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On this page, I explore some unnamed rank-2 temperaments that catched my interest.
On this page, I explore some unnamed rank-2 temperaments that catched my interest.
== 7 & 37 ==
Subgroup: 2.3.5.11.13
Comma list: [[55/54]], [[100/99]], [[512/507]]
Mapping: [{{val|1 5 8 8 2}}, {{val|0 -6 -10 -8 3}}]
POTE generator: ~160/117 = 518.2094
{{Optimal ET sequence|legend=1|7, 23bc, 30, 37, 44 }}
Badness: 1.211


== Berkenthin (19 & 239) ==
== Berkenthin (19 & 239) ==
Line 428: Line 442:


Badness: 2.875
Badness: 2.875
== 31 & 773 ==
Subgroup: 2.3.5.7
Comma list: 2401/2400, {{monzo|60 -3 -25 1}}
Mapping: [{{val|1 49 -3 12}}, {{val|0 -98 11 -19}}]
POTE generator: ~5859375/4194304 = 580.5918
{{Optimal ET sequence|legend=1|31, 556b, 587b, 618, 649, 680, 711, 1453, 3617c}}
Badness: 4.036
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 172032/171875, 820125/819896
Mapping: [{{val|1 49 -3 12 92}}, {{val|0 -98 11 -19 -183}}]
POTE generator: ~7875/5632 = 580.5924
{{Optimal ET sequence|legend=1|31, 618ee, 649e, 680e, 711, 742, 1453, 2195e, 2937e}}
Badness: 1.638


== 31 & 1063 ==
== 31 & 1063 ==
Line 1,171: Line 1,213:
Badness: 40.263
Badness: 40.263


== 53 & 1063 ==
== 53 & 733 ==


Subgroup: 2.3.5
Subgroup: 2.3.5


Comma list: {{monzo|57 -55 13}}
Comma list: {{monzo|42 -47 14}}


Mapping: [{{val|1 6 21}}, {{val|0 -13 -55}}]
Mapping: [{{val|1 0 -3}}, {{val|0 14 47}}]


POTE generator: ~163840000/129140163 = 407.5202
POTE generator: ~64000/59049 = 135.8799


{{Optimal ET sequence|legend=1|50cc, 53, 427c, 480, 533, 586, 639, 692, 745, 798, 851, 2500b, 3351b}}
{{Optimal ET sequence|legend=1| 44c, 53, 415, 468, 521, 574, 627, 680, 733}}


Badness: 22.373
Badness: 18.063
 
== 53 & 1063 ==
 
Subgroup: 2.3.5
 
Comma list: {{monzo|57 -55 13}}
 
Mapping: [{{val|1 6 21}}, {{val|0 -13 -55}}]
 
POTE generator: ~163840000/129140163 = 407.5202
 
{{Optimal ET sequence|legend=1|50cc, 53, 427c, 480, 533, 586, 639, 692, 745, 798, 851, 2500b, 3351b}}
 
Badness: 22.373


== 53 & 1193 ==
== 53 & 1193 ==
Line 1,362: Line 1,418:


Badness: 1.978
Badness: 1.978
== Wiloliquy (103 & 700) ==
Subgroup: 2.5.7.13.17
Comma list: 31250/31213, 10985/10976, 177482125/177209344
Mapping: [{{val|1 38 48 37 -4}}, {{val|0 -75 -95 -70 17}}]
POTE generator: ~50176/36125 = 570.8538
{{Optimal ET sequence|legend=1|103, 391, 494, 597, 2285cfg}}
Badness: 1.690


== 113 & 409 ==
== 113 & 409 ==
Line 1,737: Line 1,807:
Badness: 28.283
Badness: 28.283


== 311 & 379 ==
== Focus (307 & 743) ==


Subgroup: 2.3.5.7
Subgroup: 2.5.7.11.13.17


Comma list: 2401/2400, {{monzo|-23 -11 15 2}}
Comma list: 140800/140777, 40898/40817, 102487/102400, 184960/184877


Mapping: [{{val|1 -5 -2 -1}}, {{val|0 64 42 37}}]
Mapping: [{{val|1 -69 -22 -26 -37 -37}}, {{val|0 184 64 76 105 106}}]


POTE generator: ~78125/72576 = 123.4671
POTE generator: ~17/13 = 465.1430


{{Optimal ET sequence|legend=1|29bbcd, 39bc, 68, 175, 243, 311, 554, 865, 1419cd}}
{{Optimal ET sequence|legend=1|129c, 178c, 307, 743, 1050}}


Badness: 3.518
Badness: 2.436


=== 11-limit ===
=== 19-limit ===
 
Subgroup: 2.5.7.11.13.17.19
 
Comma list: 10241/10240, 1331/1330, 140800/140777, 64220/64141, 5491/5488
 
Mapping: [{{val|1 -69 -22 -26 -37 -37 12}}, {{val|0 184 64 76 105 106 -20}}]
 
POTE generator: ~17/13 = 465.1425
 
{{Optimal ET sequence|legend=1|129c, 178c, 307, 743, 1050}}
 
Badness: 1.878
 
=== 23-limit ===
 
Subgroup: 2.5.7.11.13.17.19.23
 
Comma list: 10241/10240, 140800/140777, 27209/27200, 4807/4802, 31603/31556, 608000/607453
 
Mapping: [{{val|1 -69 -22 -26 -37 -37 12 -73}}, {{val|0 184 64 76 105 106 -20 200}}]
 
POTE generator: ~17/13 = 465.1422
 
{{Optimal ET sequence|legend=1|129ci, 307, 743, 1050}}
 
Badness: 1.538
 
== 311 & 379 ==
 
Subgroup: 2.3.5.7
 
Comma list: 2401/2400, {{monzo|-23 -11 15 2}}
 
Mapping: [{{val|1 -5 -2 -1}}, {{val|0 64 42 37}}]
 
POTE generator: ~78125/72576 = 123.4671
 
{{Optimal ET sequence|legend=1|29bbcd, 39bc, 68, 175, 243, 311, 554, 865, 1419cd}}
 
Badness: 3.518
 
=== 11-limit ===


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 2,104: Line 2,216:


Badness: 1.360
Badness: 1.360
== 373 & 727 ==
Subgroup: 2.3.5.7.11
Comma list: 24057/24010, 137781/137500, 496125/495616
Mapping: [{{val|1 18 20 55 115}}, {{val|0 -39 -42 -124 -265}}]
POTE generator: ~75/56 = 505.0903
{{Optimal ET sequence|legend=1|19e, 335dee, 354, 373, 727, 1100, 1827b}}
Badness: 3.365
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 729/728, 1716/1715, 78975/78848, 34398/34375
Mapping: [{{val|1 18 20 55 115 50}}, {{val|0 -39 -42 -124 -265 -110}}]
POTE generator: ~75/56 = 505.0903
{{Optimal ET sequence|legend=1|19e, 335dee, 354, 373, 727, 1100, 1827bf}}
Badness: 1.677


== 379 & 577 ==
== 379 & 577 ==
Line 2,160: Line 2,300:


Badness: 1.045
Badness: 1.045
== Shortcrust (677 & 761) ==
Subgroup: 2.3.5
Comma list: {{monzo|159 33 -91}}
Mapping: [{{val|1 20 9}}, {{val|0 -91 -33}}]
POTE generator: ~48828125/42467328 = 242.8354
{{Optimal ET sequence|legend=1|84, 341b, 425, 509, 593, 677, 1947, 2624, 8549c}}
Badness: 94.681
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