Xenharmonic Wiki

Miscellaneous 5-limit temperaments: Difference between revisions

← Older editNewer edit →
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,019 edits
No edit summary
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,019 edits
No edit summary
Line 8: Line 8:
[[Comma]]: 273375/262144
[[Comma]]: 273375/262144


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


[[POTE generator]]: ~64/45 = 631.737
[[POTE generator]]: ~64/45 = 631.737
Line 15: Line 15:


[[Badness]]: 0.200600
[[Badness]]: 0.200600
== Undim ==
{{see also| Hemifamity temperaments #Undim }}
Subgroup: 2.3.5
[[Comma]]: 2199023255552/2179240250625
[[Mapping]]: [{{Val| 4 6 11 }}, {{Val| 0 1 -5 }}]
[[POTE generator]]: ~3/2 = 702.605
{{Val list|legend=1| 12, 140, 152, 164, 1076bc, 1228bc }}
[[Badness]]: 0.241703
== Tertiaseptal ==
{{see also| Breedsmic temperaments #Tertiaseptal }}
Subgroup: 2.3.5
[[Comma]]: 579357147216796875/576460752303423488
[[Mapping]]: [{{Val| 1 3 2 }}, {{Val| 0 -22 5 }}]
[[POTE generator]]: ~17578125/16777216 = 77.191
{{Val list|legend=1| 31, 109, 140, 171, 1679c, 1850c, 2021c, 2192c, 2363c, 2534c, 2705c, 2876c, 3047c }}
[[Badness]]: 0.297544


== Untriton ==
== Untriton ==
Line 23: Line 53:
[[Comma]]: 2270041927734375/2251799813685248
[[Comma]]: 2270041927734375/2251799813685248


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


[[POTE generator]]: ~45/32 = 588.722
[[POTE generator]]: ~45/32 = 588.722
Line 36: Line 66:
[[Comma]]: 531441/500000
[[Comma]]: 531441/500000


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


[[POTE generator]]: ~3/2 = 695.040
[[POTE generator]]: ~3/2 = 695.040
Line 43: Line 73:


[[Badness]]: 0.341757
[[Badness]]: 0.341757
== Hemififths ==
{{see also| Breedsmic temperaments #Hemififths }}
Subgroup: 2.3.5
[[Comma]]: 858993459200/847288609443
[[Mapping]]: [{{Val| 1 1 -5 }}, {{Val| 0 2 25 }}]
[[POTE generator]]: ~655360/531441 = 351.476
{{Val list|legend=1| 41, 58, 99, 239, 338, 915b, 1253bc }}
[[Badness]]: 0.372848


== Tritonic ==
== Tritonic ==
Line 77: Line 122:


Scales (Scala files): [[wizard22]]
Scales (Scala files): [[wizard22]]
== Quindromeda ==
: ''See also: [[Hemimean clan #Quintagar]] and [[Hemifamity temperaments #Quintakwai]]''
Subgroup: 2.3.5
[[Comma]]: 72057594037927936/71489976421753125
[[POTE generator]]: ~4428675/4194304 = 99.526
[[Mapping]]: [{{Val| 1 2 0 }}, {{Val| 0 -5 28 }}]
{{Val list|legend=1| 12, 193, 205, 217, 422 }}
[[Badness]]: 0.399849


== Hogzilla ==
== Hogzilla ==
Line 83: Line 143:
[[Comma]]: 4428675/4194304
[[Comma]]: 4428675/4194304


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


[[POTE generator]]: ~1215/1024 = 252.649
[[POTE generator]]: ~1215/1024 = 252.649
Line 90: Line 150:


[[Badness]]: 0.424685
[[Badness]]: 0.424685
== Quintaleap ==
: ''See also: [[Marvel temperaments #Quintapole]], [[Octagar temperaments #Quintupole]], and [[Hemifamity temperaments #Quinticosiennic]]''
Subgroup: 2.3.5
[[Comma]]: 137438953472/134521003125
[[Mapping]]: [{{Val| 1 2 1 }}, {{Val| 0 -5 16 }}]
[[POTE generator]]: ~135/128 = 99.267
{{Val list|legend=1| 12, 109, 121, 133 }}
[[Badness]]: 0.444506


== Merman ==
== Merman ==
Line 111: Line 186:
[[Comma]]: 17578125/16777216
[[Comma]]: 17578125/16777216


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


[[POTE generator]]: ~2048/1875 = 189.049
[[POTE generator]]: ~2048/1875 = 189.049
Line 126: Line 201:
[[Comma]]: 145964630126953125/144115188075855872
[[Comma]]: 145964630126953125/144115188075855872


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


[[POTE generator]]: ~16/15 = 113.240
[[POTE generator]]: ~16/15 = 113.240
Line 133: Line 208:


[[Badness]]: 0.609540
[[Badness]]: 0.609540
== Kwai ==
{{see also| Mirkwai clan #Kwai }}
Subgroup: 2.3.5
[[Comma]]: 5629499534213120/5559060566555523
[[Mapping]]: [{{Val| 1 2 16 }}, {{Val| 0 -1 -33 }}]
[[POTE generator]]: ~3/2 = 702.630
{{Val list|legend=1| 41, 111, 152 }}
[[Badness]]: 0.636715


== Septimin ==
== Septimin ==
Line 156: Line 246:
[[Comma list]]: 8968066875/8589934592
[[Comma list]]: 8968066875/8589934592


[[Mapping]]: [{{val| 1 3 -3 }}, {{val| 0 -4 15 }}]
[[Mapping]]: [{{Val| 1 3 -3 }}, {{Val| 0 -4 15 }}]


[[POTE generator]]: ~512/405 = 425.474
[[POTE generator]]: ~512/405 = 425.474
Line 171: Line 261:
[[Comma]]: 48828125/45349632
[[Comma]]: 48828125/45349632


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


[[POTE generator]]: ~3/2 = 703.829
[[POTE generator]]: ~3/2 = 703.829
Line 186: Line 276:
[[Comma list]]: 6103515625/5804752896
[[Comma list]]: 6103515625/5804752896


[[Mapping]]: [{{val| 1 5 5 }}, {{val| 0 -14 -11 }}]
[[Mapping]]: [{{Val| 1 5 5 }}, {{Val| 0 -14 -11 }}]


[[POTE generator]]: ~3125/2592 = 292.702
[[POTE generator]]: ~3125/2592 = 292.702
Line 201: Line 291:
[[Comma]]: 1220703125/1146617856
[[Comma]]: 1220703125/1146617856


[[Mapping]]: [{{Val|1 1 2}}, {{Val|0 13 7}}]
[[Mapping]]: [{{Val| 1 1 2 }}, {{Val| 0 13 7 }}]


[[POTE generator]]: ~25/24 = 53.922
[[POTE generator]]: ~25/24 = 53.922
Line 216: Line 306:
[[Comma list]]: 10460353203/9765625000
[[Comma list]]: 10460353203/9765625000


[[Mapping]]: [{{val| 1 2 3 }}, {{val| 0 -13 -21 }}]
[[Mapping]]: [{{Val| 1 2 3 }}, {{Val| 0 -13 -21 }}]


[[POTE generator]]: ~6561/6250 = 38.571
[[POTE generator]]: ~6561/6250 = 38.571
Line 229: Line 319:
[[Comma]]: 16000000/14348907
[[Comma]]: 16000000/14348907


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


[[POTE generator]]: ~10/9 = 156.861
[[POTE generator]]: ~10/9 = 156.861
Line 244: Line 334:
[[Comma]]: 145282683375/137438953472
[[Comma]]: 145282683375/137438953472


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


[[POTE generator]]: ~4096/3645 = 232.521
[[POTE generator]]: ~4096/3645 = 232.521
Line 257: Line 347:
[[Comma]]: 2359296/1953125
[[Comma]]: 2359296/1953125


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


[[POTE generator]]: ~768/625 = 212.444
[[POTE generator]]: ~768/625 = 212.444
Line 264: Line 354:


[[Badness]]: 1.404977
[[Badness]]: 1.404977
== Casablanca ==
{{see also| Starling temperaments #Casablanca }}
Subgroup: 2.3.5
[[Comma]]: 20061226008576/19073486328125
[[Mapping]]: [{{Val| 1 -7 -14 }}, {{Val| 0 19 14 }}]
[[POTE generator]]: ~864/625 = 542.208
{{Val list|legend=1| 11b, 20b, 31, 73, 104c, 135c }}
[[Badness]]: 1.423736


== Archaeotherium ==
== Archaeotherium ==
Line 272: Line 377:
[[Comma]]: 597871125/536870912
[[Comma]]: 597871125/536870912


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


[[POTE generator]]: ~1215/1024 = 230.351
[[POTE generator]]: ~1215/1024 = 230.351
Line 287: Line 392:
[[Comma]]: 2353579470675/2199023255552
[[Comma]]: 2353579470675/2199023255552


[[Mapping]]: [{{Val|1 1 9}}, {{Val|0 2 -23}}]
[[Mapping]]: [{{Val| 1 1 9 }}, {{Val| 0 2 -23 }}]


[[POTE generator]]: ~1048576/885735 = 348.600
[[POTE generator]]: ~1048576/885735 = 348.600
Line 302: Line 407:
[[Comma]]: 9685512225/8589934592
[[Comma]]: 9685512225/8589934592


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


[[POTE generator]]: ~3/2 = 691.455
[[POTE generator]]: ~3/2 = 691.455
Line 317: Line 422:
[[Comma]]: 1220703125/1073741824
[[Comma]]: 1220703125/1073741824


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


[[POTE generator]]: ~3/2 = 696.142
[[POTE generator]]: ~3/2 = 696.142
Retrieved from "https://en.xen.wiki/w/Miscellaneous_5-limit_temperaments"