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Miscellaneous 5-limit temperaments: Difference between revisions

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== Hogzilla ==
== Hogzilla ==
Comma: 4428675/4194304
Subgroup: 2.3.5


POTE generator: ~1215/1024 = 252.649
[[Comma]]: 4428675/4194304


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


EDOs: 14, 19
[[POTE generator]]: ~1215/1024 = 252.649


Badness: 0.4247
{{Val list|legend=1| 14, 19 }}
 
[[Badness]]: 0.424685


== Archaeotherium ==
== Archaeotherium ==
Comma: 597871125/536870912
Subgroup: 2.3.5
 
[[Comma]]: 597871125/536870912
 
[[Mapping]]: [{{Val|1 1 5}}, {{Val|0 3 -14}}]
 
[[POTE generator]]: ~1215/1024 = 230.351
 
{{Val list|legend=1| 21, 26, 73bc, 99bc }}
 
[[Badness]]: 1.434855


POTE generator: ~1215/1024 = 230.351
=== 7-limit ===
Subgroup: 2.3.5.7


Map: [<1 1 5|, <0 3 -14|]
[[Comma list]]: 405/392, 1029/1024


EDOs: 21, 26, 73bc, 99bc
[[Mapping]]: [{{Val|1 1 5 3}}, {{Val|0 3 -14 -1}}]


Badness: 1.4349
[[POTE generator]]: ~8/7 = 230.258
 
{{Val list|legend=1| 21, 26, 47, 73bc, 99bc }}
 
[[Badness]]: 0.146306


== Stump ==
== Stump ==
Line 25: Line 42:
{{see also| Marvel temperaments #Triton }}
{{see also| Marvel temperaments #Triton }}


Comma: 273375/262144
Subgroup: 2.3.5


POTE generator: ~64/45 = 631.737
[[Comma]]: 273375/262144


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


EDOs: 17, 19
[[POTE generator]]: ~64/45 = 631.737


Badness: 0.2006
{{Val list|legend=1| 17, 19 }}
 
[[Badness]]: 0.200600


== Unsmate ==
== Unsmate ==
Comma: 17578125/16777216
Subgroup: 2.3.5


POTE generator: ~2048/1875 = 189.049
[[Comma]]: 17578125/16777216


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


EDOs: 13, 19, 89c, 108c, 127c, 146c
[[POTE generator]]: ~2048/1875 = 189.049


Badness: 0.4602
{{Val list|legend=1| 13, 19, 89c, 108c, 127c, 146cc }}
 
[[Badness]]: 0.460168


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


POTE generator: ~25/24 = 53.922
[[Mapping]]: [{{Val|1 1 2 2}}, {{Val|0 13 7 18}}]


Map: [<1 1 2|, <0 13 7|]
[[POTE generator]]: ~25/24 = 53.816


EDOs: 22, 45, 67c, 89c
{{Val list|legend=1| 22, 45, 67c }}


Badness: 0.8428
[[Badness]]: 0.090769


== Wizard ==
== Wizard ==
{{see also| Marvel temperaments #Wizard }}
{{see also| Marvel temperaments #Wizard }}


Comma list: 2197265625/2147483648
Subgroup: 2.3.5
 
[[Comma]]: 2197265625/2147483648


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


Mapping generators: ~42875/32768, ~9375/8192
Mapping generators: ~42875/32768, ~9375/8192
Line 70: Line 108:
{{Val list|legend=1| 22, 50, 72, 166, 238c, 310c, 548bc }}
{{Val list|legend=1| 22, 50, 72, 166, 238c, 310c, 548bc }}


Badness: 0.3864
[[Badness]]: 0.386367


Scales (Scala files): [[wizard22]]
Scales (Scala files): [[wizard22]]
Line 77: Line 115:
{{see also| Marvel temperaments #Tritonic }}
{{see also| Marvel temperaments #Tritonic }}


Comma list: 553584375/536870912
Subgroup: 2.3.5


Mapping: [{{val| 1 4 -3 }}, {{val| 0 -5 11 }}]
[[Comma]]: 553584375/536870912
 
[[Mapping]]: [{{Val| 1 4 -3 }}, {{Val| 0 -5 11 }}]


[[POTE generator]]: ~45/32 = 580.219
[[POTE generator]]: ~45/32 = 580.219
Line 85: Line 125:
{{Val list|legend=1| 29, 31, 60, 91 }}
{{Val list|legend=1| 29, 31, 60, 91 }}


Badness: 0.3785
[[Badness]]: 0.378527


== Merman ==
== Merman ==
{{see also| Marvel temperaments #Merman }}
{{see also| Marvel temperaments #Merman }}


Comma list: 1121008359375/1099511627776
Sugbroup: 2.3.5


Mapping: [{{val| 1 5 -5 }}, {{val| 0 -7 15 }}]
[[Comma]]: 1121008359375/1099511627776
 
[[Mapping]]: [{{Val| 1 5 -5 }}, {{Val| 0 -7 15 }}]


[[POTE generator]]: ~45/32 = 585.634
[[POTE generator]]: ~45/32 = 585.634
Line 98: Line 140:
{{Val list|legend=1| 41, 84, 125, 209, 334c, 543bc }}
{{Val list|legend=1| 41, 84, 125, 209, 334c, 543bc }}


Badness: 0.4538
[[Badness]]: 0.453848


== Septimin ==
== Septimin ==
{{see also| Marvel temperaments #Septimin }}
{{see also| Marvel temperaments #Septimin }}


Comma list: 35595703125/34359738368
Subgroup: 2.3.5


Mapping: [{{val| 1 4 1 }}, {{val| 0 -11 6 }}]
[[Comma]]: 35595703125/34359738368
 
[[Mapping]]: [{{Val| 1 4 1 }}, {{Val| 0 -11 6 }}]


[[POTE generator]]: ~75/64 = 263.658
[[POTE generator]]: ~75/64 = 263.658
Line 111: Line 155:
{{Val list|legend=1| 9, 23b, 32, 41, 91, 132, 223c, 355bc }}
{{Val list|legend=1| 9, 23b, 32, 41, 91, 132, 223c, 355bc }}


Badness: 0.6709
[[Badness]]: 0.670947


== Undeka ==
== Undeka ==
Comma: 48828125/45349632
Subgroup: 2.3.5
 
[[Comma]]: 48828125/45349632


POTE generator: ~3/2 = 703.829
[[Mapping]]: [{{Val|11 0 8}}, {{Val|0 1 1}}]


Map: [<11 0 8|, <0 1 1|]
[[POTE generator]]: ~3/2 = 703.829


EDOs: 22, 77c, 99c, 121c
{{Val list|legend=1| 22, 77c, 99c, 121c }}


Badness: 0.7275
[[Badness]]: 0.727539


=== 7-limit ===
=== 7-limit ===
Commas: 875/864, 3200/3087
Subgroup: 2.3.5.7
 
[[Comma list]]: 875/864, 3200/3087


POTE generator: ~3/2 = 708.792
[[Mapping]]: [{{Val|11 0 8 31}}, {{Val|0 1 1 0}}]


Map: [<11 0 8 31|, <0 1 1 0|]
{{Multival|legend=1|11 11 0 -8 -31 -31}}


Wedgie: <<11 11 0 -8 -31 -31||
[[POTE generator]]: ~3/2 = 708.792


EDOs: 22
{{Val list|legend=1| 11c, 22 }}


Badness: 0.1418
[[Badness]]: 0.141782


=== 11-limit ===
=== 11-limit ===
Commas: 100/99, 352/343, 385/384
Sugbroup: 2.3.5.7.11


POTE generator: ~3/2 = 706.768
[[Comma list]]: 100/99, 352/343, 385/384


Map: [<11 0 8 31 38|, <0 1 1 0 0|]
[[Mapping]]: [{{Val|11 0 8 31 38}}, {{Val|0 1 1 0 0}}]


EDOs: 22
[[POTE generator]]: ~3/2 = 706.768


Badness: 0.0687
{{Val list|legend=1| 11c, 22 }}
 
[[Badness]]: 0.068672


=== 13-limit ===
=== 13-limit ===
Commas: 65/63, 100/99, 169/165, 352/343
Subgroup: 2.3.5.7.11.13


POTE generator: ~3/2 = 707.764
[[Comma list]]: 65/63, 100/99, 169/165, 352/343


Map: [<11 0 8 31 38 23|, <0 1 1 0 0 1|]
[[Mapping]]: [{{Val|11 0 8 31 38 23}}, {{Val|0 1 1 0 0 1}}]


EDOs: 22
[[POTE generator]]: ~3/2 = 707.764


Badness: 0.0565
{{Val list|legend=1| 11cf, 22 }}
 
[[Badness]]: 0.056528


== Triskaidekic ==
== Triskaidekic ==
Comma: 1220703125/1073741824
Subgroup: 2.3.5


POTE generator: ~3/2 = 696.142
[[Comma]]: 1220703125/1073741824


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


EDOs: 13, 26, 91c
[[POTE generator]]: ~3/2 = 696.142


Badness: 2.2416
{{Val list|legend=1| 13, 26, 91c }}
 
[[Badness]]: 2.241568


=== 7-limit ===
=== 7-limit ===
Commas: 1728/1715, 1875/1792
Subgroup: 2.3.5.7


POTE generator: ~3/2 = 694.143
[[Comma list]]: 1728/1715, 1875/1792


Map: [<13 0 30 16|, <0 1 0 1|]
[[Mapping]]: [{{Val|13 0 30 16}}, {{Val|0 1 0 1}}]


Wedgie: <<13 0 13 -30 -16 30||
{{Multival|legend=1|13 0 13 -30 -16 30}}


EDOs: 26
[[POTE generator]]: ~3/2 = 694.143


Badness: 0.2190
{{Val list|legend=1| 13d, 26 }}
 
[[Badness]]: 0.219050


=== 11-limit ===
=== 11-limit ===
Commas: 99/98, 125/121, 385/384
Subgroup: 2.3.5.7.11


POTE generator: ~3/2 = 696.296
[[Comma list]]: 99/98, 125/121, 385/384


Map: [<13 0 30 16 45|, <0 1 0 1 0|]
[[Mapping]]: [{{Val|13 0 30 16 45}}, {{Val|0 1 0 1 0}}]


EDOs: 26, 91cd
[[POTE generator]]: ~3/2 = 696.296


Badness: 0.0988
{{Val list|legend=1| 13d, 26, 91cd }}
 
[[Badness]]: 0.098847


=== 13-limit ===
=== 13-limit ===
Commas: 78/77, 99/98, 125/121, 1200/1183
Subgroup: 2.3.5.7.11.13


POTE generator: ~3/2 = 695.879
[[Comma list]]: 78/77, 99/98, 125/121, 1200/1183


Map: [<13 0 30 16 45 48|, <0 1 0 1 0 0|]
[[Mapping]]: [{{Val|13 0 30 16 45 48}}, {{Val|0 1 0 1 0 0}}]


EDOs: 26, 91cdf
[[POTE generator]]: ~3/2 = 695.879


Badness: 0.0592
{{Val list|legend=1| 13d, 26, 91cdf }}
 
[[Badness]]: 0.059216


== Phillips ==
== Phillips ==
Comma: 9685512225/8589934592
Subgroup: 2.3.5


POTE generator: ~3/2 = 691.455
[[Comma]]: 9685512225/8589934592


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


EDOs: 14, 26, 66b, 92bc, 118bc
[[POTE generator]]: ~3/2 = 691.455


Badness: 2.2289
{{Val list|legend=1| 14, 26, 66b, 92bc, 118bbc }}
 
[[Badness]]: 2.228904
 
=== 7-limit ===
Subgroup: 2.3.5.7
 
[[Comma list]]: 1728/1715, 6561/6272
 
[[Mapping]]: [{{Val|2 0 33 -7}}, {{Val|0 1 -9 4}}]
 
{{Multival|legend=1|2 -18 8 -33 7 69}}
 
[[POTE generator]]: ~3/2 = 691.174
 
{{Val list|legend=1| 14, 26, 66b, 92bc }}
 
[[Badness]]: 0.228602
 
=== 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 ==
Comma: 145282683375/137438953472
Subgroup: 2.3.5


POTE generator: ~4096/3645 = 232.521
[[Comma]]: 145282683375/137438953472


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


EDOs: 31, 98c, 129c, 160bc, 289bc
[[POTE generator]]: ~4096/3645 = 232.521


Badness: 1.2447
{{Val list|legend=1| 31, 98c, 129c, 160bc, 289bbcc }}
 
[[Badness]]: 1.244699
 
=== 7-limit ===
Subgroup: 2.3.5.7
 
[[Comma list]]: 1029/1024, 2430/2401
 
[[Mapping]]: [{{Val|1 1 6 3}}, {{Val|0 3 -19 -1}}]
 
[[POTE generator]]: ~8/7 = 232.498
 
{{Val list|legend=1| 31, 98c, 129c, 160bc }}
 
[[Badness]]: 0.088384


== Quasimoha ==
== Quasimoha ==
Comma: 2353579470675/2199023255552
Subgroup: 2.3.5
 
[[Comma]]: 2353579470675/2199023255552


POTE generator: ~1048576/885735 = 348.600
[[Mapping]]: [{{Val|1 1 9}}, {{Val|0 2 -23}}]


Map: [<1 1 9|, <0 2 -23|]
[[POTE generator]]: ~1048576/885735 = 348.600


EDOs: 31, 117c, 148bc, 179bc
{{Val list|legend=1| 31, 117c, 148bc, 179bc }}


Badness: 1.9867
[[Badness]]: 1.986675
 
=== 7-limit ===
Subgroup: 2.3.5.7
 
[[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 ==
== Genocchi ==
Comma: 2359296/1953125
Subgroup: 2.3.5


POTE generator: ~768/625 = 212.444
[[Comma]]: 2359296/1953125


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


EDOs: 17c
[[POTE generator]]: ~768/625 = 212.444


Badness: 1.4050
{{Val list|legend=1| 6b, 11b, 17c }}
 
[[Badness]]: 1.404977


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


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