Porwell temperaments: Difference between revisions

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


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


Badness: 0.13800
Badness: 0.137995


== 11-limit ==
== 11-limit ==
Line 224: 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: {{EDOs| 46, 121, 167, 288be, 455bcde }}
EDOs: {{Val list| 46, 121, 167, 288be, 455bcde }}


Badness: 0.0511
Badness: 0.051131


== 13-limit ==
== 13-limit ==
Line 235: 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: {{EDOs| 46, 121, 167, 288be }}
EDOs: {{Val list| 46, 121, 167, 288be }}


Badness: 0.0303
Badness: 0.030292


== 17-limit ==
== 17-limit ==
Line 246: 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: {{EDOs| 46, 121, 167, 288beg }}
EDOs: {{Val list| 46, 121, 167, 288beg }}


Badness: 0.0191
Badness: 0.019051
 
= Icositritonic =
The ''icositritonic'' temperament (46&161, named by [[User:Xenllium|Xenllium]]) has a period of 1/23 octave, so six period represents [[6/5]] and nine period represents [[21/16]].
 
Commas: 6144/6125, 9920232/9765625
 
Map: [<23 37 54 64|, <0 -1 -1 1|]
 
POTE generator: ~64/63 = 29.3586
 
EDOs: 23, 46, 69, 115, 161, 207
 
Badness: 0.196622
 
== 11-limit ==
Commas: 441/440, 6144/6125, 35937/35840
 
Map: [<23 37 54 64 79|, <0 -1 -1 1 1|]
 
POTE generator: ~64/63 = 29.3980
 
EDOs: 23, 46, 69, 115, 161, 207
 
Badness: 0.064613
 
== 13-limit ==
Commas: 351/350, 441/440, 847/845, 3584/3575
 
Map: [<23 37 54 64 79 84|, <0 -1 -1 1 1 2|]
 
POTE generator: ~64/63 = 29.2830
 
EDOs: 46, 115, 161, 207
 
Badness: 0.040484
 
== 17-limit ==
Commas: 351/350, 441/440, 561/560, 847/845, 1089/1088
 
Map: [<23 37 54 64 79 84 94|, <0 -1 -1 1 1 2 0|]
 
POTE generator: ~64/63 = 29.2800
 
EDOs: 46, 115, 161, 207
 
Badness: 0.024676
 
== 19-limit ==
Commas: 351/350, 441/440, 456/455, 476/475, 513/512, 847/845
 
Map: [<23 37 54 64 79 84 94 96|, <0 -1 -1 1 1 2 0 3|]
 
POTE generator: ~64/63 = 29.3760
 
EDOs: 46, 115, 161, 207
 
Badness: 0.021579
 
== 23-limit ==
Commas: 276/275, 351/350, 391/390, 441/440, 456/455, 476/475, 847/845
 
Map: [<23 37 54 64 79 84 94 96 104|, <0 -1 -1 1 1 2 0 3 0|]
 
POTE generator: ~64/63 = 29.3471
 
EDOs: 46, 115, 161, 207
 
Badness: 0.017745


[[Category:Theory]]
[[Category:Theory]]

Revision as of 22:10, 19 April 2021

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: Template:Val list

Badness: 0.137995

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: Template:Val list

Badness: 0.051131

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: Template:Val list

Badness: 0.030292

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: Template:Val list

Badness: 0.019051

Icositritonic

The icositritonic temperament (46&161, named by Xenllium) has a period of 1/23 octave, so six period represents 6/5 and nine period represents 21/16.

Commas: 6144/6125, 9920232/9765625

Map: [<23 37 54 64|, <0 -1 -1 1|]

POTE generator: ~64/63 = 29.3586

EDOs: 23, 46, 69, 115, 161, 207

Badness: 0.196622

11-limit

Commas: 441/440, 6144/6125, 35937/35840

Map: [<23 37 54 64 79|, <0 -1 -1 1 1|]

POTE generator: ~64/63 = 29.3980

EDOs: 23, 46, 69, 115, 161, 207

Badness: 0.064613

13-limit

Commas: 351/350, 441/440, 847/845, 3584/3575

Map: [<23 37 54 64 79 84|, <0 -1 -1 1 1 2|]

POTE generator: ~64/63 = 29.2830

EDOs: 46, 115, 161, 207

Badness: 0.040484

17-limit

Commas: 351/350, 441/440, 561/560, 847/845, 1089/1088

Map: [<23 37 54 64 79 84 94|, <0 -1 -1 1 1 2 0|]

POTE generator: ~64/63 = 29.2800

EDOs: 46, 115, 161, 207

Badness: 0.024676

19-limit

Commas: 351/350, 441/440, 456/455, 476/475, 513/512, 847/845

Map: [<23 37 54 64 79 84 94 96|, <0 -1 -1 1 1 2 0 3|]

POTE generator: ~64/63 = 29.3760

EDOs: 46, 115, 161, 207

Badness: 0.021579

23-limit

Commas: 276/275, 351/350, 391/390, 441/440, 456/455, 476/475, 847/845

Map: [<23 37 54 64 79 84 94 96 104|, <0 -1 -1 1 1 2 0 3 0|]

POTE generator: ~64/63 = 29.3471

EDOs: 46, 115, 161, 207

Badness: 0.017745

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