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]], [[Kleismic family #Hemikleismic|hemikleismic]], and [[Meantone family #Mohajira|mohajira]].  


=Hendecatonic=
= Hendecatonic =
Commas: 6144/6125, 10976/10935
Commas: 6144/6125, 10976/10935


Line 14: Line 12:
Wedgie: <<11 -11 22 -43 4 82||
Wedgie: <<11 -11 22 -43 4 82||


EDOs: 22, 55, 77, [[99edo|99]]
EDOs: {{EDOs| 22, 55, 77, 99 }}


Badness: 0.0411
Badness: 0.0411


==11-limit==
== 11-limit ==
Commas: 121/120, 176/175, 10976/10935
Commas: 121/120, 176/175, 10976/10935


Line 25: Line 23:
Map: [<11 0 43 -4 38], <0 1 -1 2 0|]
Map: [<11 0 43 -4 38], <0 1 -1 2 0|]


EDOs: 22, 55, 77, 99, 176e, 275e
EDOs: {{EDOs| 22, 55, 77, 99, 176e, 275e }}


Badness: 0.0461
Badness: 0.0461


==Icosidillic==
== Icosidillic ==
Commas: 3388/3375, 6144/6125, 9801/9800
Commas: 3388/3375, 6144/6125, 9801/9800


Line 36: Line 34:
Map: [<22 0 86 -8 111|, <0 1 -1 2 -1|]
Map: [<22 0 86 -8 111|, <0 1 -1 2 -1|]


EDOs: 22, 154, 176, 198, 968, 1166
EDOs: {{EDOs| 22, 154, 176, 198, 968bcc, 1166bcccd }}


Badness: 0.0577
Badness: 0.0577


=Hemischis=
= Hemischis =
{{see also| Schismatic family }}
 
Commas: 6144/6125, 19683/19600
Commas: 6144/6125, 19683/19600


Line 49: Line 49:
Wedgie: <<2 -16 25 -30 34 103||
Wedgie: <<2 -16 25 -30 34 103||


EDOs: 5, 9, 14, 19, 24, 29, 53, 130, 183, 313
EDOs: {{EDOs| 24, 53, 130, 183, 313 }}


Badness: 0.0458
Badness: 0.0458


==11-limit==
== 11-limit ==
Commas: 540/539, 8019/8000, 5632/5625
Commas: 540/539, 8019/8000, 5632/5625


Line 60: Line 60:
Map: [<1 0 15 -17 51|, <0 2 -16 25 -60|]
Map: [<1 0 15 -17 51|, <0 2 -16 25 -60|]


EDOs: 5, 9, 14, 19, 24, 29, 53, 130, 183, 313
EDOs: {{EDOs| 24e, 53, 130, 183, 313 }}


Badness: 0.0363
Badness: 0.0363


==13-limit==
== 13-limit ==
Commas: 351/350, 540/539, 676/675, 4096/4095
Commas: 351/350, 540/539, 676/675, 4096/4095


Line 71: Line 71:
Map: [<1 0 15 -17 51 14|, <0 2 -16 25 -60 -13|]
Map: [<1 0 15 -17 51 14|, <0 2 -16 25 -60 -13|]


EDOs: 5, 9, 14, 19, 24, 29, 53, 130, 183, 313
EDOs: {{EDOs| 24e, 53, 130, 183, 313 }}


Badness: 0.0208
Badness: 0.0208


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


EDOs: 5, 9, 14, 19, 24, 29, 53, 130, 183, 679
EDOs: {{EDOs| 24egg, 53, 130, 183, 679df }}


Badness: 0.0211
Badness: 0.0211


=Twothirdtonic=
= Twothirdtonic =
Commas: 686/675, 6144/6125
Commas: 686/675, 6144/6125


Line 95: Line 95:
Wedgie: <<13 -3 11 -35 -19 34||
Wedgie: <<13 -3 11 -35 -19 34||


EDOs: 9, 10, 19, 28, 37, 46
EDOs: {{EDOs| 9, 28b, 37, 46 }}


Badness: 0.0996
Badness: 0.0996


==11-limit==
== 11-limit ==
Commas: 121/120, 176/175, 686/675
Commas: 121/120, 176/175, 686/675


Line 106: Line 106:
Map: [<1 3 2 4 4|, <0 -13 3 -11 -5|]
Map: [<1 3 2 4 4|, <0 -13 3 -11 -5|]


EDOs: 9, 10, 19, 28, 37, 46
EDOs: {{EDOs| 9, 28b, 37, 46 }}


Badness: 0.0408
Badness: 0.0408


==13-limit==
== 13-limit ==
Commas: 91/90, 121/120, 169/168, 176/175
Commas: 91/90, 121/120, 169/168, 176/175


Line 117: Line 117:
Map: [<1 3 2 4 4 5|, <0 -13 3 -11 -5 -12|]
Map: [<1 3 2 4 4 5|, <0 -13 3 -11 -5 -12|]


EDOs: 9, 10, 19, 28, 37, 46
EDOs: {{EDOs| 9, 28b, 37, 46 }}


Badness: 0.0259
Badness: 0.0259


=Nessafof=
= Nessafof =
Commas: 6144/6125, 250047/250000
Commas: 6144/6125, 250047/250000


Line 130: Line 130:
Wedgie: <<21 15 -12 -25 -78 -70||
Wedgie: <<21 15 -12 -25 -78 -70||


EDOs: 15, 69, 84, 99, 282, 381
EDOs: {{EDOs| 15, 54b, 69, 84, 99, 282, 381 }}


Badness: 0.0450
Badness: 0.0450


=Septisuperfourth=
= Septisuperfourth =
Commas: 6144/6125, 118098/117649
Commas: 6144/6125, 118098/117649


Line 143: Line 143:
Wedgie: <<18 -14 30 -64 -3 109||
Wedgie: <<18 -14 30 -64 -3 109||


EDOs: 22, 86, 108, 130, 152, 282
EDOs: {{EDOs| 22, 86, 108, 130, 152, 282 }}


Badness: 0.0592
Badness: 0.0592


==11-limit==
== 11-limit ==
Commas: 540/539, 4000/3993, 5632/5625
Commas: 540/539, 4000/3993, 5632/5625


Line 154: Line 154:
Map: [<2 4 4 7 6|, <0 -9 7 -15 10|]
Map: [<2 4 4 7 6|, <0 -9 7 -15 10|]


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


Badness: 0.0246
Badness: 0.0246


==13-limit==
=== 13-limit ===
Commas: 540/539 729/728 4000/3993 21168/21125
Commas: 540/539, 729/728, 4000/3993, 21168/21125


POTE generator: ~48/35 = 544.675
POTE generator: ~48/35 = 544.675
Line 165: Line 165:
Map: [<2 4 4 7 6 11|, <0 -9 7 -15 10 -39|]
Map: [<2 4 4 7 6 11|, <0 -9 7 -15 10 -39|]


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


Badness: 0.0229
Badness: 0.0229


==Septisuperquad==
=== Septisuperquad ===
Commas: 351/350, 364/363, 540/539, 5632/5625
Commas: 351/350, 364/363, 540/539, 5632/5625


Line 176: Line 176:
Map: [<2 4 4 7 6 5|, <0 -9 7 -15 10 26|]
Map: [<2 4 4 7 6 5|, <0 -9 7 -15 10 26|]


EDOs: 22, 108, 130
EDOs: {{EDOs| 22, 86f, 108, 130 }}


Badness: 0.0330
Badness: 0.0330


=Whoops=
= Whoops =
{{see also| Very high accuracy temperaments #Whoosh }}
 
Commas: 6144/6125, 244140625/243045684
Commas: 6144/6125, 244140625/243045684


Line 189: Line 191:
Wedgie: <<33 25 -21 -37 -126 -119||
Wedgie: <<33 25 -21 -37 -126 -119||


EDOs: 15, 122d, 137, 152, 608d, 623bd, 775bcd
EDOs: {{EDOs| 15, 122d, 137, 152, 608d, 623bd, 775bcd }}


Badness: 0.1758
Badness: 0.1758


==11-limit==
== 11-limit ==
Commas: 6144/6125, 3025/3024, 4000/3993
Commas: 6144/6125, 3025/3024, 4000/3993


Line 200: Line 202:
Map: [<1 17 14 -7 10|, <0 -33 -25 21 -14|]
Map: [<1 17 14 -7 10|, <0 -33 -25 21 -14|]


EDOs: 15, 122d, 137, 152, 608de, 623bde, 775bcde
EDOs: {{EDOs| 15, 122d, 137, 152, 608de, 623bde, 775bcde }}


Badness: 0.0437
Badness: 0.0437


=Polypyth=
= Polypyth =
Commas: 6144/6125, 179200/177147
Commas: 6144/6125, 179200/177147


Line 211: Line 213:
Map: [<1 0 -31 52|, <0 1 21 -31|]
Map: [<1 0 -31 52|, <0 1 21 -31|]


EDOs: 46, 121, 167, 288b, 455bcd, 743bcd
EDOs: {{EDOs| 46, 121, 167, 288b, 455bcd, 743bcd }}


Badness: 0.13800
Badness: 0.13800


==11-limit==
== 11-limit ==
Commas: 896/891, 2200/2187, 6144/6125
Commas: 896/891, 2200/2187, 6144/6125


Line 222: Line 224:
Map: [<1 0 -31 52 59|, <0 1 21 -31 -35|]
Map: [<1 0 -31 52 59|, <0 1 21 -31 -35|]


EDOs: 46, 121, 167, 288be, 455bcde
EDOs: {{EDOs| 46, 121, 167, 288be, 455bcde }}


Badness: 0.0511
Badness: 0.0511


==13-limit==
== 13-limit ==
Commas: 325/324, 352/351, 364/363, 1716/1715
Commas: 325/324, 352/351, 364/363, 1716/1715


Line 233: Line 235:
Map: [<1 0 -31 52 59 64|, <0 1 21 -31 -35 -38|]
Map: [<1 0 -31 52 59 64|, <0 1 21 -31 -35 -38|]


EDOs: 46, 121, 167, 288be
EDOs: {{EDOs| 46, 121, 167, 288be }}


Badness: 0.0303
Badness: 0.0303


==17-limit==
== 17-limit ==
Commas: 256/255, 325/324, 352/351, 364/363, 1716/1715
Commas: 256/255, 325/324, 352/351, 364/363, 1716/1715


Line 244: Line 246:
Map: [<1 0 -31 52 59 64 39|, <0 1 21 -31 -35 -38 -22|]
Map: [<1 0 -31 52 59 64 39|, <0 1 21 -31 -35 -38 -22|]


EDOs: 46, 121, 167, 288beg
EDOs: {{EDOs| 46, 121, 167, 288beg }}


Badness: 0.0191
Badness: 0.0191
[[Category:hemischis]]
 
[[Category:hendecatonic]]
[[Category:Theory]]
[[Category:porwell]]
[[Category:Temperament]]
[[Category:rank_2]]
[[Category:Porwell]]
[[Category:temperament]]
[[Category:Hemischis]]
[[Category:Hendecatonic]]
[[Category:Rank 2]]

Revision as of 08:38, 28 November 2020

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

Discussed elsewhere are hemiwürschmidt, orwell, amity, valentine, porcupine, shrutar, hexadecimal, grendel, hemikleismic, and mohajira.

Hendecatonic

Commas: 6144/6125, 10976/10935

POTE generator: ~3/2 = 703.054

Map: [<11 0 43 -4], <0 1 -1 2|]

Wedgie: <<11 -11 22 -43 4 82||

EDOs: 22, 55, 77, 99

Badness: 0.0411

11-limit

Commas: 121/120, 176/175, 10976/10935

POTE generator: ~3/2 = 702.636

Map: [<11 0 43 -4 38], <0 1 -1 2 0|]

EDOs: 22, 55, 77, 99, 176e, 275e

Badness: 0.0461

Icosidillic

Commas: 3388/3375, 6144/6125, 9801/9800

POTE generator: 702.914

Map: [<22 0 86 -8 111|, <0 1 -1 2 -1|]

EDOs: 22, 154, 176, 198, 968bcc, 1166bcccd

Badness: 0.0577

Hemischis

See also: Schismatic family

Commas: 6144/6125, 19683/19600

POTE generator: ~81/70 = 249.203

Map: [<1 0 15 -17|, <0 2 -16 25|]

Wedgie: <<2 -16 25 -30 34 103||

EDOs: 24, 53, 130, 183, 313

Badness: 0.0458

11-limit

Commas: 540/539, 8019/8000, 5632/5625

POTE generator: ~81/70 = 249.199

Map: [<1 0 15 -17 51|, <0 2 -16 25 -60|]

EDOs: 24e, 53, 130, 183, 313

Badness: 0.0363

13-limit

Commas: 351/350, 540/539, 676/675, 4096/4095

POTE generator: ~15/13 = 249.199

Map: [<1 0 15 -17 51 14|, <0 2 -16 25 -60 -13|]

EDOs: 24e, 53, 130, 183, 313

Badness: 0.0208

17-limit

Commas: 351/350, 442/441, 561/560, 676/675, 4096/4095

POTE generator: ~15/13 = 249.190

Map: [<1 0 15 -17 51 14 -49|, <0 2 -16 25 -60 -13 67|]

EDOs: 24egg, 53, 130, 183, 679df

Badness: 0.0211

Twothirdtonic

Commas: 686/675, 6144/6125

POTE generator: ~15/14 = 130.401

Map: [<1 3 2 4|, <0 -13 3 -11|]

Wedgie: <<13 -3 11 -35 -19 34||

EDOs: 9, 28b, 37, 46

Badness: 0.0996

11-limit

Commas: 121/120, 176/175, 686/675

POTE generator: ~15/14 = 130.430

Map: [<1 3 2 4 4|, <0 -13 3 -11 -5|]

EDOs: 9, 28b, 37, 46

Badness: 0.0408

13-limit

Commas: 91/90, 121/120, 169/168, 176/175

POTE generator: ~15/14 = 130.409

Map: [<1 3 2 4 4 5|, <0 -13 3 -11 -5 -12|]

EDOs: 9, 28b, 37, 46

Badness: 0.0259

Nessafof

Commas: 6144/6125, 250047/250000

POTE generator: ~35/32 = 157.420

Map: [<3 2 5 10|, <0 7 5 -4|]

Wedgie: <<21 15 -12 -25 -78 -70||

EDOs: 15, 54b, 69, 84, 99, 282, 381

Badness: 0.0450

Septisuperfourth

Commas: 6144/6125, 118098/117649

POTE generator: ~48/35 = 544.680

Map: [<2 4 4 7|, <0 -9 7 -15|]

Wedgie: <<18 -14 30 -64 -3 109||

EDOs: 22, 86, 108, 130, 152, 282

Badness: 0.0592

11-limit

Commas: 540/539, 4000/3993, 5632/5625

POTE generator: ~48/35 = 544.696

Map: [<2 4 4 7 6|, <0 -9 7 -15 10|]

EDOs: 22, 86, 108, 130, 152, 282, 434de, 716de

Badness: 0.0246

13-limit

Commas: 540/539, 729/728, 4000/3993, 21168/21125

POTE generator: ~48/35 = 544.675

Map: [<2 4 4 7 6 11|, <0 -9 7 -15 10 -39|]

EDOs: 22f, 108f, 130, 282

Badness: 0.0229

Septisuperquad

Commas: 351/350, 364/363, 540/539, 5632/5625

POTE generator: ~48/35 = 544.641

Map: [<2 4 4 7 6 5|, <0 -9 7 -15 10 26|]

EDOs: 22, 86f, 108, 130

Badness: 0.0330

Whoops

See also: Very high accuracy temperaments § Whoosh

Commas: 6144/6125, 244140625/243045684

POTE generator: ~441/320 = 560.519

Map: [<1 17 14 -7|, <0 -33 -25 21|]

Wedgie: <<33 25 -21 -37 -126 -119||

EDOs: 15, 122d, 137, 152, 608d, 623bd, 775bcd

Badness: 0.1758

11-limit

Commas: 6144/6125, 3025/3024, 4000/3993

POTE generator: ~242/175 = 560.519

Map: [<1 17 14 -7 10|, <0 -33 -25 21 -14|]

EDOs: 15, 122d, 137, 152, 608de, 623bde, 775bcde

Badness: 0.0437

Polypyth

Commas: 6144/6125, 179200/177147

POTE generator: ~3/2 = 704.174

Map: [<1 0 -31 52|, <0 1 21 -31|]

EDOs: 46, 121, 167, 288b, 455bcd, 743bcd

Badness: 0.13800

11-limit

Commas: 896/891, 2200/2187, 6144/6125

POTE generator: ~3/2 = 704.177

Map: [<1 0 -31 52 59|, <0 1 21 -31 -35|]

EDOs: 46, 121, 167, 288be, 455bcde

Badness: 0.0511

13-limit

Commas: 325/324, 352/351, 364/363, 1716/1715

POTE generator: ~3/2 = 704.168

Map: [<1 0 -31 52 59 64|, <0 1 21 -31 -35 -38|]

EDOs: 46, 121, 167, 288be

Badness: 0.0303

17-limit

Commas: 256/255, 325/324, 352/351, 364/363, 1716/1715

POTE generator: ~3/2 = 704.168

Map: [<1 0 -31 52 59 64 39|, <0 1 21 -31 -35 -38 -22|]

EDOs: 46, 121, 167, 288beg

Badness: 0.0191

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