Miscellaneous 5-limit temperaments: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,016 edits
No edit summary
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,016 edits
No edit summary
Line 39: Line 39:


== Stump ==
== Stump ==
{{see also| Sensamagic clan #Pycnic }}
: ''See also: [[Sensamagic clan #Pycnic]] and [[Marvel temperaments #Triton]]''
{{see also| Marvel temperaments #Triton }}


Subgroup: 2.3.5
Subgroup: 2.3.5
Line 66: Line 65:


[[Badness]]: 0.460168
[[Badness]]: 0.460168
== Chromo ==
Subgroup: 2.3.5
[[Comma]]: 1220703125/1146617856
[[Mapping]]: [{{Val|1 1 2}}, {{Val|0 13 7}}]
[[POTE generator]]: ~25/24 = 53.922
{{Val list|legend=1| 22, 45, 67c, 89c }}
[[Badness]]: 0.842835
=== 7-limit ===
Subgroup: 2.3.5.7
[[Comma list]]: 875/864, 2430/2401
[[Mapping]]: [{{Val|1 1 2 2}}, {{Val|0 13 7 18}}]
[[POTE generator]]: ~25/24 = 53.816
{{Val list|legend=1| 22, 45, 67c }}
[[Badness]]: 0.090769


== Wizard ==
== Wizard ==
Line 141: Line 114:


[[Badness]]: 0.453848
[[Badness]]: 0.453848
== Untriton ==
: ''See also: [[Marvel temperaments #Untriton]] and [[Porwell temperaments #Aufo]]''
Subgroup: 2.3.5
[[Comma]]: 2270041927734375/2251799813685248
[[Mapping]]: [{{Val|1 6 -7}}, {{Val|0 -9 19}}]
[[POTE generator]]: ~45/32 = 588.722
{{Val list|legend=1| 51, 53, 267, 320, 373, 426, 479, 532, 2607bc }}
[[Badness]]: 0.307073


== Septimin ==
== Septimin ==
Line 157: Line 145:
[[Badness]]: 0.670947
[[Badness]]: 0.670947


== Undeka ==
== Misneb ==
{{see also| Marvel temperaments #Misneb }}
 
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 48828125/45349632
[[Comma]]: 145964630126953125/144115188075855872


[[Mapping]]: [{{Val|11 0 8}}, {{Val|0 1 1}}]
[[Mapping]]: [{{Val|1 3 1}}, {{Val|0 -15 14}}]


[[POTE generator]]: ~3/2 = 703.829
[[POTE generator]]: ~16/15 = 113.240


{{Val list|legend=1| 22, 77c, 99c, 121c }}
{{Val list|legend=1| 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc }}


[[Badness]]: 0.727539
[[Badness]]: 0.609540


=== 7-limit ===
== Quasitemp ==
Subgroup: 2.3.5.7
{{see also| Keemic temperaments #Quasitemp }}


[[Comma list]]: 875/864, 3200/3087
Subgroup: 2.3.5


[[Mapping]]: [{{Val|11 0 8 31}}, {{Val|0 1 1 0}}]
[[Comma list]]: 6103515625/5804752896


{{Multival|legend=1|11 11 0 -8 -31 -31}}
[[Mapping]]: [{{val| 1 5 5 }}, {{val| 0 -14 -11 }}]


[[POTE generator]]: ~3/2 = 708.792
[[POTE generator]]: ~3125/2592 = 292.702


{{Val list|legend=1| 11c, 22 }}
{{Val list|legend=1| 4, 37, 41 }}


[[Badness]]: 0.141782
[[Badness]]: 0.767824


=== 11-limit ===
== Chromo ==
Sugbroup: 2.3.5.7.11
{{see also| Keemic temperaments #Chromo }}


[[Comma list]]: 100/99, 352/343, 385/384
Subgroup: 2.3.5


[[Mapping]]: [{{Val|11 0 8 31 38}}, {{Val|0 1 1 0 0}}]
[[Comma]]: 1220703125/1146617856


[[POTE generator]]: ~3/2 = 706.768
[[Mapping]]: [{{Val|1 1 2}}, {{Val|0 13 7}}]


{{Val list|legend=1| 11c, 22 }}
[[POTE generator]]: ~25/24 = 53.922


[[Badness]]: 0.068672
{{Val list|legend=1| 22, 45, 67c, 89c }}


=== 13-limit ===
[[Badness]]: 0.842835
Subgroup: 2.3.5.7.11.13


[[Comma list]]: 65/63, 100/99, 169/165, 352/343
== Undeka ==
 
{{see also| Keemic temperaments #Undeka }}
[[Mapping]]: [{{Val|11 0 8 31 38 23}}, {{Val|0 1 1 0 0 1}}]
 
[[POTE generator]]: ~3/2 = 707.764
 
{{Val list|legend=1| 11cf, 22 }}
 
[[Badness]]: 0.056528


== Triskaidekic ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 1220703125/1073741824
[[Comma]]: 48828125/45349632


[[Mapping]]: [{{Val|13 0 30}}, {{Val|0 1 0}}]
[[Mapping]]: [{{Val|11 0 8}}, {{Val|0 1 1}}]


[[POTE generator]]: ~3/2 = 696.142
[[POTE generator]]: ~3/2 = 703.829


{{Val list|legend=1| 13, 26, 91c }}
{{Val list|legend=1| 22, 77c, 99c, 121c }}


[[Badness]]: 2.241568
[[Badness]]: 0.727539


=== 7-limit ===
== Sentinel ==
Subgroup: 2.3.5.7
{{see also| Orwellismic temperaments #Sentinel }}


[[Comma list]]: 1728/1715, 1875/1792
Subgroup: 2.3.5


[[Mapping]]: [{{Val|13 0 30 16}}, {{Val|0 1 0 1}}]
[[Comma list]]: 8968066875/8589934592


{{Multival|legend=1|13 0 13 -30 -16 30}}
[[Mapping]]: [{{val| 1 3 -3 }}, {{val| 0 -4 15 }}]


[[POTE generator]]: ~3/2 = 694.143
[[POTE generator]]: ~512/405 = 425.474


{{Val list|legend=1| 13d, 26 }}
{{Val list|legend=1| 14, 17, 31, 79, 110, 361bc }}


[[Badness]]: 0.219050
[[Badness]]: 0.723413


=== 11-limit ===
== Diesic ==
Subgroup: 2.3.5.7.11
{{see also| Orwellismic temperaments #Diesic }}


[[Comma list]]: 99/98, 125/121, 385/384
Subgroup: 2.3.5


[[Mapping]]: [{{Val|13 0 30 16 45}}, {{Val|0 1 0 1 0}}]
[[Comma list]]: 10460353203/9765625000


[[POTE generator]]: ~3/2 = 696.296
[[Mapping]]: [{{val| 1 2 3 }}, {{val| 0 -13 -21 }}]


{{Val list|legend=1| 13d, 26, 91cd }}
[[POTE generator]]: ~6561/6250 = 38.571


[[Badness]]: 0.098847
{{Val list|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}


=== 13-limit ===
[[Badness]]: 1.344681
Subgroup: 2.3.5.7.11.13


[[Comma list]]: 78/77, 99/98, 125/121, 1200/1183
== Phillips ==
{{see also| Orwellismic temperaments #Phillips }}


[[Mapping]]: [{{Val|13 0 30 16 45 48}}, {{Val|0 1 0 1 0 0}}]
[[POTE generator]]: ~3/2 = 695.879
{{Val list|legend=1| 13d, 26, 91cdf }}
[[Badness]]: 0.059216
== Phillips ==
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 278: Line 250:
[[Badness]]: 2.228904
[[Badness]]: 2.228904


=== 7-limit ===
== Triskaidekic ==
Subgroup: 2.3.5.7
{{see also| Orwellismic temperaments #Triskaidekic }}


[[Comma list]]: 1728/1715, 6561/6272
Subgroup: 2.3.5


[[Mapping]]: [{{Val|2 0 33 -7}}, {{Val|0 1 -9 4}}]
[[Comma]]: 1220703125/1073741824


{{Multival|legend=1|2 -18 8 -33 7 69}}
[[Mapping]]: [{{Val|13 0 30}}, {{Val|0 1 0}}]


[[POTE generator]]: ~3/2 = 691.174
[[POTE generator]]: ~3/2 = 696.142


{{Val list|legend=1| 14, 26, 66b, 92bc }}
{{Val list|legend=1| 13, 26, 91c }}


[[Badness]]: 0.228602
[[Badness]]: 2.241568
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
[[Comma list]]: 99/98, 385/384, 729/704
 
[[Mapping]]: [{{Val|2 0 33 -7 -12}}, {{Val|0 1 -9 4 6}}]
 
[[POTE generator]]: ~3/2 = 691.040
 
{{Val list|legend=1| 14, 26, 40, 66b }}
 
[[Badness]]: 0.095777


== Oncle ==
== Oncle ==
Line 383: Line 342:


[[Badness]]: 1.404977
[[Badness]]: 1.404977
== Misneb ==
Subgroup: 2.3.5
[[Comma]]: 145964630126953125/144115188075855872
[[Mapping]]: [{{Val|1 3 1}}, {{Val|0 -15 14}}]
[[POTE generator]]: ~16/15 = 113.240
{{Val list|legend=1| 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc }}
[[Badness]]: 0.609540
=== 7-limit ===
Subgroup: 2.3.5.7
[[Comma list]]: 225/224, 4194304/4117715
[[Mapping]]: [{{Val|1 3 1 3}}, {{Val|0 -15 14 -2}}]
{{Multival|legend=1|15 -14 2 -57 -39 44}}
[[POTE generator]]: ~16/15 = 113.235
{{Val list|legend=1| 21, 32, 53 }}
[[Badness]]: 0.140970
=== 11-limit ===
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
Vals: {{Val list| 21, 32e, 53, 127, 180de }}
Badness: 0.085390
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 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
Vals: {{Val list| 21, 32e, 53, 127, 180de }}
Badness: 0.045569
=== Musneb ===
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 66550/64827
Mapping: [{{Val|1 3 1 3 6}}, {{Val|0 -15 14 -2 -27}}]
POTE generator: ~16/15 = 113.142
Vals: {{Val list| 32, 53, 191de, 244cddee, 297cddee }}
Badness: 0.087333
== Untriton ==
Subgroup: 2.3.5
[[Comma]]: 2270041927734375/2251799813685248
[[Mapping]]: [{{Val|1 6 -7}}, {{Val|0 -9 19}}]
[[POTE generator]]: ~45/32 = 588.722
{{Val list|legend=1| 51, 53, 267, 320, 373, 426, 479, 532, 2607bc }}
[[Badness]]: 0.307073
=== 7-limit ===
Subgroup: 2.3.5.7
[[Comma list]]: 225/224, 125000000/121060821
[[Mapping]]: [{{Val|1 6 -7 -7}}, {{Val|0 -9 19 20}}]
{{Multival|legend=1|9 -19 -20 -51 -57 7}}
[[POTE generator]]: ~7/5 = 588.641
{{Val list|legend=1| 51, 53, 316cd, 369cdd, 422cdd }}
[[Badness]]: 0.143976
==== 11-limit ====
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
Vals: {{Val list| 51, 53 }}
Badness: 0.074295
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 225/224, 275/273, 1040/1029
Mapping: [{{Val|1 6 -7 -7 1 -12}}, {{Val|0 -9 19 20 5 32}}]
POTE generator: ~7/5 = 588.654
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
Comma list: 121/120, 176/175, 177147/175616
Mapping: [{{Val|1 6 -7 19 1}}, {{Val|0 -9 19 -33 5}}]
POTE generator: ~45/32 = 588.811
Vals: {{Val list| 53, 108e, 161e }}
Badness: 0.088631
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 176/175, 351/350, 58806/57967
Mapping: [{{Val|1 6 -7 19 1 -12}}, {{Val|0 -9 19 -33 5 32}}]
POTE generator: ~45/32 = 588.788
Vals: {{Val list| 53, 108e, 161e, 214ee }}
Badness: 0.058507


== Vinegar ==
== Vinegar ==

Revision as of 08:29, 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 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

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

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

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

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

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

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

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

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

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

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

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

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

Retrieved from "https://en.xen.wiki/index.php?title=Miscellaneous_5-limit_temperaments&oldid=79269"