Miscellaneous 5-limit temperaments: Difference between revisions

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Line 8: Line 8:
[[Comma]]: 273375/262144
[[Comma]]: 273375/262144


[[Mapping]]: [{{Val|1 0 6}}, {{Val|0 3 -7}}]
[[Mapping]]: [{{Val| 1 0 6 }}, {{Val| 0 3 -7 }}]


[[POTE generator]]: ~64/45 = 631.737
[[POTE generator]]: ~64/45 = 631.737
Line 15: Line 15:


[[Badness]]: 0.200600
[[Badness]]: 0.200600
== Undim ==
{{see also| Hemifamity temperaments #Undim }}
Subgroup: 2.3.5
[[Comma]]: 2199023255552/2179240250625
[[Mapping]]: [{{Val| 4 6 11 }}, {{Val| 0 1 -5 }}]
[[POTE generator]]: ~3/2 = 702.605
{{Val list|legend=1| 12, 140, 152, 164, 1076bc, 1228bc }}
[[Badness]]: 0.241703
== Tertiaseptal ==
{{see also| Breedsmic temperaments #Tertiaseptal }}
Subgroup: 2.3.5
[[Comma]]: 579357147216796875/576460752303423488
[[Mapping]]: [{{Val| 1 3 2 }}, {{Val| 0 -22 5 }}]
[[POTE generator]]: ~17578125/16777216 = 77.191
{{Val list|legend=1| 31, 109, 140, 171, 1679c, 1850c, 2021c, 2192c, 2363c, 2534c, 2705c, 2876c, 3047c }}
[[Badness]]: 0.297544


== Untriton ==
== Untriton ==
Line 23: Line 53:
[[Comma]]: 2270041927734375/2251799813685248
[[Comma]]: 2270041927734375/2251799813685248


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


[[POTE generator]]: ~45/32 = 588.722
[[POTE generator]]: ~45/32 = 588.722
Line 36: Line 66:
[[Comma]]: 531441/500000
[[Comma]]: 531441/500000


[[Mapping]]: [{{Val|6 0 -5}}, {{Val|0 1 2}}]
[[Mapping]]: [{{Val| 6 0 -5 }}, {{Val| 0 1 2 }}]


[[POTE generator]]: ~3/2 = 695.040
[[POTE generator]]: ~3/2 = 695.040
Line 43: Line 73:


[[Badness]]: 0.341757
[[Badness]]: 0.341757
== Hemififths ==
{{see also| Breedsmic temperaments #Hemififths }}
Subgroup: 2.3.5
[[Comma]]: 858993459200/847288609443
[[Mapping]]: [{{Val| 1 1 -5 }}, {{Val| 0 2 25 }}]
[[POTE generator]]: ~655360/531441 = 351.476
{{Val list|legend=1| 41, 58, 99, 239, 338, 915b, 1253bc }}
[[Badness]]: 0.372848


== Tritonic ==
== Tritonic ==
Line 77: Line 122:


Scales (Scala files): [[wizard22]]
Scales (Scala files): [[wizard22]]
== Quindromeda ==
: ''See also: [[Hemimean clan #Quintagar]] and [[Hemifamity temperaments #Quintakwai]]''
Subgroup: 2.3.5
[[Comma]]: 72057594037927936/71489976421753125
[[POTE generator]]: ~4428675/4194304 = 99.526
[[Mapping]]: [{{Val| 1 2 0 }}, {{Val| 0 -5 28 }}]
{{Val list|legend=1| 12, 193, 205, 217, 422 }}
[[Badness]]: 0.399849


== Hogzilla ==
== Hogzilla ==
Line 83: Line 143:
[[Comma]]: 4428675/4194304
[[Comma]]: 4428675/4194304


[[Mapping]]: [{{Val|1 0 11}}, {{Val|0 2 -11}}]
[[Mapping]]: [{{Val| 1 0 11 }}, {{Val| 0 2 -11 }}]


[[POTE generator]]: ~1215/1024 = 252.649
[[POTE generator]]: ~1215/1024 = 252.649
Line 90: Line 150:


[[Badness]]: 0.424685
[[Badness]]: 0.424685
== Quintaleap ==
: ''See also: [[Marvel temperaments #Quintapole]], [[Octagar temperaments #Quintupole]], and [[Hemifamity temperaments #Quinticosiennic]]''
Subgroup: 2.3.5
[[Comma]]: 137438953472/134521003125
[[Mapping]]: [{{Val| 1 2 1 }}, {{Val| 0 -5 16 }}]
[[POTE generator]]: ~135/128 = 99.267
{{Val list|legend=1| 12, 109, 121, 133 }}
[[Badness]]: 0.444506


== Merman ==
== Merman ==
Line 111: Line 186:
[[Comma]]: 17578125/16777216
[[Comma]]: 17578125/16777216


[[Mapping]]: [{{Val|1 3 2}}, {{Val|0 -9 2}}]
[[Mapping]]: [{{Val| 1 3 2 }}, {{Val| 0 -9 2 }}]


[[POTE generator]]: ~2048/1875 = 189.049
[[POTE generator]]: ~2048/1875 = 189.049
Line 126: Line 201:
[[Comma]]: 145964630126953125/144115188075855872
[[Comma]]: 145964630126953125/144115188075855872


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


[[POTE generator]]: ~16/15 = 113.240
[[POTE generator]]: ~16/15 = 113.240
Line 133: Line 208:


[[Badness]]: 0.609540
[[Badness]]: 0.609540
== Kwai ==
{{see also| Mirkwai clan #Kwai }}
Subgroup: 2.3.5
[[Comma]]: 5629499534213120/5559060566555523
[[Mapping]]: [{{Val| 1 2 16 }}, {{Val| 0 -1 -33 }}]
[[POTE generator]]: ~3/2 = 702.630
{{Val list|legend=1| 41, 111, 152 }}
[[Badness]]: 0.636715


== Septimin ==
== Septimin ==
Line 156: Line 246:
[[Comma list]]: 8968066875/8589934592
[[Comma list]]: 8968066875/8589934592


[[Mapping]]: [{{val| 1 3 -3 }}, {{val| 0 -4 15 }}]
[[Mapping]]: [{{Val| 1 3 -3 }}, {{Val| 0 -4 15 }}]


[[POTE generator]]: ~512/405 = 425.474
[[POTE generator]]: ~512/405 = 425.474
Line 171: Line 261:
[[Comma]]: 48828125/45349632
[[Comma]]: 48828125/45349632


[[Mapping]]: [{{Val|11 0 8}}, {{Val|0 1 1}}]
[[Mapping]]: [{{Val| 11 0 8 }}, {{Val| 0 1 1 }}]


[[POTE generator]]: ~3/2 = 703.829
[[POTE generator]]: ~3/2 = 703.829
Line 186: Line 276:
[[Comma list]]: 6103515625/5804752896
[[Comma list]]: 6103515625/5804752896


[[Mapping]]: [{{val| 1 5 5 }}, {{val| 0 -14 -11 }}]
[[Mapping]]: [{{Val| 1 5 5 }}, {{Val| 0 -14 -11 }}]


[[POTE generator]]: ~3125/2592 = 292.702
[[POTE generator]]: ~3125/2592 = 292.702
Line 201: Line 291:
[[Comma]]: 1220703125/1146617856
[[Comma]]: 1220703125/1146617856


[[Mapping]]: [{{Val|1 1 2}}, {{Val|0 13 7}}]
[[Mapping]]: [{{Val| 1 1 2 }}, {{Val| 0 13 7 }}]


[[POTE generator]]: ~25/24 = 53.922
[[POTE generator]]: ~25/24 = 53.922
Line 216: Line 306:
[[Comma list]]: 10460353203/9765625000
[[Comma list]]: 10460353203/9765625000


[[Mapping]]: [{{val| 1 2 3 }}, {{val| 0 -13 -21 }}]
[[Mapping]]: [{{Val| 1 2 3 }}, {{Val| 0 -13 -21 }}]


[[POTE generator]]: ~6561/6250 = 38.571
[[POTE generator]]: ~6561/6250 = 38.571
Line 229: Line 319:
[[Comma]]: 16000000/14348907
[[Comma]]: 16000000/14348907


[[Mapping]]: [{{Val|3 0 -5}}, {{Val|0 2 5}}]
[[Mapping]]: [{{Val| 3 0 -5 }}, {{Val| 0 2 5 }}]


[[POTE generator]]: ~10/9 = 156.861
[[POTE generator]]: ~10/9 = 156.861
Line 244: Line 334:
[[Comma]]: 145282683375/137438953472
[[Comma]]: 145282683375/137438953472


[[Mapping]]: [{{Val|1 1 6}}, {{Val|0 3 -19}}]
[[Mapping]]: [{{Val| 1 1 6 }}, {{Val| 0 3 -19 }}]


[[POTE generator]]: ~4096/3645 = 232.521
[[POTE generator]]: ~4096/3645 = 232.521
Line 257: Line 347:
[[Comma]]: 2359296/1953125
[[Comma]]: 2359296/1953125


[[Mapping]]: [{{Val|1 0 2}}, {{Val|0 9 2}}]
[[Mapping]]: [{{Val| 1 0 2 }}, {{Val| 0 9 2 }}]


[[POTE generator]]: ~768/625 = 212.444
[[POTE generator]]: ~768/625 = 212.444
Line 264: Line 354:


[[Badness]]: 1.404977
[[Badness]]: 1.404977
== Casablanca ==
{{see also| Starling temperaments #Casablanca }}
Subgroup: 2.3.5
[[Comma]]: 20061226008576/19073486328125
[[Mapping]]: [{{Val| 1 -7 -14 }}, {{Val| 0 19 14 }}]
[[POTE generator]]: ~864/625 = 542.208
{{Val list|legend=1| 11b, 20b, 31, 73, 104c, 135c }}
[[Badness]]: 1.423736


== Archaeotherium ==
== Archaeotherium ==
Line 272: Line 377:
[[Comma]]: 597871125/536870912
[[Comma]]: 597871125/536870912


[[Mapping]]: [{{Val|1 1 5}}, {{Val|0 3 -14}}]
[[Mapping]]: [{{Val| 1 1 5 }}, {{Val| 0 3 -14 }}]


[[POTE generator]]: ~1215/1024 = 230.351
[[POTE generator]]: ~1215/1024 = 230.351
Line 287: Line 392:
[[Comma]]: 2353579470675/2199023255552
[[Comma]]: 2353579470675/2199023255552


[[Mapping]]: [{{Val|1 1 9}}, {{Val|0 2 -23}}]
[[Mapping]]: [{{Val| 1 1 9 }}, {{Val| 0 2 -23 }}]


[[POTE generator]]: ~1048576/885735 = 348.600
[[POTE generator]]: ~1048576/885735 = 348.600
Line 302: Line 407:
[[Comma]]: 9685512225/8589934592
[[Comma]]: 9685512225/8589934592


[[Mapping]]: [{{Val|2 0 33}}, {{Val|0 1 -9}}]
[[Mapping]]: [{{Val| 2 0 33 }}, {{Val| 0 1 -9 }}]


[[POTE generator]]: ~3/2 = 691.455
[[POTE generator]]: ~3/2 = 691.455
Line 317: Line 422:
[[Comma]]: 1220703125/1073741824
[[Comma]]: 1220703125/1073741824


[[Mapping]]: [{{Val|13 0 30}}, {{Val|0 1 0}}]
[[Mapping]]: [{{Val| 13 0 30 }}, {{Val| 0 1 0 }}]


[[POTE generator]]: ~3/2 = 696.142
[[POTE generator]]: ~3/2 = 696.142

Revision as of 10:43, 9 October 2021

Below are listed some high badness temperaments (Badness > 0.2).

Stump

See also: Sensamagic clan #Pycnic and 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

Undim

See also: Hemifamity temperaments § Undim

Subgroup: 2.3.5

Comma: 2199023255552/2179240250625

Mapping: [⟨4 6 11], ⟨0 1 -5]]

POTE generator: ~3/2 = 702.605

Template:Val list

Badness: 0.241703

Tertiaseptal

See also: Breedsmic temperaments § Tertiaseptal

Subgroup: 2.3.5

Comma: 579357147216796875/576460752303423488

Mapping: [⟨1 3 2], ⟨0 -22 5]]

POTE generator: ~17578125/16777216 = 77.191

Template:Val list

Badness: 0.297544

Untriton

See also: Marvel temperaments #Untriton and Porwell temperaments #Aufo

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

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

Hemififths

See also: Breedsmic temperaments § Hemififths

Subgroup: 2.3.5

Comma: 858993459200/847288609443

Mapping: [⟨1 1 -5], ⟨0 2 25]]

POTE generator: ~655360/531441 = 351.476

Template:Val list

Badness: 0.372848

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

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

Quindromeda

See also: Hemimean clan #Quintagar and Hemifamity temperaments #Quintakwai

Subgroup: 2.3.5

Comma: 72057594037927936/71489976421753125

POTE generator: ~4428675/4194304 = 99.526

Mapping: [⟨1 2 0], ⟨0 -5 28]]

Template:Val list

Badness: 0.399849

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

Quintaleap

See also: Marvel temperaments #Quintapole, Octagar temperaments #Quintupole, and Hemifamity temperaments #Quinticosiennic

Subgroup: 2.3.5

Comma: 137438953472/134521003125

Mapping: [⟨1 2 1], ⟨0 -5 16]]

POTE generator: ~135/128 = 99.267

Template:Val list

Badness: 0.444506

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

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

Misneb

See also: Marvel temperaments § 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

Kwai

See also: Mirkwai clan § Kwai

Subgroup: 2.3.5

Comma: 5629499534213120/5559060566555523

Mapping: [⟨1 2 16], ⟨0 -1 -33]]

POTE generator: ~3/2 = 702.630

Template:Val list

Badness: 0.636715

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

Sentinel

See also: Orwellismic temperaments § Sentinel

Subgroup: 2.3.5

Comma list: 8968066875/8589934592

Mapping: [⟨1 3 -3], ⟨0 -4 15]]

POTE generator: ~512/405 = 425.474

Template:Val list

Badness: 0.723413

Undeka

See also: Keemic temperaments § 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

Quasitemp

See also: Keemic temperaments § Quasitemp

Subgroup: 2.3.5

Comma list: 6103515625/5804752896

Mapping: [⟨1 5 5], ⟨0 -14 -11]]

POTE generator: ~3125/2592 = 292.702

Template:Val list

Badness: 0.767824

Chromo

See also: Keemic temperaments § 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

Diesic

See also: Orwellismic temperaments § Diesic

Subgroup: 2.3.5

Comma list: 10460353203/9765625000

Mapping: [⟨1 2 3], ⟨0 -13 -21]]

POTE generator: ~6561/6250 = 38.571

Template:Val list

Badness: 1.344681

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

Oncle

See also: Gamelismic clan § 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

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

Casablanca

See also: Starling temperaments § Casablanca

Subgroup: 2.3.5

Comma: 20061226008576/19073486328125

Mapping: [⟨1 -7 -14], ⟨0 19 14]]

POTE generator: ~864/625 = 542.208

Template:Val list

Badness: 1.423736

Archaeotherium

See also: Gamelismic clan § 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

Quasimoha

See also: Breedsmic temperaments § 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

Phillips

See also: Orwellismic temperaments § 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

Triskaidekic

See also: Orwellismic temperaments § 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

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