Porwell temperaments: Difference between revisions

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* ''[[Trident]]'' → [[Tricot family #Trident]]
* ''[[Trident]]'' → [[Tricot family #Trident]]


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


Line 31: Line 31:
[[Badness]]: 0.041081
[[Badness]]: 0.041081


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


Line 44: Line 44:
Badness: 0.046088
Badness: 0.046088


=== Icosidillic ===
=== Icosidillic ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 57: Line 57:
Badness: 0.057725
Badness: 0.057725


== Hemischis ==
== Hemischis ==
{{see also| Schismatic family }}
{{see also| Schismatic family }}


Line 74: Line 74:
[[Badness]]: 0.045817
[[Badness]]: 0.045817


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


Line 87: Line 87:
Badness: 0.036289
Badness: 0.036289


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 100: Line 100:
Badness: 0.020816
Badness: 0.020816


=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 113: Line 113:
Badness: 0.021073
Badness: 0.021073


== Twothirdtonic ==
== Twothirdtonic ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 128: Line 128:
[[Badness]]: 0.099601
[[Badness]]: 0.099601


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


Line 141: Line 141:
Badness: 0.040768
Badness: 0.040768


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 148: Line 148:
Mapping: [{{val| 1 3 2 4 4 5 }}, {{val| 0 -13 3 -11 -5 -12 }}]
Mapping: [{{val| 1 3 2 4 4 5 }}, {{val| 0 -13 3 -11 -5 -12 }}]


POTE generator: ~15/14 = 130.409
POTE generator: ~13/12 = 130.409


Vals: {{Val list| 9, 28b, 37, 46 }}
Vals: {{Val list| 9, 28b, 37, 46 }}
Line 154: Line 154:
Badness: 0.025941
Badness: 0.025941


== Nessafof ==
== Nessafof ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 169: Line 169:
[[Badness]]: 0.045048
[[Badness]]: 0.045048


== Septisuperfourth ==
== Septisuperfourth ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 184: Line 184:
[[Badness]]: 0.059241
[[Badness]]: 0.059241


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


Line 197: Line 197:
Badness: 0.024619
Badness: 0.024619


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 210: Line 210:
Badness: 0.022887
Badness: 0.022887


=== Septisuperquad ===
=== Septisuperquad ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 223: Line 223:
Badness: 0.033038
Badness: 0.033038


== Whoops ==
== Whoops ==
{{see also| Very high accuracy temperaments #Whoosh }}
{{see also| Very high accuracy temperaments #Whoosh }}


Line 240: Line 240:
[[Badness]]: 0.1758
[[Badness]]: 0.1758


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


Line 253: Line 253:
Badness: 0.0437
Badness: 0.0437


== Polypyth ==
== Polypyth ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 266: Line 266:
[[Badness]]: 0.137995
[[Badness]]: 0.137995


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


Line 279: Line 279:
Badness: 0.051131
Badness: 0.051131


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 292: Line 292:
Badness: 0.030292
Badness: 0.030292


=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 305: Line 305:
Badness: 0.019051
Badness: 0.019051


== Icositritonic ==
== 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]].
The ''icositritonic'' temperament (46&161) has a period of 1/23 octave, so six period represents [[6/5]] and nine period represents [[21/16]].


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 322: Line 322:
[[Badness]]: 0.196622
[[Badness]]: 0.196622


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


Line 335: Line 335:
Badness: 0.064613
Badness: 0.064613


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 348: Line 348:
Badness: 0.040484
Badness: 0.040484


=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 361: Line 361:
Badness: 0.024676
Badness: 0.024676


=== 19-limit ===
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Line 374: Line 374:
Badness: 0.021579
Badness: 0.021579


=== 23-limit ===
=== 23-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23
Subgroup: 2.3.5.7.11.13.17.19.23


Line 387: Line 387:
Badness: 0.017745
Badness: 0.017745


== Countermiracle ==
== Countermiracle ==
The ''countermiracle'' temperament (31&145, named by [[User:Xenllium|Xenllium]]) tempers out the trimyna, 50421/50000 and the [[Quince clan|quince comma]], 823543/819200.
The ''countermiracle'' temperament (31&145) tempers out the trimyna, 50421/50000 and the [[Quince clan|quince comma]], 823543/819200.


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 394: Line 394:
[[Comma list]]: 6144/6125, 50421/50000
[[Comma list]]: 6144/6125, 50421/50000


[[Mapping]]: [{{val|1 4 3 3}}, {{val|0 -25 -7 -2}}]
[[Mapping]]: [{{val| 1 4 3 3 }}, {{val| 0 -25 -7 -2 }}]


{{Multival|legend=1| 25 7 2 -47 -67 -15 }}
{{Multival|legend=1| 25 7 2 -47 -67 -15 }}
Line 404: Line 404:
[[Badness]]: 0.102326
[[Badness]]: 0.102326


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


Comma list: 441/440, 3388/3375, 6144/6125
Comma list: 441/440, 3388/3375, 6144/6125


Mapping: [{{val|1 4 3 3 8}}, {{val|0 -25 -7 -2 -47}}]
Mapping: [{{val| 1 4 3 3 8 }}, {{val| 0 -25 -7 -2 -47 }}]


POTE generator: ~77/72 = 115.916
POTE generator: ~77/72 = 115.916
Line 417: Line 417:
Badness: 0.039162
Badness: 0.039162


==== Countermiraculous ====
==== Countermiraculous ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 196/195, 352/351, 1001/1000, 6144/6125
Comma list: 196/195, 352/351, 1001/1000, 6144/6125


Mapping: [{{val|1 4 3 3 8 1}}, {{val|0 -25 -7 -2 -47 28}}]
Mapping: [{{val| 1 4 3 3 8 1 }}, {{val| 0 -25 -7 -2 -47 28 }}]


POTE generator: ~77/72 = 115.880
POTE generator: ~77/72 = 115.880
Line 430: Line 430:
Badness: 0.039271
Badness: 0.039271


==== Counterbenediction ====
==== Counterbenediction ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 351/350, 441/440, 3146/3125, 3584/3575
Comma list: 351/350, 441/440, 3146/3125, 3584/3575


Mapping: [{{val|1 4 3 3 8 -2}}, {{val|0 -25 -7 -2 -47 59}}]
Mapping: [{{val| 1 4 3 3 8 -2 }}, {{val| 0 -25 -7 -2 -47 59 }}]


POTE generator: ~77/72 = 115.933
POTE generator: ~77/72 = 115.933
Line 443: Line 443:
Badness: 0.045569
Badness: 0.045569


=== Counterrevelation ===
=== Counterrevelation ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 121/120, 176/175, 50421/50000
Comma list: 121/120, 176/175, 50421/50000


Mapping: [{{val|1 4 3 3 5}}, {{val|0 -25 -7 -2 -16}}]
Mapping: [{{val| 1 4 3 3 5 }}, {{val| 0 -25 -7 -2 -16 }}]


POTE generator: ~343/320 = 115.919
POTE generator: ~343/320 = 115.919
Line 456: Line 456:
Badness: 0.064070
Badness: 0.064070


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 121/120, 176/175, 196/195, 13750/13689
Comma list: 121/120, 176/175, 196/195, 13750/13689


Mapping: [{{val|1 4 3 3 5 1}}, {{val|0 -25 -7 -2 -16 28}}]
Mapping: [{{val| 1 4 3 3 5 1 }}, {{val| 0 -25 -7 -2 -16 28 }}]


POTE generator: ~273/256 = 115.862
POTE generator: ~273/256 = 115.862

Revision as of 03:42, 5 June 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:

Hendecatonic

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

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7.11

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

Subgroup: 2.3.5.7.11

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

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7.11

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

Subgroup: 2.3.5.7.11.13

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

Subgroup: 2.3.5.7.11.13.17

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

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7.11

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

Subgroup: 2.3.5.7.11.13

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: ~13/12 = 130.409

Vals: Template:Val list

Badness: 0.025941

Nessafof

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7.11

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

Subgroup: 2.3.5.7.11.13

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

Subgroup: 2.3.5.7.11.13

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

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7.11

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

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

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7.11

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

Subgroup: 2.3.5.7.11.13

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

Subgroup: 2.3.5.7.11.13.17

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) has a period of 1/23 octave, so six period represents 6/5 and nine period represents 21/16.

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7.11

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

Subgroup: 2.3.5.7.11.13

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

Subgroup: 2.3.5.7.11.13.17

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

Subgroup: 2.3.5.7.11.13.17.19

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

Subgroup: 2.3.5.7.11.13.17.19.23

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

Countermiracle

The countermiracle temperament (31&145) tempers out the trimyna, 50421/50000 and the quince comma, 823543/819200.

Subgroup: 2.3.5.7

Comma list: 6144/6125, 50421/50000

Mapping: [⟨1 4 3 3], ⟨0 -25 -7 -2]]

Wedgie: ⟨⟨ 25 7 2 -47 -67 -15 ]]

POTE generator: ~343/320 = 115.917

Template:Val list

Badness: 0.102326

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 3388/3375, 6144/6125

Mapping: [⟨1 4 3 3 8], ⟨0 -25 -7 -2 -47]]

POTE generator: ~77/72 = 115.916

Vals: Template:Val list

Badness: 0.039162

Countermiraculous

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 352/351, 1001/1000, 6144/6125

Mapping: [⟨1 4 3 3 8 1], ⟨0 -25 -7 -2 -47 28]]

POTE generator: ~77/72 = 115.880

Vals: Template:Val list

Badness: 0.039271

Counterbenediction

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 441/440, 3146/3125, 3584/3575

Mapping: [⟨1 4 3 3 8 -2], ⟨0 -25 -7 -2 -47 59]]

POTE generator: ~77/72 = 115.933

Vals: Template:Val list

Badness: 0.045569

Counterrevelation

Subgroup: 2.3.5.7.11

Comma list: 121/120, 176/175, 50421/50000

Mapping: [⟨1 4 3 3 5], ⟨0 -25 -7 -2 -16]]

POTE generator: ~343/320 = 115.919

Vals: Template:Val list

Badness: 0.064070

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 176/175, 196/195, 13750/13689

Mapping: [⟨1 4 3 3 5 1], ⟨0 -25 -7 -2 -16 28]]

POTE generator: ~273/256 = 115.862

Vals: Template:Val list

Badness: 0.057497

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