Porwell temperaments: Difference between revisions

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


[[Wedgie]]: <<11 -11 22 -43 4 82||
{{Multival|legend=1| 11 -11 22 -43 4 82 }}


[[POTE tuning|POTE generator]]: ~3/2 = 703.054
[[POTE generator]]: ~3/2 = 703.054


[[EDO|Vals]]: {{Val list| 22, 55, 77, 99 }}
{{Val list|legend=1| 22, 55, 77, 99 }}


[[Badness]]: 0.041081
[[Badness]]: 0.041081
Line 47: Line 47:
[[Mapping]]: [<1 0 15 -17|, <0 2 -16 25|]
[[Mapping]]: [<1 0 15 -17|, <0 2 -16 25|]


[[Wedgie]]: <<2 -16 25 -30 34 103||
{{Multival|legend=1| 2 -16 25 -30 34 103 }}


[[POTE tuning|POTE generator]]: ~81/70 = 249.203
[[POTE generator]]: ~81/70 = 249.203


[[EDO|Vals]]: {{Val list| 24, 53, 130, 183, 313 }}
{{Val list|legend=1| 24, 53, 130, 183, 313 }}


[[Badness]]: 0.045817
[[Badness]]: 0.045817
Line 93: Line 93:
[[Mapping]]: [<1 3 2 4|, <0 -13 3 -11|]
[[Mapping]]: [<1 3 2 4|, <0 -13 3 -11|]


[[Wedgie]]: <<13 -3 11 -35 -19 34||
{{Multival|legend=1| 13 -3 11 -35 -19 34 }}


[[POTE tuning|POTE generator]]: ~15/14 = 130.401
[[POTE generator]]: ~15/14 = 130.401


[[EDO|Vals]]: {{Val list| 9, 28b, 37, 46 }}
{{Val list|legend=1| 9, 28b, 37, 46 }}


[[Badness]]: 0.099601
[[Badness]]: 0.099601
Line 128: Line 128:
[[Mapping]]: [<3 2 5 10|, <0 7 5 -4|]
[[Mapping]]: [<3 2 5 10|, <0 7 5 -4|]


[[Wedgie]]: <<21 15 -12 -25 -78 -70||
{{Multival|legend=1| 21 15 -12 -25 -78 -70 }}


[[POTE tuning|POTE generator]]: ~35/32 = 157.480
[[POTE generator]]: ~35/32 = 157.480


[[EDO|Vals]]: {{Val list| 15, 54b, 69, 84, 99, 282, 381 }}
{{Val list|legend=1| 15, 54b, 69, 84, 99, 282, 381 }}


[[Badness]]: 0.045048
[[Badness]]: 0.045048
Line 141: Line 141:
[[Mapping]]: [<2 4 4 7|, <0 -9 7 -15|]
[[Mapping]]: [<2 4 4 7|, <0 -9 7 -15|]


[[Wedgie]]: <<18 -14 30 -64 -3 109||
{{Multival|legend=1| 18 -14 30 -64 -3 109 }}


[[POTE tuning|POTE generator]]: ~48/35 = 544.680
[[POTE generator]]: ~48/35 = 544.680


[[EDO|Vals]]: {{Val list| 22, 86, 108, 130, 152, 282 }}
{{Val list|legend=1| 22, 86, 108, 130, 152, 282 }}


[[Badness]]: 0.059241
[[Badness]]: 0.059241
Line 185: Line 185:
{{see also| Very high accuracy temperaments #Whoosh }}
{{see also| Very high accuracy temperaments #Whoosh }}


Commas: 6144/6125, 244140625/243045684
[[Comma list]]: 6144/6125, 244140625/243045684


POTE generator: ~441/320 = 560.519
[[Mapping]]: [<1 17 14 -7|, <0 -33 -25 21|]


Map: [<1 17 14 -7|, <0 -33 -25 21|]
{{Multival|legend=1| 33 25 -21 -37 -126 -119 }}


Wedgie: <<33 25 -21 -37 -126 -119||
[[POTE generator]]: ~441/320 = 560.519


EDOs: {{EDOs| 15, 122d, 137, 152, 608d, 623bd, 775bcd }}
{{Val list|legend=1| 15, 122d, 137, 152, 608d, 623bd, 775bcd }}


Badness: 0.1758
[[Badness]]: 0.1758


== 11-limit ==
== 11-limit ==
Commas: 6144/6125, 3025/3024, 4000/3993
Comma list: 6144/6125, 3025/3024, 4000/3993
 
Mapping: [<1 17 14 -7 10|, <0 -33 -25 21 -14|]


POTE generator: ~242/175 = 560.519
POTE generator: ~242/175 = 560.519


Map: [<1 17 14 -7 10|, <0 -33 -25 21 -14|]
Vals: {{Val list| 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
[[Comma list]]: 6144/6125, 179200/177147


POTE generator: ~3/2 = 704.174
[[Mapping]]: [<1 0 -31 52|, <0 1 21 -31|]


Map: [<1 0 -31 52|, <0 1 21 -31|]
[[POTE generator]]: ~3/2 = 704.174


EDOs: {{Val list| 46, 121, 167, 288b, 455bcd, 743bcd }}
{{Val list|legend=1| 46, 121, 167, 288b, 455bcd, 743bcd }}


Badness: 0.137995
[[Badness]]: 0.137995


== 11-limit ==
== 11-limit ==
Commas: 896/891, 2200/2187, 6144/6125
Comma list: 896/891, 2200/2187, 6144/6125
 
Mapping: [<1 0 -31 52 59|, <0 1 21 -31 -35|]


POTE generator: ~3/2 = 704.177
POTE generator: ~3/2 = 704.177


Map: [<1 0 -31 52 59|, <0 1 21 -31 -35|]
Vals: {{Val list| 46, 121, 167, 288be, 455bcde }}
 
EDOs: {{Val list| 46, 121, 167, 288be, 455bcde }}


Badness: 0.051131
Badness: 0.051131


== 13-limit ==
== 13-limit ==
Commas: 325/324, 352/351, 364/363, 1716/1715
Comma list: 325/324, 352/351, 364/363, 1716/1715
 
Mapping: [<1 0 -31 52 59 64|, <0 1 21 -31 -35 -38|]


POTE generator: ~3/2 = 704.168
POTE generator: ~3/2 = 704.168


Map: [<1 0 -31 52 59 64|, <0 1 21 -31 -35 -38|]
Vals: {{Val list| 46, 121, 167, 288be }}
 
EDOs: {{Val list| 46, 121, 167, 288be }}


Badness: 0.030292
Badness: 0.030292


== 17-limit ==
== 17-limit ==
Commas: 256/255, 325/324, 352/351, 364/363, 1716/1715
Comma list: 256/255, 325/324, 352/351, 364/363, 1716/1715
 
Mapping: [<1 0 -31 52 59 64 39|, <0 1 21 -31 -35 -38 -22|]


POTE generator: ~3/2 = 704.168
POTE generator: ~3/2 = 704.168


Map: [<1 0 -31 52 59 64 39|, <0 1 21 -31 -35 -38 -22|]
Vals: {{Val list| 46, 121, 167, 288beg }}
 
EDOs: {{Val list| 46, 121, 167, 288beg }}


Badness: 0.019051
Badness: 0.019051
Line 259: Line 259:
[[Mapping]]: [<23 37 54 64|, <0 -1 -1 1|]
[[Mapping]]: [<23 37 54 64|, <0 -1 -1 1|]


[[Wedgie]]: <<23 23 -23 -17 -101 -118||
{{Multival|legend=1| 23 23 -23 -17 -101 -118 }}


[[POTE tuning|POTE generator]]: ~64/63 = 29.3586
[[POTE generator]]: ~64/63 = 29.3586


[[EDO|Vals]]: {{Val list| 23, 46, 115, 161, 207, 368c }}
{{Val list|legend=1| 23, 46, 115, 161, 207, 368c }}


[[Badness]]: 0.196622
[[Badness]]: 0.196622
Line 322: Line 322:
Badness: 0.017745
Badness: 0.017745


[[Category:Theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament]]
[[Category:Temperament collection]]
[[Category:Porwell]]
[[Category:Porwell]]
[[Category:Hemischis]]
[[Category:Hemischis]]
[[Category:Hendecatonic]]
[[Category:Hendecatonic]]
[[Category:Rank 2]]
[[Category:Rank 2]]

Revision as of 07:44, 10 May 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, trident, hemikleismic, and mohajira.

Hendecatonic

The hendecatonic temperament has a period of 1/11 octave, which represents 16/15 and four times of which represents 9/7.

Comma list: 6144/6125, 10976/10935

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

Wedgie: ⟨⟨ 11 -11 22 -43 4 82 ]]

POTE generator: ~3/2 = 703.054

Template:Val list

Badness: 0.041081

11-limit

Comma list: 121/120, 176/175, 10976/10935

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

POTE generator: ~3/2 = 702.636

Vals: Template:Val list

Badness: 0.046088

Icosidillic

Comma list: 3388/3375, 6144/6125, 9801/9800

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

POTE generator: ~3/2 = 702.914

Vals: Template:Val list

Badness: 0.057725

Hemischis

See also: Schismatic family

Comma list: 6144/6125, 19683/19600

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

Wedgie: ⟨⟨ 2 -16 25 -30 34 103 ]]

POTE generator: ~81/70 = 249.203

Template:Val list

Badness: 0.045817

11-limit

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

Vals: Template:Val list

Badness: 0.036289

13-limit

Comma list: 351/350, 540/539, 676/675, 4096/4095

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

POTE generator: ~15/13 = 249.199

Vals: Template:Val list

Badness: 0.020816

17-limit

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

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

POTE generator: ~15/13 = 249.190

Vals: Template:Val list

Badness: 0.021073

Twothirdtonic

Comma list: 686/675, 6144/6125

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

Wedgie: ⟨⟨ 13 -3 11 -35 -19 34 ]]

POTE generator: ~15/14 = 130.401

Template:Val list

Badness: 0.099601

11-limit

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

Vals: Template:Val list

Badness: 0.040768

13-limit

Comma list: 91/90, 121/120, 169/168, 176/175

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

POTE generator: ~15/14 = 130.409

Vals: Template:Val list

Badness: 0.025941

Nessafof

Comma list: 6144/6125, 250047/250000

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

Wedgie: ⟨⟨ 21 15 -12 -25 -78 -70 ]]

POTE generator: ~35/32 = 157.480

Template:Val list

Badness: 0.045048

Septisuperfourth

Comma list: 6144/6125, 118098/117649

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

Wedgie: ⟨⟨ 18 -14 30 -64 -3 109 ]]

POTE generator: ~48/35 = 544.680

Template:Val list

Badness: 0.059241

11-limit

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

Vals: Template:Val list

Badness: 0.024619

13-limit

Comma list: 540/539, 729/728, 4000/3993, 21168/21125

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

POTE generator: ~48/35 = 544.675

Vals: Template:Val list

Badness: 0.022887

Septisuperquad

Comma list: 351/350, 364/363, 540/539, 5632/5625

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

POTE generator: ~48/35 = 544.641

Vals: Template:Val list

Badness: 0.033038

Whoops

See also: Very high accuracy temperaments § Whoosh

Comma list: 6144/6125, 244140625/243045684

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

Wedgie: ⟨⟨ 33 25 -21 -37 -126 -119 ]]

POTE generator: ~441/320 = 560.519

Template:Val list

Badness: 0.1758

11-limit

Comma list: 6144/6125, 3025/3024, 4000/3993

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

POTE generator: ~242/175 = 560.519

Vals: Template:Val list

Badness: 0.0437

Polypyth

Comma list: 6144/6125, 179200/177147

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

POTE generator: ~3/2 = 704.174

Template:Val list

Badness: 0.137995

11-limit

Comma list: 896/891, 2200/2187, 6144/6125

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

POTE generator: ~3/2 = 704.177

Vals: Template:Val list

Badness: 0.051131

13-limit

Comma list: 325/324, 352/351, 364/363, 1716/1715

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

POTE generator: ~3/2 = 704.168

Vals: Template:Val list

Badness: 0.030292

17-limit

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

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

POTE generator: ~3/2 = 704.168

Vals: 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.

Comma list: 6144/6125, 9920232/9765625

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

Wedgie: ⟨⟨ 23 23 -23 -17 -101 -118 ]]

POTE generator: ~64/63 = 29.3586

Template:Val list

Badness: 0.196622

11-limit

Comma list: 441/440, 6144/6125, 35937/35840

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

POTE generator: ~64/63 = 29.3980

Vals: Template:Val list

Badness: 0.064613

13-limit

Comma list: 351/350, 441/440, 847/845, 3584/3575

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

POTE generator: ~64/63 = 29.2830

Vals: Template:Val list

Badness: 0.040484

17-limit

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

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

POTE generator: ~64/63 = 29.2800

Vals: Template:Val list

Badness: 0.024676

19-limit

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

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

POTE generator: ~64/63 = 29.3760

Vals: Template:Val list

Badness: 0.021579

23-limit

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

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

POTE generator: ~64/63 = 29.3471

Vals: Template:Val list

Badness: 0.017745

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