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Miscellaneous 5-limit temperaments: Difference between revisions

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== Misneb ==
== Misneb ==
Comma: 145964630126953125/144115188075855872
Subgroup: 2.3.5


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


POTE generator: ~16/15 = 113.240
[[Mapping]]: [{{Val|1 3 1}}, {{Val|0 -15 14}}]


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


Badness: 0.6095
{{Val list|legend=1| 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc }}
 
[[Badness]]: 0.609540


=== 7-limit ===
=== 7-limit ===
Commas: 225/224, 4194304/4117715
Subgroup: 2.3.5.7


POTE generator: ~16/15 = 113.235
[[Comma list]]: 225/224, 4194304/4117715


Map: [<1 3 1 3|, <0 -15 14 -2|]
[[Mapping]]: [{{Val|1 3 1 3}}, {{Val|0 -15 14 -2}}]


Wedgie: <<15 -14 2 -57 -39 44||
{{Multival|legend=1|15 -14 2 -57 -39 44}}


EDOs: 21, 32, 53
[[POTE generator]]: ~16/15 = 113.235


Badness: 0.1410
{{Val list|legend=1| 21, 32, 53 }}
 
[[Badness]]: 0.140970


=== 11-limit ===
=== 11-limit ===
Commas: 99/98, 176/175, 1310720/1294139
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
POTE generator: ~16/15 = 113.323


Map: [<1 3 1 3 1|, <0 -15 14 -2 26|]
Vals: {{Val list| 21, 32e, 53, 127, 180de }}


EDOS: 21, 53, 127, 180de
Badness: 0.085390


Badness: 0.0854
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


==== 13-limit ====
Comma list: 99/98, 176/175, 640/637, 847/845
Commas: 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
POTE generator: ~16/15 = 113.323


Map: [<1 3 1 3 1 2|, <0 -15 14 -2 26 18|]
Vals: {{Val list| 21, 32e, 53, 127, 180de }}
 
Badness: 0.045569


EDOs: 21, 53, 127, 189de
=== Musneb ===
Subgroup: 2.3.5.7.11


Badness: 0.0456
Comma list: 225/224, 385/384, 66550/64827


=== Musneb ===
Mapping: [{{Val|1 3 1 3 6}}, {{Val|0 -15 14 -2 -27}}]
Commas: 225/224, 385/384, 66550/64827


POTE generator: ~16/15 = 113.142
POTE generator: ~16/15 = 113.142


Map: [<1 3 1 3 6|, <0 -15 14 -2 -27|]
Vals: {{Val list| 32, 53, 191de, 244cddee, 297cddee }}


EDOS: 32, 53, 191de, 244cde, 297cde
Badness: 0.087333


Badness: 0.0873
== Untriton ==
Subgroup: 2.3.5


== Untriton ==
[[Comma]]: 2270041927734375/2251799813685248
Comma: 2270041927734375/2251799813685248


POTE generator: ~45/32 = 588.722
[[Mapping]]: [{{Val|1 6 -7}}, {{Val|0 -9 19}}]


Map: [<1 6 -7|, <0 -9 19|]
[[POTE generator]]: ~45/32 = 588.722


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


Badness: 0.3071
[[Badness]]: 0.307073


=== 7-limit ===
=== 7-limit ===
Commas: 225/224, 125000000/121060821
Subgroup: 2.3.5.7


POTE generator: ~7/5 = 588.641
[[Comma list]]: 225/224, 125000000/121060821


Map: [<1 6 -7 -7|, <0 -9 19 20|]
[[Mapping]]: [{{Val|1 6 -7 -7}}, {{Val|0 -9 19 20}}]


Wedgie: <<9 -19 -20 -51 -57 7||
{{Multival|legend=1|9 -19 -20 -51 -57 7}}


EDOs: 51, 53, 316cd, 369cd, 422cd
[[POTE generator]]: ~7/5 = 588.641


Badness: 0.1440
{{Val list|legend=1| 51, 53, 316cd, 369cdd, 422cdd }}
 
[[Badness]]: 0.143976


==== 11-limit ====
==== 11-limit ====
Commas: 121/120, 225/224, 22000/21609
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
POTE generator: ~7/5 = 588.626


Map: [<1 6 -7 -7 1|, <0 -9 19 20 5|]
Vals: {{Val list| 51, 53 }}
 
Badness: 0.074295


EDOs: 51, 53
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Badness: 0.0743
Comma list: 121/120, 225/224, 275/273, 1040/1029


==== 13-limit ====
Mapping: [{{Val|1 6 -7 -7 1 -12}}, {{Val|0 -9 19 20 5 32}}]
Commas: 121/120, 225/224, 275/273, 1040/1029


POTE generator: ~7/5 = 588.654
POTE generator: ~7/5 = 588.654


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


EDOs: 53
Comma list: 121/120, 176/175, 177147/175616


Badness: 0.0474
Mapping: [{{Val|1 6 -7 19 1}}, {{Val|0 -9 19 -33 5}}]


=== Aufo ===
POTE generator: ~45/32 = 588.811
Commas: 6144/6125, 177147/175616
 
Vals: {{Val list| 53, 108e, 161e }}
 
Badness: 0.088631
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


POTE generator: ~45/32 = 588.782
Comma list: 121/120, 176/175, 351/350, 58806/57967


Map: [<1 6 -7 19|, <0 -9 19 -33|]
Mapping: [{{Val|1 6 -7 19 1 -12}}, {{Val|0 -9 19 -33 5 32}}]


Wedgie: <<9 -19 33 -51 27 130||
POTE generator: ~45/32 = 588.788


EDOs: 53, 55, 108, 161, 214, 267
Vals: {{Val list| 53, 108e, 161e, 214ee }}


Badness: 0.1214
Badness: 0.058507


== Vinegar ==
== Vinegar ==
Comma: 16000000/14348907
Subgroup: 2.3.5
 
[[Comma]]: 16000000/14348907


POTE generator: ~10/9 = 156.861
[[Mapping]]: [{{Val|3 0 -5}}, {{Val|0 2 5}}]


Map: [<3 0 -5|, <0 2 5|]
[[POTE generator]]: ~10/9 = 156.861


EDOs: 15, 39c, 54, 69b, 84b
{{Val list|legend=1| 15, 39c, 54, 69b, 84b }}


Badness: 0.9030
[[Badness]]: 0.903002


== Wronecki ==
== Wronecki ==
Comma: 531441/500000
Subgroup: 2.3.5
 
[[Comma]]: 531441/500000


POTE generator: ~3/2 = 695.040
[[Mapping]]: [{{Val|6 0 -5}}, {{Val|0 1 2}}]


Map: [<6 0 -5|, <0 1 2|]
[[POTE generator]]: ~3/2 = 695.040


EDOs: 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bc
{{Val list|legend=1| 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bbc }}


Badness: 0.3418
[[Badness]]: 0.341757


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