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
5,024 edits
No edit summary
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,024 edits
No edit summary
Line 1: Line 1:
== Hogzilla ==
Below are listed some high badness temperaments (Badness > 0.2).
Subgroup: 2.3.5


[[Comma]]: 4428675/4194304
== Stump ==
: ''See also: [[Sensamagic clan #Pycnic]] and [[Marvel temperaments #Triton]]''


[[Mapping]]: [{{Val|1 0 11}}, {{Val|0 2 -11}}]
[[POTE generator]]: ~1215/1024 = 252.649
{{Val list|legend=1| 14, 19 }}
[[Badness]]: 0.424685
== Archaeotherium ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 597871125/536870912
[[Comma]]: 273375/262144


[[Mapping]]: [{{Val|1 1 5}}, {{Val|0 3 -14}}]
[[Mapping]]: [{{Val|1 0 6}}, {{Val|0 3 -7}}]


[[POTE generator]]: ~1215/1024 = 230.351
[[POTE generator]]: ~64/45 = 631.737


{{Val list|legend=1| 21, 26, 73bc, 99bc }}
{{Val list|legend=1| 17, 19 }}


[[Badness]]: 1.434855
[[Badness]]: 0.200600


=== 7-limit ===
== Untriton ==
Subgroup: 2.3.5.7
: ''See also: [[Marvel temperaments #Untriton]] and [[Porwell temperaments #Aufo]]''


[[Comma list]]: 405/392, 1029/1024
Subgroup: 2.3.5


[[Mapping]]: [{{Val|1 1 5 3}}, {{Val|0 3 -14 -1}}]
[[Comma]]: 2270041927734375/2251799813685248


[[POTE generator]]: ~8/7 = 230.258
[[Mapping]]: [{{Val|1 6 -7}}, {{Val|0 -9 19}}]


{{Val list|legend=1| 21, 26, 47, 73bc, 99bc }}
[[POTE generator]]: ~45/32 = 588.722


[[Badness]]: 0.146306
{{Val list|legend=1| 51, 53, 267, 320, 373, 426, 479, 532, 2607bc }}


== Stump ==
[[Badness]]: 0.307073
: ''See also: [[Sensamagic clan #Pycnic]] and [[Marvel temperaments #Triton]]''


== Wronecki ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 273375/262144
[[Comma]]: 531441/500000
 
[[Mapping]]: [{{Val|6 0 -5}}, {{Val|0 1 2}}]


[[Mapping]]: [{{Val|1 0 6}}, {{Val|0 3 -7}}]
[[POTE generator]]: ~3/2 = 695.040


[[POTE generator]]: ~64/45 = 631.737
{{Val list|legend=1| 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bbc }}


{{Val list|legend=1| 17, 19 }}
[[Badness]]: 0.341757


[[Badness]]: 0.200600
== Tritonic ==
{{see also| Marvel temperaments #Tritonic }}


== Unsmate ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 17578125/16777216
[[Comma]]: 553584375/536870912


[[Mapping]]: [{{Val|1 3 2}}, {{Val|0 -9 2}}]
[[Mapping]]: [{{Val| 1 4 -3 }}, {{Val| 0 -5 11 }}]


[[POTE generator]]: ~2048/1875 = 189.049
[[POTE generator]]: ~45/32 = 580.219


{{Val list|legend=1| 13, 19, 89c, 108c, 127c, 146cc }}
{{Val list|legend=1| 29, 31, 60, 91 }}


[[Badness]]: 0.460168
[[Badness]]: 0.378527


== Wizard ==
== Wizard ==
Line 85: Line 78:
Scales (Scala files): [[wizard22]]
Scales (Scala files): [[wizard22]]


== Tritonic ==
== Hogzilla ==
{{see also| Marvel temperaments #Tritonic }}
 
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 553584375/536870912
[[Comma]]: 4428675/4194304


[[Mapping]]: [{{Val| 1 4 -3 }}, {{Val| 0 -5 11 }}]
[[Mapping]]: [{{Val|1 0 11}}, {{Val|0 2 -11}}]


[[POTE generator]]: ~45/32 = 580.219
[[POTE generator]]: ~1215/1024 = 252.649


{{Val list|legend=1| 29, 31, 60, 91 }}
{{Val list|legend=1| 14, 19 }}


[[Badness]]: 0.378527
[[Badness]]: 0.424685


== Merman ==
== Merman ==
Line 115: Line 106:
[[Badness]]: 0.453848
[[Badness]]: 0.453848


== Untriton ==
== Unsmate ==
: ''See also: [[Marvel temperaments #Untriton]] and [[Porwell temperaments #Aufo]]''
Subgroup: 2.3.5
 
[[Comma]]: 17578125/16777216
 
[[Mapping]]: [{{Val|1 3 2}}, {{Val|0 -9 2}}]
 
[[POTE generator]]: ~2048/1875 = 189.049
 
{{Val list|legend=1| 13, 19, 89c, 108c, 127c, 146cc }}
 
[[Badness]]: 0.460168
 
== Misneb ==
{{see also| Marvel temperaments #Misneb }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 2270041927734375/2251799813685248
[[Comma]]: 145964630126953125/144115188075855872


[[Mapping]]: [{{Val|1 6 -7}}, {{Val|0 -9 19}}]
[[Mapping]]: [{{Val|1 3 1}}, {{Val|0 -15 14}}]


[[POTE generator]]: ~45/32 = 588.722
[[POTE generator]]: ~16/15 = 113.240


{{Val list|legend=1| 51, 53, 267, 320, 373, 426, 479, 532, 2607bc }}
{{Val list|legend=1| 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc }}


[[Badness]]: 0.307073
[[Badness]]: 0.609540


== Septimin ==
== Septimin ==
Line 145: Line 149:
[[Badness]]: 0.670947
[[Badness]]: 0.670947


== Misneb ==
== Sentinel ==
{{see also| Marvel temperaments #Misneb }}
{{see also| Orwellismic temperaments #Sentinel }}
 
Subgroup: 2.3.5
 
[[Comma list]]: 8968066875/8589934592
 
[[Mapping]]: [{{val| 1 3 -3 }}, {{val| 0 -4 15 }}]
 
[[POTE generator]]: ~512/405 = 425.474
 
{{Val list|legend=1| 14, 17, 31, 79, 110, 361bc }}
 
[[Badness]]: 0.723413
 
== Undeka ==
{{see also| Keemic temperaments #Undeka }}


Subgroup: 2.3.5
Subgroup: 2.3.5


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


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


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


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


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


== Quasitemp ==
== Quasitemp ==
Line 189: Line 208:


[[Badness]]: 0.842835
[[Badness]]: 0.842835
== Undeka ==
{{see also| Keemic temperaments #Undeka }}
Subgroup: 2.3.5
[[Comma]]: 48828125/45349632
[[Mapping]]: [{{Val|11 0 8}}, {{Val|0 1 1}}]
[[POTE generator]]: ~3/2 = 703.829
{{Val list|legend=1| 22, 77c, 99c, 121c }}
[[Badness]]: 0.727539
== Sentinel ==
{{see also| Orwellismic temperaments #Sentinel }}
Subgroup: 2.3.5
[[Comma list]]: 8968066875/8589934592
[[Mapping]]: [{{val| 1 3 -3 }}, {{val| 0 -4 15 }}]
[[POTE generator]]: ~512/405 = 425.474
{{Val list|legend=1| 14, 17, 31, 79, 110, 361bc }}
[[Badness]]: 0.723413


== Diesic ==
== Diesic ==
Line 235: Line 224:
[[Badness]]: 1.344681
[[Badness]]: 1.344681


== Phillips ==
== Vinegar ==
{{see also| Orwellismic temperaments #Phillips }}
 
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 9685512225/8589934592
[[Comma]]: 16000000/14348907


[[Mapping]]: [{{Val|2 0 33}}, {{Val|0 1 -9}}]
[[Mapping]]: [{{Val|3 0 -5}}, {{Val|0 2 5}}]


[[POTE generator]]: ~3/2 = 691.455
[[POTE generator]]: ~10/9 = 156.861


{{Val list|legend=1| 14, 26, 66b, 92bc, 118bbc }}
{{Val list|legend=1| 15, 39c, 54, 69b, 84b }}


[[Badness]]: 2.228904
[[Badness]]: 0.903002


== Triskaidekic ==
== Oncle ==
{{see also| Orwellismic temperaments #Triskaidekic }}
{{see also| Gamelismic clan #Oncle }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 1220703125/1073741824
[[Comma]]: 145282683375/137438953472


[[Mapping]]: [{{Val|13 0 30}}, {{Val|0 1 0}}]
[[Mapping]]: [{{Val|1 1 6}}, {{Val|0 3 -19}}]


[[POTE generator]]: ~3/2 = 696.142
[[POTE generator]]: ~4096/3645 = 232.521


{{Val list|legend=1| 13, 26, 91c }}
{{Val list|legend=1| 31, 98c, 129c, 160bc, 289bbcc }}


[[Badness]]: 2.241568
[[Badness]]: 1.244699


== Oncle ==
== Genocchi ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 145282683375/137438953472
[[Comma]]: 2359296/1953125
 
[[Mapping]]: [{{Val|1 0 2}}, {{Val|0 9 2}}]


[[Mapping]]: [{{Val|1 1 6}}, {{Val|0 3 -19}}]
[[POTE generator]]: ~768/625 = 212.444


[[POTE generator]]: ~4096/3645 = 232.521
{{Val list|legend=1| 6b, 11b, 17c }}


{{Val list|legend=1| 31, 98c, 129c, 160bc, 289bbcc }}
[[Badness]]: 1.404977


[[Badness]]: 1.244699
== Archaeotherium ==
{{see also| Gamelismic clan #Archaeotherium }}


=== 7-limit ===
Subgroup: 2.3.5
Subgroup: 2.3.5.7


[[Comma list]]: 1029/1024, 2430/2401
[[Comma]]: 597871125/536870912


[[Mapping]]: [{{Val|1 1 6 3}}, {{Val|0 3 -19 -1}}]
[[Mapping]]: [{{Val|1 1 5}}, {{Val|0 3 -14}}]


[[POTE generator]]: ~8/7 = 232.498
[[POTE generator]]: ~1215/1024 = 230.351


{{Val list|legend=1| 31, 98c, 129c, 160bc }}
{{Val list|legend=1| 21, 26, 73bc, 99bc }}


[[Badness]]: 0.088384
[[Badness]]: 1.434855


== Quasimoha ==
== Quasimoha ==
{{see also| Breedsmic temperaments #Quasimoha }}
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 304: Line 295:
[[Badness]]: 1.986675
[[Badness]]: 1.986675


=== 7-limit ===
== Phillips ==
Subgroup: 2.3.5.7
{{see also| Orwellismic temperaments #Phillips }}
 
[[Comma list]]: 2401/2400, 3645/3584
 
[[Mapping]]: [{{Val|1 1 9 6}}, {{Val|0 2 -23 -11}}]
 
[[POTE generator]]: ~49/40 = 348.603
 
{{Val list|legend=1| 31, 117c, 148bc, 179bc }}
 
[[Badness]]: 0.110820
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
[[Comma list]]: 243/242, 441/440, 1815/1792
 
[[Mapping]]: [{{Val|1 1 9 6 2}}, {{Val|0 2 -23 -11 5}}]
 
[[POTE generator]]: ~11/9 = 348.639
 
{{Val list|legend=1| 31, 86ce, 117ce, 148bce }}
 
[[Badness]]: 0.046181


== Genocchi ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 2359296/1953125
[[Comma]]: 9685512225/8589934592


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


[[POTE generator]]: ~768/625 = 212.444
[[POTE generator]]: ~3/2 = 691.455


{{Val list|legend=1| 6b, 11b, 17c }}
{{Val list|legend=1| 14, 26, 66b, 92bc, 118bbc }}


[[Badness]]: 1.404977
[[Badness]]: 2.228904


== Vinegar ==
== Triskaidekic ==
Subgroup: 2.3.5
{{see also| Orwellismic temperaments #Triskaidekic }}
 
[[Comma]]: 16000000/14348907
 
[[Mapping]]: [{{Val|3 0 -5}}, {{Val|0 2 5}}]
 
[[POTE generator]]: ~10/9 = 156.861
 
{{Val list|legend=1| 15, 39c, 54, 69b, 84b }}
 
[[Badness]]: 0.903002


== Wronecki ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 531441/500000
[[Comma]]: 1220703125/1073741824


[[Mapping]]: [{{Val|6 0 -5}}, {{Val|0 1 2}}]
[[Mapping]]: [{{Val|13 0 30}}, {{Val|0 1 0}}]


[[POTE generator]]: ~3/2 = 695.040
[[POTE generator]]: ~3/2 = 696.142


{{Val list|legend=1| 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bbc }}
{{Val list|legend=1| 13, 26, 91c }}


[[Badness]]: 0.341757
[[Badness]]: 2.241568


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

Revision as of 09:01, 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

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

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

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

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

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

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

Retrieved from "https://en.xen.wiki/index.php?title=Miscellaneous_5-limit_temperaments&oldid=79272"