Miscellaneous 5-limit temperaments: Difference between revisions

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Make "untriton" the 5-limit title
Fix subtitle levels; remove databoxes introduced during RTT restriction era
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= Hogzilla =
== Hogzilla ==
Comma: 4428675/4194304
Comma: 4428675/4194304


Line 10: Line 10:
Badness: 0.4247
Badness: 0.4247


= Archaeotherium =
== Archaeotherium ==
Comma: 597871125/536870912
Comma: 597871125/536870912


Line 21: Line 21:
Badness: 1.4349
Badness: 1.4349


= Stump =
== Stump ==
{{see also| Sensamagic clan #Pycnic }}
{{see also| Sensamagic clan #Pycnic }}
{{see also| Marvel temperaments #Triton }}
{{see also| Marvel temperaments #Triton }}
Line 35: Line 35:
Badness: 0.2006
Badness: 0.2006


= Unsmate =
== Unsmate ==
Comma: 17578125/16777216
Comma: 17578125/16777216


Line 46: Line 46:
Badness: 0.4602
Badness: 0.4602


= Chromo =
== Chromo ==
Comma: 1220703125/1146617856
Comma: 1220703125/1146617856


Line 57: Line 57:
Badness: 0.8428
Badness: 0.8428


= Wizard =
== Wizard ==
 
{{see also| Marvel temperaments #Wizard }}
{{see also| Marvel temperaments #Wizard }}
Period: 1\2
Optimal ([[POTE]]) generator: ~5/4 = 383.212
EDO generators: [[22edo|7\22]], [[50edo|16\50]], [[72edo|23\72]], [[94edo|30\94]]
Scales (Scala files): [[wizard22]]
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Comma list: 2197265625/2147483648
Comma list: 2197265625/2147483648
Line 78: Line 65:


Mapping generators: ~42875/32768, ~9375/8192
Mapping generators: ~42875/32768, ~9375/8192
[[POTE generator]]: ~5/4 = 383.212


{{Val list|legend=1| 22, 50, 72, 166, 238c, 310c, 548bc }}
{{Val list|legend=1| 22, 50, 72, 166, 238c, 310c, 548bc }}
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Badness: 0.3864
Badness: 0.3864


</div></div>
Scales (Scala files): [[wizard22]]
 
= Tritonic =


== Tritonic ==
{{see also| Marvel temperaments #Tritonic }}
{{see also| Marvel temperaments #Tritonic }}
Period: 1\1
Optimal ([[POTE]]) generator: ~45/32 = 580.219
EDO generators: [[29edo|14\29]], [[31edo|15\31]], [[60edo|29\60]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Comma list: 553584375/536870912
Comma list: 553584375/536870912


Mapping: [{{val| 1 4 -3 }}, {{val| 0 -5 11 }}]
Mapping: [{{val| 1 4 -3 }}, {{val| 0 -5 11 }}]
[[POTE generator]]: ~45/32 = 580.219


{{Val list|legend=1| 29, 31, 60, 91 }}
{{Val list|legend=1| 29, 31, 60, 91 }}
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Badness: 0.3785
Badness: 0.3785


</div></div>
== Merman ==
 
= Merman =
 
{{see also| Marvel temperaments #Merman }}
{{see also| Marvel temperaments #Merman }}
Period: 1\1
Optimal ([[POTE]]) generator: ~45/32 = 585.634
EDO generators: [[41edo|20\41]], [[43edo|21\43]], [[84edo|41\84]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Comma list: 1121008359375/1099511627776
Comma list: 1121008359375/1099511627776


Mapping: [{{val| 1 5 -5 }}, {{val| 0 -7 15 }}]
Mapping: [{{val| 1 5 -5 }}, {{val| 0 -7 15 }}]
[[POTE generator]]: ~45/32 = 585.634


{{Val list|legend=1| 41, 84, 125, 209, 334c, 543bc }}
{{Val list|legend=1| 41, 84, 125, 209, 334c, 543bc }}
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Badness: 0.4538
Badness: 0.4538


</div></div>
== Septimin ==
 
= Septimin =
 
{{see also| Marvel temperaments #Septimin }}
{{see also| Marvel temperaments #Septimin }}
Period: 1\1
Optimal ([[POTE]]) generator: ~75/64 = 263.658
EDO generators: [[41edo|9\41]], [[50edo|11\50]], [[91edo|20\91]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Comma list: 35595703125/34359738368
Comma list: 35595703125/34359738368


Mapping: [{{val| 1 4 1 }}, {{val| 0 -11 6 }}]
Mapping: [{{val| 1 4 1 }}, {{val| 0 -11 6 }}]
[[POTE generator]]: ~75/64 = 263.658


{{Val list|legend=1| 9, 23b, 32, 41, 91, 132, 223c, 355bc }}
{{Val list|legend=1| 9, 23b, 32, 41, 91, 132, 223c, 355bc }}
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Badness: 0.6709
Badness: 0.6709


</div></div>
== Undeka ==
 
= Undeka =
Comma: 48828125/45349632
Comma: 48828125/45349632


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Badness: 0.7275
Badness: 0.7275


== 7-limit ==
=== 7-limit ===
Commas: 875/864, 3200/3087
Commas: 875/864, 3200/3087


Line 187: Line 137:
Badness: 0.1418
Badness: 0.1418


== 11-limit ==
=== 11-limit ===
Commas: 100/99, 352/343, 385/384
Commas: 100/99, 352/343, 385/384


Line 198: Line 148:
Badness: 0.0687
Badness: 0.0687


== 13-limit ==
=== 13-limit ===
Commas: 65/63, 100/99, 169/165, 352/343
Commas: 65/63, 100/99, 169/165, 352/343


Line 209: Line 159:
Badness: 0.0565
Badness: 0.0565


= Triskaidekic =
== Triskaidekic ==
Comma: 1220703125/1073741824
Comma: 1220703125/1073741824


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Badness: 2.2416
Badness: 2.2416


== 7-limit ==
=== 7-limit ===
Commas: 1728/1715, 1875/1792
Commas: 1728/1715, 1875/1792


Line 233: Line 183:
Badness: 0.2190
Badness: 0.2190


== 11-limit ==
=== 11-limit ===
Commas: 99/98, 125/121, 385/384
Commas: 99/98, 125/121, 385/384


Line 244: Line 194:
Badness: 0.0988
Badness: 0.0988


== 13-limit ==
=== 13-limit ===
Commas: 78/77, 99/98, 125/121, 1200/1183
Commas: 78/77, 99/98, 125/121, 1200/1183


Line 255: Line 205:
Badness: 0.0592
Badness: 0.0592


= Phillips =
== Phillips ==
Comma: 9685512225/8589934592
Comma: 9685512225/8589934592


Line 266: Line 216:
Badness: 2.2289
Badness: 2.2289


= Oncle =
== Oncle ==
Comma: 145282683375/137438953472
Comma: 145282683375/137438953472


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Badness: 1.2447
Badness: 1.2447


= Quasimoha =
== Quasimoha ==
Comma: 2353579470675/2199023255552
Comma: 2353579470675/2199023255552


Line 288: Line 238:
Badness: 1.9867
Badness: 1.9867


= Genocchi =
== Genocchi ==
Comma: 2359296/1953125
Comma: 2359296/1953125


Line 299: Line 249:
Badness: 1.4050
Badness: 1.4050


= Misneb =
== Misneb ==
Commas: 145964630126953125/144115188075855872
Commas: 145964630126953125/144115188075855872


Line 310: Line 260:
Badness: 0.6095
Badness: 0.6095


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


Line 323: Line 273:
Badness: 0.1410
Badness: 0.1410


== 11-limit ==
=== 11-limit ===
Commas: 99/98, 176/175, 1310720/1294139
Commas: 99/98, 176/175, 1310720/1294139


Line 334: Line 284:
Badness: 0.0854
Badness: 0.0854


=== 13-limit ===
==== 13-limit ====
Commas: 99/98, 176/175, 640/637 847/845
Commas: 99/98, 176/175, 640/637 847/845


Line 345: Line 295:
Badness: 0.0456
Badness: 0.0456


== Musneb ==
=== Musneb ===
Commas: 225/224, 385/384, 66550/64827
Commas: 225/224, 385/384, 66550/64827


Line 356: Line 306:
Badness: 0.0873
Badness: 0.0873


= Untriton =
== Untriton ==
Comma: 2270041927734375/2251799813685248
Comma: 2270041927734375/2251799813685248


Line 367: Line 317:
Badness: 0.3071
Badness: 0.3071


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


Line 380: Line 330:
Badness: 0.1440
Badness: 0.1440


=== 11-limit ===
==== 11-limit ====
Commas: 121/120, 225/224, 22000/21609
Commas: 121/120, 225/224, 22000/21609


Line 391: Line 341:
Badness: 0.0743
Badness: 0.0743


=== 13-limit ===
==== 13-limit ====
Commas: 121/120, 225/224, 275/273, 1040/1029
Commas: 121/120, 225/224, 275/273, 1040/1029


Line 402: Line 352:
Badness: 0.0474
Badness: 0.0474


== Aufo ==
=== Aufo ===
Commas: 6144/6125, 177147/175616
Commas: 6144/6125, 177147/175616


Line 415: Line 365:
Badness: 0.1214
Badness: 0.1214


= Vinegar =
== Vinegar ==
Comma: 16000000/14348907
Comma: 16000000/14348907


Line 426: Line 376:
Badness: 0.9030
Badness: 0.9030


= Wronecki =
== Wronecki ==
Comma: 531441/500000
Comma: 531441/500000


Line 437: Line 387:
Badness: 0.3418
Badness: 0.3418


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

Revision as of 09:31, 27 June 2021

Hogzilla

Comma: 4428675/4194304

POTE generator: ~1215/1024 = 252.649

Map: [<1 0 11|, <0 2 -11|]

EDOs: 14, 19

Badness: 0.4247

Archaeotherium

Comma: 597871125/536870912

POTE generator: ~1215/1024 = 230.351

Map: [<1 1 5|, <0 3 -14|]

EDOs: 21, 26, 73bc, 99bc

Badness: 1.4349

Stump

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

Comma: 273375/262144

POTE generator: ~64/45 = 631.737

Map: [<1 0 6|, <0 3 -7|]

EDOs: 17, 19

Badness: 0.2006

Unsmate

Comma: 17578125/16777216

POTE generator: ~2048/1875 = 189.049

Map: [<1 3 2|, <0 -9 2|]

EDOs: 13, 19, 89c, 108c, 127c, 146c

Badness: 0.4602

Chromo

Comma: 1220703125/1146617856

POTE generator: ~25/24 = 53.922

Map: [<1 1 2|, <0 13 7|]

EDOs: 22, 45, 67c, 89c

Badness: 0.8428

Wizard

See also: Marvel temperaments § Wizard

Comma list: 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: 0.3864

Scales (Scala files): wizard22

Tritonic

See also: Marvel temperaments § Tritonic

Comma list: 553584375/536870912

Mapping: [⟨1 4 -3], ⟨0 -5 11]]

POTE generator: ~45/32 = 580.219

Template:Val list

Badness: 0.3785

Merman

See also: Marvel temperaments § Merman

Comma list: 1121008359375/1099511627776

Mapping: [⟨1 5 -5], ⟨0 -7 15]]

POTE generator: ~45/32 = 585.634

Template:Val list

Badness: 0.4538

Septimin

See also: Marvel temperaments § Septimin

Comma list: 35595703125/34359738368

Mapping: [⟨1 4 1], ⟨0 -11 6]]

POTE generator: ~75/64 = 263.658

Template:Val list

Badness: 0.6709

Undeka

Comma: 48828125/45349632

POTE generator: ~3/2 = 703.829

Map: [<11 0 8|, <0 1 1|]

EDOs: 22, 77c, 99c, 121c

Badness: 0.7275

7-limit

Commas: 875/864, 3200/3087

POTE generator: ~3/2 = 708.792

Map: [<11 0 8 31|, <0 1 1 0|]

Wedgie: <<11 11 0 -8 -31 -31||

EDOs: 22

Badness: 0.1418

11-limit

Commas: 100/99, 352/343, 385/384

POTE generator: ~3/2 = 706.768

Map: [<11 0 8 31 38|, <0 1 1 0 0|]

EDOs: 22

Badness: 0.0687

13-limit

Commas: 65/63, 100/99, 169/165, 352/343

POTE generator: ~3/2 = 707.764

Map: [<11 0 8 31 38 23|, <0 1 1 0 0 1|]

EDOs: 22

Badness: 0.0565

Triskaidekic

Comma: 1220703125/1073741824

POTE generator: ~3/2 = 696.142

Map: [<13 0 30|, <0 1 0|]

EDOs: 13, 26, 91c

Badness: 2.2416

7-limit

Commas: 1728/1715, 1875/1792

POTE generator: ~3/2 = 694.143

Map: [<13 0 30 16|, <0 1 0 1|]

Wedgie: <<13 0 13 -30 -16 30||

EDOs: 26

Badness: 0.2190

11-limit

Commas: 99/98, 125/121, 385/384

POTE generator: ~3/2 = 696.296

Map: [<13 0 30 16 45|, <0 1 0 1 0|]

EDOs: 26, 91cd

Badness: 0.0988

13-limit

Commas: 78/77, 99/98, 125/121, 1200/1183

POTE generator: ~3/2 = 695.879

Map: [<13 0 30 16 45 48|, <0 1 0 1 0 0|]

EDOs: 26, 91cdf

Badness: 0.0592

Phillips

Comma: 9685512225/8589934592

POTE generator: ~3/2 = 691.455

Map: [<2 0 33|, <0 1 -9|]

EDOs: 14, 26, 66b, 92bc, 118bc

Badness: 2.2289

Oncle

Comma: 145282683375/137438953472

POTE generator: ~4096/3645 = 232.521

Map: [<1 1 6|, <0 3 -19|]

EDOs: 31, 98c, 129c, 160bc, 289bc

Badness: 1.2447

Quasimoha

Comma: 2353579470675/2199023255552

POTE generator: ~1048576/885735 = 348.600

Map: [<1 1 9|, <0 2 -23|]

EDOs: 31, 117c, 148bc, 179bc

Badness: 1.9867

Genocchi

Comma: 2359296/1953125

POTE generator: ~768/625 = 212.444

Map: [<1 0 2|, <0 9 2|]

EDOs: 17c

Badness: 1.4050

Misneb

Commas: 145964630126953125/144115188075855872

POTE generator: ~16/15 = 113.240

Map: [<1 3 1|, <0 -15 14|]

EDOs: 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bc

Badness: 0.6095

7-limit

Commas: 225/224, 4194304/4117715

POTE generator: ~16/15 = 113.235

Map: [<1 3 1 3|, <0 -15 14 -2|]

Wedgie: <<15 -14 2 -57 -39 44||

EDOs: 21, 32, 53

Badness: 0.1410

11-limit

Commas: 99/98, 176/175, 1310720/1294139

POTE generator: ~16/15 = 113.323

Map: [<1 3 1 3 1|, <0 -15 14 -2 26|]

EDOS: 21, 53, 127, 180de

Badness: 0.0854

13-limit

Commas: 99/98, 176/175, 640/637 847/845

POTE generator: ~16/15 = 113.323

Map: [<1 3 1 3 1 2|, <0 -15 14 -2 26 18|]

EDOs: 21, 53, 127, 189de

Badness: 0.0456

Musneb

Commas: 225/224, 385/384, 66550/64827

POTE generator: ~16/15 = 113.142

Map: [<1 3 1 3 6|, <0 -15 14 -2 -27|]

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

Badness: 0.0873

Untriton

Comma: 2270041927734375/2251799813685248

POTE generator: ~45/32 = 588.722

Map: [<1 6 -7|, <0 -9 19|]

EDOs: 51, 53, 267, 320, 373, 426, 479, 532, 2607bc

Badness: 0.3071

7-limit

Commas: 225/224, 125000000/121060821

POTE generator: ~7/5 = 588.641

Map: [<1 6 -7 -7|, <0 -9 19 20|]

Wedgie: <<9 -19 -20 -51 -57 7||

EDOs: 51, 53, 316cd, 369cd, 422cd

Badness: 0.1440

11-limit

Commas: 121/120, 225/224, 22000/21609

POTE generator: ~7/5 = 588.626

Map: [<1 6 -7 -7 1|, <0 -9 19 20 5|]

EDOs: 51, 53

Badness: 0.0743

13-limit

Commas: 121/120, 225/224, 275/273, 1040/1029

POTE generator: ~7/5 = 588.654

Map: [<1 6 -7 -7 1 -12|, <0 -9 19 20 5 32|]

EDOs: 53

Badness: 0.0474

Aufo

Commas: 6144/6125, 177147/175616

POTE generator: ~45/32 = 588.782

Map: [<1 6 -7 19|, <0 -9 19 -33|]

Wedgie: <<9 -19 33 -51 27 130||

EDOs: 53, 55, 108, 161, 214, 267

Badness: 0.1214

Vinegar

Comma: 16000000/14348907

POTE generator: ~10/9 = 156.861

Map: [<3 0 -5|, <0 2 5|]

EDOs: 15, 39c, 54, 69b, 84b

Badness: 0.9030

Wronecki

Comma: 531441/500000

POTE generator: ~3/2 = 695.040

Map: [<6 0 -5|, <0 1 2|]

EDOs: 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bc

Badness: 0.3418

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