048


= Septisuperfourth =
= Septisuperfourth =
Commas: 6144/6125, 118098/117649
[[Comma list]]: 6144/6125, 118098/117649


POTE generator: ~48/35 = 544.680
[[Mapping]]: [<2 4 4 7|, <0 -9 7 -15|]


Map: [<2 4 4 7|, <0 -9 7 -15|]
[[Wedgie]]: <<18 -14 30 -64 -3 109||


Wedgie: <<18 -14 30 -64 -3 109||
[[POTE tuning|POTE generator]]: ~48/35 = 544.680


EDOs: {{EDOs| 22, 86, 108, 130, 152, 282 }}
[[EDO|Vals]]: {{Val list| 22, 86, 108, 130, 152, 282 }}


Badness: 0.0592
[[Badness]]: 0.059241


== 11-limit ==
== 11-limit ==
Commas: 540/539, 4000/3993, 5632/5625
Comma list: 540/539, 4000/3993, 5632/5625
 
Mapping: [<2 4 4 7 6|, <0 -9 7 -15 10|]


POTE generator: ~48/35 = 544.696
POTE generator: ~48/35 = 544.696


Map: [<2 4 4 7 6|, <0 -9 7 -15 10|]
Vals: {{Val list| 22, 86, 108, 130, 152, 282, 434de, 716de }}


EDOs: {{EDOs| 22, 86, 108, 130, 152, 282, 434de, 716de }}
Badness: 0.024619


Badness: 0.0246
=== 13-limit ===
Comma list: 540/539, 729/728, 4000/3993, 21168/21125


=== 13-limit ===
Mapping: [<2 4 4 7 6 11|, <0 -9 7 -15 10 -39|]
Commas: 540/539, 729/728, 4000/3993, 21168/21125


POTE generator: ~48/35 = 544.675
POTE generator: ~48/35 = 544.675


Map: [<2 4 4 7 6 11|, <0 -9 7 -15 10 -39|]
Vals: {{Val list| 22f, 108f, 130, 282 }}


EDOs: {{EDOs| 22f, 108f, 130, 282 }}
Badness: 0.022887


Badness: 0.0229
=== Septisuperquad ===
Comma list: 351/350, 364/363, 540/539, 5632/5625


=== Septisuperquad ===
Mapping: [<2 4 4 7 6 5|, <0 -9 7 -15 10 26|]
Commas: 351/350, 364/363, 540/539, 5632/5625


POTE generator: ~48/35 = 544.641
POTE generator: ~48/35 = 544.641


Map: [<2 4 4 7 6 5|, <0 -9 7 -15 10 26|]
Vals: {{Val list| 22, 86f, 108, 130 }}
 
EDOs: {{EDOs| 22, 86f, 108, 130 }}


Badness: 0.0330
Badness: 0.033038


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