Xenharmonic Wiki

User:Francium/Miscellaneous rank-2 temperaments: Difference between revisions

← Older edit
VisualWikitext
Francium (talk | contribs)
4,860 edits
+ 3041 & 4349
Francium (talk | contribs)
4,860 edits
+ 2053 & 3217
 
(3 intermediate revisions by the same user not shown)
Line 2,704: Line 2,704:


Badness: 3.762
Badness: 3.762
== 457 & 541 ==
Subgroup: 2.5.7.13
Comma list: 10985/10976, 25044381618499755859375/24939997987655313784832
Mapping: [{{val|1 5 -21 -21}}, {{val|0 -9 80 83}}]
POTE generator: ~16777216/13671875 = 357.1090
{{Optimal ET sequence|legend=1|37df, 84, 289, 373, 457, 830, 1287, 2117cf}}
Badness: 3.521
=== 17-limit ===
Subgroup: 2.5.7.13.17
Comma list: 10985/10976, 1953125/1949696, 1073741824/1073446283
Mapping: [{{val|1 5 -21 -21 52}}, {{val|0 -9 80 83 -161}}]
POTE generator: ~1024/833 = 357.1118
{{Optimal ET sequence|legend=1|84, 373, 457}}
Badness: 3.336
=== 19-limit ===
Subgroup: 2.5.7.13.17.19
Comma list: 10985/10976, 524875/524288, 500000/499681, 300352/300125
Mapping: [{{val|1 5 -21 -21 52 -27}}, {{val|0 -9 80 83 -161 105}}]
POTE generator: ~3325/2704 = 357.1127
{{Optimal ET sequence|legend=1|84, 373, 457, 1455h}}
Badness: 2.258
=== 23-limit ===
Subgroup: 2.5.7.13.17.19.23
Comma list: 2875/2873, 52003/52000, 153125/153088, 186875/186592, 300352/300125
Mapping: [{{val|1 5 -21 -21 52 -27 -5}}, {{val|0 -9 80 83 -161 105 32}}]
POTE generator: ~1024/833 = 357.1127
{{Optimal ET sequence|legend=1|84, 373, 457, 1455hi}}
Badness: 1.565
=== 29-limit ===
Subgroup: 2.5.7.13.17.19.23.29
Comma list: 1625/1624, 52003/52000, 4901/4900, 153125/153088, 3335/3332, 1245335/1245184
Mapping: [{{val|1 5 -21 -21 52 -27 -5 12}}, {{val|0 -9 80 83 -161 105 32 -24}}]
POTE generator: ~30875/25088 = 357.1127
{{Optimal ET sequence|legend=1|84, 373, 457, 1455hi}}
Badness: 1.195
=== 31-limit ===
Subgroup: 2.5.7.13.17.19.23.29.31
Comma list: 1625/1624, 1520/1519, 52003/52000, 4901/4900, 153125/153088, 3335/3332, 9425/9424
Mapping: [{{val|1 5 -21 -21 52 -27 -5 12 24}}, {{val|0 -9 80 83 -161 105 32 -24 -64}}]
POTE generator: ~30875/25088 = 357.1128
{{Optimal ET sequence|legend=1|84, 373, 457, 1455hi}}
Badness: 1.024
=== 37-limit ===
Subgroup: 2.5.7.13.17.19.23.29.31.37
Comma list: 1625/1624, 1520/1519, 52003/52000, 4901/4900, 153125/153088, 3335/3332, 9425/9424, 25415/25382
Mapping: [{{val|1 5 -21 -21 52 -27 -5 12 24 93}}, {{val|0 -9 80 83 -161 105 32 -24 -64 -295}}]
POTE generator: ~30875/25088 = 357.1138
{{Optimal ET sequence|legend=1|84l, 457, 998i}}
Badness: 1.427


== 487 & 691 ==
== 487 & 691 ==
Line 2,732: Line 2,830:


Badness: 1.045
Badness: 1.045
== 653 & 1759 ==
Subgroup: 2.3.5.7.11.13.17
Comma list: 3025/3024, 2500/2499, 56595/56576, 14875/14872, 256000/255879
Mapping: [{{val|1 2 -84 -108 35 -259 -120}}, {{val|0 -1 208 267 -76 633 299}}]
POTE generator: ~4/3 = 498.0104
{{Optimal ET sequence|legend=1|453f, 653, 1106, 1759, 2865}}
Badness: 1.722
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 3025/3024, 2500/2499, 5985/5984, 6175/6174, 14875/14872, 256000/255879
Mapping: [{{val|1 2 -84 -108 35 -259 -120 108}}, {{val|0 -1 208 267 -76 633 299 -250}}]
POTE generator: ~4/3 = 498.0103
{{Optimal ET sequence|legend=1|653, 1106, 1759}}
Badness: 1.596
=== 23-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 3025/3024, 2500/2499, 5985/5984, 6175/6174, 3520/3519, 14875/14872, 76545/76544
Mapping: [{{val|1 2 -84 -108 35 -259 -120 108 73}}, {{val|0 -1 208 267 -76 633 299 -250 -165}}]
POTE generator: ~4/3 = 498.0104
{{Optimal ET sequence|legend=1|653, 1106, 1759}}
Badness: 1.409
=== 29-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 3025/3024, 2500/2499, 5985/5984, 6175/6174, 3520/3519, 14875/14872, 7425/7424, 12397/12393
Mapping: [{{val|1 2 -84 -108 35 -259 -120 108 73 -135}}, {{val|0 -1 208 267 -76 633 299 -250 -165 337}}]
POTE generator: ~4/3 = 498.0104
{{Optimal ET sequence|legend=1|653, 1106, 1759, 2865}}
Badness: 1.233
=== 31-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23.29.31
Comma list: 3025/3024, 2500/2499, 5985/5984, 6175/6174, 3520/3519, 14875/14872, 5104/5103, 12397/12393, 6076/6075
Mapping: [{{val|1 2 -84 -108 35 -259 -120 108 73 -135 56}}, {{val|0 -1 208 267 -76 633 299 -250 -165 337 -123}}]
POTE generator: ~4/3 = 498.0103
{{Optimal ET sequence|legend=1|653, 1106, 1759}}
Badness: 1.311


== Shortcrust (677 & 761) ==
== Shortcrust (677 & 761) ==
Line 2,760: Line 2,928:


Badness: 8.800
Badness: 8.800
== 1889 & 6079 ==
Subgroup: 2.3.5.7.11
Comma list: 14348907/14348180, 6576668672/6576582375, 3955078125/3954653486
Mapping: [{{val|1 3 -93 -92 80}}, {{val|0 -11 741 737 -595}}]
POTE generator: ~375/343 = 154.3675
{{Optimal ET sequence|legend=1|412, 1477, 1889, 4190, 6079, 28506d, 34585de, 40664de, 46743de}}
Badness: 2.229
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 123201/123200, 1664000/1663893, 1574640/1574573, 2480930816/2480878125
Mapping: [{{val|1 3 -93 -92 80 -105}}, {{val|0 -11 741 737 -595 845}}]
POTE generator: ~375/343 = 154.3675
{{Optimal ET sequence|legend=1|412, 1477f, 1889, 4190, 6079, 22427, 28506d, 34585de, 40664de}}
Badness: 0.866
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Comma list: 14400/14399, 123201/123200, 37180/37179, 194481/194480, 62390625/62390272
Mapping: [{{val|1 3 -93 -92 80 -105 -242}}, {{val|0 -11 741 737 -595 845 1913}}]
POTE generator: ~14553/13312 = 154.3675
{{Optimal ET sequence|legend=1|1889, 4190g, 6079, 14047, 20126g}}
Badness: 1.271
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 14400/14399, 89376/89375, 123201/123200, 165376/165375, 37180/37179, 10830/10829
Mapping: [{{val|1 3 -93 -92 80 -105 -242 -221}}, {{val|0 -11 741 737 -595 845 1913 1751}}]
POTE generator: ~375/343 = 154.3675
{{Optimal ET sequence|legend=1|1889, 4190g, 6079}}
Badness: 1.330
=== 23-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 14400/14399, 21736/21735, 25025/25024, 123201/123200, 37180/37179, 194481/194480, 43264/43263
Mapping: [{{val|1 3 -93 -92 80 -105 -242 -221 -67}}, {{val|0 -11 741 737 -595 845 1913 1751 556}}]
POTE generator: ~14553/13312 = 154.3675
{{Optimal ET sequence|legend=1|1889,4190g,6079}}
Badness: 1.134
=== 29-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 14400/14399, 89376/89375, 25025/25024, 123201/123200, 165376/165375, 20736/20735, 126225/126224, 10830/10829
Mapping: [{{val|1 3 -93 -92 80 -105 -242 -221 -67 138}}, {{val|0 -11 741 737 -595 845 1913 1751 556 -1035}}]
POTE generator: ~375/343 = 154.3675
{{Optimal ET sequence|legend=1|1889, 4190g, 6079}}
Badness: 1.243
== 2053 & 3217 ==
Subgroup: 2.3.5.11
Comma list: 3489136640/3486784401, {{monzo|-16 17 -36 21}}
Mapping: [{{val|1 56 201 300}}, {{val|0 -129 -471 -703}}]
POTE generator: ~21434787/16000000 = 506.186
{{Optimal ET sequence|legend=1|275e, 614cee, 889, 1164, 2053, 5270, 7323c}}
Badness: 29.558
=== 19-limit ===
Subgroup: 2.3.5.11.19
Comma list: 5000211/5000000, 3489136640/3486784401, 2310905821257/2310400000000
Mapping: [{{val|1 56 201 300 359}}, {{val|0 -129 -471 -703 -841}}]
POTE generator: 21434787/16000000 = 506.1860
{{Optimal ET sequence|legend=1|275eh, 614ceehh, 889, 1164, 2053, 5270, 7323c}}
Badness: 5.768
=== 31-limit ===
Subgroup: 2.3.5.11.19.31
Comma list: 3751/3750, 5000211/5000000, 3489136640/3486784401, 113379904/113308875
Mapping: [{{val|1 56 201 300 359 261}}, {{val|0 -129 -471 -703 -841 -607}}]
POTE generator: 531441/396800 = 506.1860
{{Optimal ET sequence|legend=1|275ehk, 614ceehhk, 889, 1164, 2053, 5270, 7323c}}
Badness: 2.547
=== 37-limit ===
Subgroup: 2.3.5.11.19.31.37
Comma list: 3751/3750, 30976/30969, 22385/22382, 62010927/62000000, 473600000/473513931
Mapping: [{{val|1 56 201 300 359 261 179}}, {{val|0 -129 -471 -703 -841 -607 -412}}]
POTE generator: ~1628/1215 = 506.1860
{{Optimal ET sequence|legend=1|275ehk, 614ceehhkl, 889, 1164, 2053, 5270, 7323c}}
Badness: 1.677


== 3041 & 4349 ==
== 3041 & 4349 ==
Retrieved from "https://en.xen.wiki/w/User:Francium/Miscellaneous_rank-2_temperaments"