Miscellaneous 5-limit temperaments: Difference between revisions

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== Misneb ==
== Misneb ==
Comma: 145964630126953125/144115188075855872
Subgroup: 2.3.5


Map: [<1 3 1|, <0 -15 14|]
[[Comma]]: 145964630126953125/144115188075855872


POTE generator: ~16/15 = 113.240
[[Mapping]]: [{{Val|1 3 1}}, {{Val|0 -15 14}}]


EDOs: 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bc
[[POTE generator]]: ~16/15 = 113.240


Badness: 0.6095
{{Val list|legend=1| 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc }}
 
[[Badness]]: 0.609540


=== 7-limit ===
=== 7-limit ===
Commas: 225/224, 4194304/4117715
Subgroup: 2.3.5.7


POTE generator: ~16/15 = 113.235
[[Comma list]]: 225/224, 4194304/4117715


Map: [<1 3 1 3|, <0 -15 14 -2|]
[[Mapping]]: [{{Val|1 3 1 3}}, {{Val|0 -15 14 -2}}]


Wedgie: <<15 -14 2 -57 -39 44||
{{Multival|legend=1|15 -14 2 -57 -39 44}}


EDOs: 21, 32, 53
[[POTE generator]]: ~16/15 = 113.235


Badness: 0.1410
{{Val list|legend=1| 21, 32, 53 }}
 
[[Badness]]: 0.140970


=== 11-limit ===
=== 11-limit ===
Commas: 99/98, 176/175, 1310720/1294139
Subgroup: 2.3.5.7.11
 
Comma list: 99/98, 176/175, 1310720/1294139
 
Mapping: [{{Val|1 3 1 3 1}}, {{Val|0 -15 14 -2 26}}]


POTE generator: ~16/15 = 113.323
POTE generator: ~16/15 = 113.323


Map: [<1 3 1 3 1|, <0 -15 14 -2 26|]
Vals: {{Val list| 21, 32e, 53, 127, 180de }}


EDOS: 21, 53, 127, 180de
Badness: 0.085390


Badness: 0.0854
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


==== 13-limit ====
Comma list: 99/98, 176/175, 640/637, 847/845
Commas: 99/98, 176/175, 640/637 847/845
 
Mapping: [{{Val|1 3 1 3 1 2}}, {{Val|0 -15 14 -2 26 18}}]


POTE generator: ~16/15 = 113.323
POTE generator: ~16/15 = 113.323


Map: [<1 3 1 3 1 2|, <0 -15 14 -2 26 18|]
Vals: {{Val list| 21, 32e, 53, 127, 180de }}
 
Badness: 0.045569


EDOs: 21, 53, 127, 189de
=== Musneb ===
Subgroup: 2.3.5.7.11


Badness: 0.0456
Comma list: 225/224, 385/384, 66550/64827


=== Musneb ===
Mapping: [{{Val|1 3 1 3 6}}, {{Val|0 -15 14 -2 -27}}]
Commas: 225/224, 385/384, 66550/64827


POTE generator: ~16/15 = 113.142
POTE generator: ~16/15 = 113.142


Map: [<1 3 1 3 6|, <0 -15 14 -2 -27|]
Vals: {{Val list| 32, 53, 191de, 244cddee, 297cddee }}


EDOS: 32, 53, 191de, 244cde, 297cde
Badness: 0.087333


Badness: 0.0873
== Untriton ==
Subgroup: 2.3.5


== Untriton ==
[[Comma]]: 2270041927734375/2251799813685248
Comma: 2270041927734375/2251799813685248


POTE generator: ~45/32 = 588.722
[[Mapping]]: [{{Val|1 6 -7}}, {{Val|0 -9 19}}]


Map: [<1 6 -7|, <0 -9 19|]
[[POTE generator]]: ~45/32 = 588.722


EDOs: 51, 53, 267, 320, 373, 426, 479, 532, 2607bc
{{Val list|legend=1| 51, 53, 267, 320, 373, 426, 479, 532, 2607bc }}


Badness: 0.3071
[[Badness]]: 0.307073


=== 7-limit ===
=== 7-limit ===
Commas: 225/224, 125000000/121060821
Subgroup: 2.3.5.7


POTE generator: ~7/5 = 588.641
[[Comma list]]: 225/224, 125000000/121060821


Map: [<1 6 -7 -7|, <0 -9 19 20|]
[[Mapping]]: [{{Val|1 6 -7 -7}}, {{Val|0 -9 19 20}}]


Wedgie: <<9 -19 -20 -51 -57 7||
{{Multival|legend=1|9 -19 -20 -51 -57 7}}


EDOs: 51, 53, 316cd, 369cd, 422cd
[[POTE generator]]: ~7/5 = 588.641


Badness: 0.1440
{{Val list|legend=1| 51, 53, 316cd, 369cdd, 422cdd }}
 
[[Badness]]: 0.143976


==== 11-limit ====
==== 11-limit ====
Commas: 121/120, 225/224, 22000/21609
Subgroup: 2.3.5.7.11
 
Comma list: 121/120, 225/224, 22000/21609
 
Mapping: [{{Val|1 6 -7 -7 1}}, {{Val|0 -9 19 20 5}}]


POTE generator: ~7/5 = 588.626
POTE generator: ~7/5 = 588.626


Map: [<1 6 -7 -7 1|, <0 -9 19 20 5|]
Vals: {{Val list| 51, 53 }}
 
Badness: 0.074295


EDOs: 51, 53
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Badness: 0.0743
Comma list: 121/120, 225/224, 275/273, 1040/1029


==== 13-limit ====
Mapping: [{{Val|1 6 -7 -7 1 -12}}, {{Val|0 -9 19 20 5 32}}]
Commas: 121/120, 225/224, 275/273, 1040/1029


POTE generator: ~7/5 = 588.654
POTE generator: ~7/5 = 588.654


Map: [<1 6 -7 -7 1 -12|, <0 -9 19 20 5 32|]
Vals: {{Val list| 51f, 53 }}
 
Badness: 0.047441
 
=== Aufo ===
Subgroup: 2.3.5.7
 
[[Comma list]]: 6144/6125, 177147/175616
 
[[Mapping]]: [{{Val|1 6 -7 19}}, {{Val|0 -9 19 -33}}]
 
{{Multival|legend=1|9 -19 33 -51 27 130}}
 
[[POTE generator]]: ~45/32 = 588.782
 
{{Val list|legend=1| 53, 161, 214 }}
 
[[Badness]]: 0.121428
 
==== 11-limit ====
Subgroup: 2.3.5.7.11


EDOs: 53
Comma list: 121/120, 176/175, 177147/175616


Badness: 0.0474
Mapping: [{{Val|1 6 -7 19 1}}, {{Val|0 -9 19 -33 5}}]


=== Aufo ===
POTE generator: ~45/32 = 588.811
Commas: 6144/6125, 177147/175616
 
Vals: {{Val list| 53, 108e, 161e }}
 
Badness: 0.088631
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


POTE generator: ~45/32 = 588.782
Comma list: 121/120, 176/175, 351/350, 58806/57967


Map: [<1 6 -7 19|, <0 -9 19 -33|]
Mapping: [{{Val|1 6 -7 19 1 -12}}, {{Val|0 -9 19 -33 5 32}}]


Wedgie: <<9 -19 33 -51 27 130||
POTE generator: ~45/32 = 588.788


EDOs: 53, 55, 108, 161, 214, 267
Vals: {{Val list| 53, 108e, 161e, 214ee }}


Badness: 0.1214
Badness: 0.058507


== Vinegar ==
== Vinegar ==
Comma: 16000000/14348907
Subgroup: 2.3.5
 
[[Comma]]: 16000000/14348907


POTE generator: ~10/9 = 156.861
[[Mapping]]: [{{Val|3 0 -5}}, {{Val|0 2 5}}]


Map: [<3 0 -5|, <0 2 5|]
[[POTE generator]]: ~10/9 = 156.861


EDOs: 15, 39c, 54, 69b, 84b
{{Val list|legend=1| 15, 39c, 54, 69b, 84b }}


Badness: 0.9030
[[Badness]]: 0.903002


== Wronecki ==
== Wronecki ==
Comma: 531441/500000
Subgroup: 2.3.5
 
[[Comma]]: 531441/500000


POTE generator: ~3/2 = 695.040
[[Mapping]]: [{{Val|6 0 -5}}, {{Val|0 1 2}}]


Map: [<6 0 -5|, <0 1 2|]
[[POTE generator]]: ~3/2 = 695.040


EDOs: 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bc
{{Val list|legend=1| 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bbc }}


Badness: 0.3418
[[Badness]]: 0.341757


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament collection]]
[[Category:Temperament collection]]

Revision as of 07:43, 9 October 2021

Hogzilla

Subgroup: 2.3.5

Comma: 4428675/4194304

Mapping: [⟨1 0 11], ⟨0 2 -11]]

POTE generator: ~1215/1024 = 252.649

Template:Val list

Badness: 0.424685

Archaeotherium

Subgroup: 2.3.5

Comma: 597871125/536870912

Mapping: [⟨1 1 5], ⟨0 3 -14]]

POTE generator: ~1215/1024 = 230.351

Template:Val list

Badness: 1.434855

7-limit

Subgroup: 2.3.5.7

Comma list: 405/392, 1029/1024

Mapping: [⟨1 1 5 3], ⟨0 3 -14 -1]]

POTE generator: ~8/7 = 230.258

Template:Val list

Badness: 0.146306

Stump

See also: Sensamagic clan § Pycnic
See also: Marvel temperaments § Triton

Subgroup: 2.3.5

Comma: 273375/262144

Mapping: [⟨1 0 6], ⟨0 3 -7]]

POTE generator: ~64/45 = 631.737

Template:Val list

Badness: 0.200600

Unsmate

Subgroup: 2.3.5

Comma: 17578125/16777216

Mapping: [⟨1 3 2], ⟨0 -9 2]]

POTE generator: ~2048/1875 = 189.049

Template:Val list

Badness: 0.460168

Chromo

Subgroup: 2.3.5

Comma: 1220703125/1146617856

Mapping: [⟨1 1 2], ⟨0 13 7]]

POTE generator: ~25/24 = 53.922

Template:Val list

Badness: 0.842835

7-limit

Subgroup: 2.3.5.7

Comma list: 875/864, 2430/2401

Mapping: [⟨1 1 2 2], ⟨0 13 7 18]]

POTE generator: ~25/24 = 53.816

Template:Val list

Badness: 0.090769

Wizard

See also: Marvel temperaments § Wizard

Subgroup: 2.3.5

Comma: 2197265625/2147483648

Mapping: [⟨2 1 5], ⟨0 6 -1]]

Mapping generators: ~42875/32768, ~9375/8192

POTE generator: ~5/4 = 383.212

Template:Val list

Badness: 0.386367

Scales (Scala files): wizard22

Tritonic

See also: Marvel temperaments § Tritonic

Subgroup: 2.3.5

Comma: 553584375/536870912

Mapping: [⟨1 4 -3], ⟨0 -5 11]]

POTE generator: ~45/32 = 580.219

Template:Val list

Badness: 0.378527

Merman

See also: Marvel temperaments § Merman

Sugbroup: 2.3.5

Comma: 1121008359375/1099511627776

Mapping: [⟨1 5 -5], ⟨0 -7 15]]

POTE generator: ~45/32 = 585.634

Template:Val list

Badness: 0.453848

Septimin

See also: Marvel temperaments § Septimin

Subgroup: 2.3.5

Comma: 35595703125/34359738368

Mapping: [⟨1 4 1], ⟨0 -11 6]]

POTE generator: ~75/64 = 263.658

Template:Val list

Badness: 0.670947

Undeka

Subgroup: 2.3.5

Comma: 48828125/45349632

Mapping: [⟨11 0 8], ⟨0 1 1]]

POTE generator: ~3/2 = 703.829

Template:Val list

Badness: 0.727539

7-limit

Subgroup: 2.3.5.7

Comma list: 875/864, 3200/3087

Mapping: [⟨11 0 8 31], ⟨0 1 1 0]]

Wedgie: ⟨⟨ 11 11 0 -8 -31 -31 ]]

POTE generator: ~3/2 = 708.792

Template:Val list

Badness: 0.141782

11-limit

Sugbroup: 2.3.5.7.11

Comma list: 100/99, 352/343, 385/384

Mapping: [⟨11 0 8 31 38], ⟨0 1 1 0 0]]

POTE generator: ~3/2 = 706.768

Template:Val list

Badness: 0.068672

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 65/63, 100/99, 169/165, 352/343

Mapping: [⟨11 0 8 31 38 23], ⟨0 1 1 0 0 1]]

POTE generator: ~3/2 = 707.764

Template:Val list

Badness: 0.056528

Triskaidekic

Subgroup: 2.3.5

Comma: 1220703125/1073741824

Mapping: [⟨13 0 30], ⟨0 1 0]]

POTE generator: ~3/2 = 696.142

Template:Val list

Badness: 2.241568

7-limit

Subgroup: 2.3.5.7

Comma list: 1728/1715, 1875/1792

Mapping: [⟨13 0 30 16], ⟨0 1 0 1]]

Wedgie: ⟨⟨ 13 0 13 -30 -16 30 ]]

POTE generator: ~3/2 = 694.143

Template:Val list

Badness: 0.219050

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 125/121, 385/384

Mapping: [⟨13 0 30 16 45], ⟨0 1 0 1 0]]

POTE generator: ~3/2 = 696.296

Template:Val list

Badness: 0.098847

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 78/77, 99/98, 125/121, 1200/1183

Mapping: [⟨13 0 30 16 45 48], ⟨0 1 0 1 0 0]]

POTE generator: ~3/2 = 695.879

Template:Val list

Badness: 0.059216

Phillips

Subgroup: 2.3.5

Comma: 9685512225/8589934592

Mapping: [⟨2 0 33], ⟨0 1 -9]]

POTE generator: ~3/2 = 691.455

Template:Val list

Badness: 2.228904

7-limit

Subgroup: 2.3.5.7

Comma list: 1728/1715, 6561/6272

Mapping: [⟨2 0 33 -7], ⟨0 1 -9 4]]

Wedgie: ⟨⟨ 2 -18 8 -33 7 69 ]]

POTE generator: ~3/2 = 691.174

Template:Val list

Badness: 0.228602

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 385/384, 729/704

Mapping: [⟨2 0 33 -7 -12], ⟨0 1 -9 4 6]]

POTE generator: ~3/2 = 691.040

Template:Val list

Badness: 0.095777

Oncle

Subgroup: 2.3.5

Comma: 145282683375/137438953472

Mapping: [⟨1 1 6], ⟨0 3 -19]]

POTE generator: ~4096/3645 = 232.521

Template:Val list

Badness: 1.244699

7-limit

Subgroup: 2.3.5.7

Comma list: 1029/1024, 2430/2401

Mapping: [⟨1 1 6 3], ⟨0 3 -19 -1]]

POTE generator: ~8/7 = 232.498

Template:Val list

Badness: 0.088384

Quasimoha

Subgroup: 2.3.5

Comma: 2353579470675/2199023255552

Mapping: [⟨1 1 9], ⟨0 2 -23]]

POTE generator: ~1048576/885735 = 348.600

Template:Val list

Badness: 1.986675

7-limit

Subgroup: 2.3.5.7

Comma list: 2401/2400, 3645/3584

Mapping: [⟨1 1 9 6], ⟨0 2 -23 -11]]

POTE generator: ~49/40 = 348.603

Template:Val list

Badness: 0.110820

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 441/440, 1815/1792

Mapping: [⟨1 1 9 6 2], ⟨0 2 -23 -11 5]]

POTE generator: ~11/9 = 348.639

Template:Val list

Badness: 0.046181

Genocchi

Subgroup: 2.3.5

Comma: 2359296/1953125

Mapping: [⟨1 0 2], ⟨0 9 2]]

POTE generator: ~768/625 = 212.444

Template:Val list

Badness: 1.404977

Misneb

Subgroup: 2.3.5

Comma: 145964630126953125/144115188075855872

Mapping: [⟨1 3 1], ⟨0 -15 14]]

POTE generator: ~16/15 = 113.240

Template:Val list

Badness: 0.609540

7-limit

Subgroup: 2.3.5.7

Comma list: 225/224, 4194304/4117715

Mapping: [⟨1 3 1 3], ⟨0 -15 14 -2]]

Wedgie: ⟨⟨ 15 -14 2 -57 -39 44 ]]

POTE generator: ~16/15 = 113.235

Template:Val list

Badness: 0.140970

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 1310720/1294139

Mapping: [⟨1 3 1 3 1], ⟨0 -15 14 -2 26]]

POTE generator: ~16/15 = 113.323

Vals: Template:Val list

Badness: 0.085390

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 176/175, 640/637, 847/845

Mapping: [⟨1 3 1 3 1 2], ⟨0 -15 14 -2 26 18]]

POTE generator: ~16/15 = 113.323

Vals: Template:Val list

Badness: 0.045569

Musneb

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 66550/64827

Mapping: [⟨1 3 1 3 6], ⟨0 -15 14 -2 -27]]

POTE generator: ~16/15 = 113.142

Vals: Template:Val list

Badness: 0.087333

Untriton

Subgroup: 2.3.5

Comma: 2270041927734375/2251799813685248

Mapping: [⟨1 6 -7], ⟨0 -9 19]]

POTE generator: ~45/32 = 588.722

Template:Val list

Badness: 0.307073

7-limit

Subgroup: 2.3.5.7

Comma list: 225/224, 125000000/121060821

Mapping: [⟨1 6 -7 -7], ⟨0 -9 19 20]]

Wedgie: ⟨⟨ 9 -19 -20 -51 -57 7 ]]

POTE generator: ~7/5 = 588.641

Template:Val list

Badness: 0.143976

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 225/224, 22000/21609

Mapping: [⟨1 6 -7 -7 1], ⟨0 -9 19 20 5]]

POTE generator: ~7/5 = 588.626

Vals: Template:Val list

Badness: 0.074295

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 225/224, 275/273, 1040/1029

Mapping: [⟨1 6 -7 -7 1 -12], ⟨0 -9 19 20 5 32]]

POTE generator: ~7/5 = 588.654

Vals: Template:Val list

Badness: 0.047441

Aufo

Subgroup: 2.3.5.7

Comma list: 6144/6125, 177147/175616

Mapping: [⟨1 6 -7 19], ⟨0 -9 19 -33]]

Wedgie: ⟨⟨ 9 -19 33 -51 27 130 ]]

POTE generator: ~45/32 = 588.782

Template:Val list

Badness: 0.121428

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 176/175, 177147/175616

Mapping: [⟨1 6 -7 19 1], ⟨0 -9 19 -33 5]]

POTE generator: ~45/32 = 588.811

Vals: Template:Val list

Badness: 0.088631

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 176/175, 351/350, 58806/57967

Mapping: [⟨1 6 -7 19 1 -12], ⟨0 -9 19 -33 5 32]]

POTE generator: ~45/32 = 588.788

Vals: Template:Val list

Badness: 0.058507

Vinegar

Subgroup: 2.3.5

Comma: 16000000/14348907

Mapping: [⟨3 0 -5], ⟨0 2 5]]

POTE generator: ~10/9 = 156.861

Template:Val list

Badness: 0.903002

Wronecki

Subgroup: 2.3.5

Comma: 531441/500000

Mapping: [⟨6 0 -5], ⟨0 1 2]]

POTE generator: ~3/2 = 695.040

Template:Val list

Badness: 0.341757

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