Xenharmonic Wiki

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

← Older edit
VisualWikitext
Francium (talk | contribs)
4,839 edits
+ 373 & 509
Francium (talk | contribs)
4,839 edits
+ 653 & 1759
 
(5 intermediate revisions by the same user not shown)
Line 500: Line 500:


Badness: 6.211
Badness: 6.211
== 31 & 523 ==
Subgroup: 2.3.5.7
Comma list:  2401/2400, 13904571533203125/13792273858822144
Mapping: [{{val|1 -17 8 1}}, {{val|0 72 -22 7}}]
POTE tuning: ~448/375 = 309.7449
{{Optimal ET sequence|legend=1|31, 430, 461, 492, 523, 554, 585, 1139cd, 1724ccd}}
Badness: 6.842
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list:  2401/2400, 496125/495616, 166375/165888
Mapping: [{{val|1 -17 8 1 -27}}, {{val|0 72 -22 7 118}}]
POTE tuning: ~448/375 = 309.7469
{{Optimal ET sequence|legend=1|31, 430, 461, 492, 523, 554e}}
Badness: 2,784


== Adriansonka (31 & 569) ==
== Adriansonka (31 & 569) ==
Line 2,143: Line 2,171:
Badness: 3.125
Badness: 3.125


== 311 & 503 ==
== 311 & 431 ==


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7.11


Comma list: 2401/2400, {{monzo|-95 21 29 -2}}
Comma list: 2401/2400, 820125/819896, 22478848/22460625


Mapping: [{{val|1 43 -28 -2}}, {{val|0 -112 82 13}}]
Mapping: [{{val|1 -27 55 22 -19}}, {{val|0 70 -129 -47 55}}]


POTE generator: ~18984375/14680064 = 443.7335
POTE generator: ~896/675 = 490.0279


{{Optimal ET sequence|legend=1|119, 192, 311, 814, 1125, 3064d, 4189cdd, 5314cdd}}
{{Optimal ET sequence|legend=1|120, 191, 311, 742, 1053, 1795}}


Badness: 7.820 
Badness: 1.729


=== 11-limit ===
=== 13-limit ===


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11.13


Comma list: 2401/2400, 496125/495616, 100663296/100656875
Comma list: 4096/4095, 2401/2400, 59535/59488, 6656/6655


Mapping: [{{val|1 43 -28 -2 36}}, {{val|0 -112 82 13 -88}}]
Mapping: [{{val|1 -27 55 22 -19 -11}}, {{val|0 70 -129 -47 55 36}}]


POTE generator: ~21175/16384 = 443.7337
POTE generator: ~896/675 = 490.0277


{{Optimal ET sequence|legend=1|119, 192, 311, 503, 814, 1125, 1939}}
{{Optimal ET sequence|legend=1|120, 191, 311, 742, 1053, 1795f}}


Badness: 2.599
Badness: 1.343


=== 13-limit ===
=== 17-limit ===


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13.17


Comma list: 2401/2400, 4225/4224, 59535/59488, 6656/6655
Comma list: 4096/4095, 12376/12375, 2401/2400, 14400/14399, 11016/11011


Mapping: [{{val|1 43 -28 -2 36 71}}, {{val|0 -112 82 13 -88 -182}}]
Mapping: [{{val|1 -27 55 22 -19 -11 78}}, {{val|0 70 -129 -47 55 36 -181}}]


POTE generator: ~84/65 = 443.7338
POTE generator: ~896/675 = 490.0276


{{Optimal ET sequence|legend=1|119f, 192, 311, 503, 814, 1125, 1939}}
{{Optimal ET sequence|legend=1|120g, 191g, 311, 431, 742, 1795f}}


Badness: 1.410
Badness: 1.070


=== 17-limit ===
=== 19-limit ===


Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 12376/12375, 2401/2400, 14400/14399, 4225/4224, 11016/11011
Comma list: 2926/2925, 4096/4095, 3136/3135, 12376/12375, 5985/5984, 11016/11011


Mapping: [{{val|1 43 -28 -2 36 71 -34}}, {{val|0 -112 82 13 -88 -182 103}}]
Mapping: [{{val|1 -27 55 22 -19 -11 78 41}}, {{val|0 70 -129 -47 55 36 -181 -90}}]


POTE generator: ~84/65 = 443.7340
POTE generator: ~896/675 = 490.0276


{{Optimal ET sequence|legend=1|192, 311, 503, 814, 1939g, 2753dg}}
{{Optimal ET sequence|legend=1|120g, 191g, 311, 431, 742, 1795f}}


Badness: 1.111
Badness: 0.838


== 311 & 509 ==
=== 23-limit ===


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11.13.17.19.23


Comma list: 3025/3024, 2401/2400, 7168000/7144929
Comma list: 2926/2925, 4096/4095, 3136/3135, 12376/12375, 2025/2024, 5985/5984, 11016/11011


Mapping: [{{val|1 3 6 5 3}}, {{val|0 -40 -104 -62 13}}]
Mapping: [{{val|1 -27 55 22 -19 -11 78 41 18}}, {{val|0 70 -129 -47 55 36 -181 -90 -33}}]


POTE generator: ~6400/6237 = 42.4391
POTE generator: ~896/675 = 490.0275


{{Optimal ET sequence|legend=1|85c, 113, 198, 311, 509, 820}}
{{Optimal ET sequence|legend=1|120g, 191g, 311, 431, 742i}}


Badness: 1.926
Badness: 1.010


=== 13-limit ===
=== 29-limit ===


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13.17.19.23.29
 
Comma list: 2926/2925, 4096/4095, 3136/3135, 12376/12375, 2025/2024, 5985/5984, 11016/11011, 2205/2204


Comma list: 2080/2079, 3025/3024, 4459/4455, 313600/312741
Mapping: [{{val|1 -27 55 22 -19 -11 78 41 18 2}}, {{val|0 70 -129 -47 55 36 -181 -90 -33 7}}]


Mapping: [{{val|1 3 6 5 3 6}}, {{val|0 -40 -104 -62 13 -65}}]
POTE generator: ~896/675 = 490.0274


POTE generator: ~40/39 = 42.4391
{{Optimal ET sequence|legend=1|120g, 191g, 311, 431, 742i}}


{{Optimal ET sequence|legend=1|85c, 113, 198, 311, 509, 820f}}
Badness: 0.969


Badness: 1.168
== 311 & 503 ==


=== 17-limit ===
Subgroup: 2.3.5.7


Subgroup: 2.3.5.7.11.13.17
Comma list: 2401/2400, {{monzo|-95 21 29 -2}}


Comma list: 2080/2079, 1225/1224, 2431/2430, 2500/2499, 7616/7605
Mapping: [{{val|1 43 -28 -2}}, {{val|0 -112 82 13}}]


POTE generator: ~40/39 = 42.4389
POTE generator: ~18984375/14680064 = 443.7335


{{Optimal ET sequence|legend=1|113g, 198g, 311, 509, 820f}}
{{Optimal ET sequence|legend=1|119, 192, 311, 814, 1125, 3064d, 4189cdd, 5314cdd}}


Badness: 1.357
Badness: 7.820 


== 311 & 571 ==
=== 11-limit ===


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 3025/3024, 2401/2400, 294885080956928/294197433834375
Comma list: 2401/2400, 496125/495616, 100663296/100656875


Mapping: [{{val|1 11 -22 -7 37}}, {{val|0 -48 124 50 -171}}]
Mapping: [{{val|1 43 -28 -2 36}}, {{val|0 -112 82 13 -88}}]


POTE generator: ~63/55 = 235.3736
POTE generator: ~21175/16384 = 443.7337


{{Optimal ET sequence|legend=1|10, 18bcd, 21e, 23bc, 31, 41, 72, 167, 198, 239, 270, 342, 612, 954, 1566, 3101de, 3443de, 4055de, 4397cdee, 4667dee, 5009cddee}}
{{Optimal ET sequence|legend=1|119, 192, 311, 503, 814, 1125, 1939}}


Badness: 2.441
Badness: 2.599


=== 13-limit ===
=== 13-limit ===
Line 2,257: Line 2,287:
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 3025/3024, 2401/2400, 47432/47385, 114345/114244
Comma list: 2401/2400, 4225/4224, 59535/59488, 6656/6655
 
Mapping: [{{val|1 43 -28 -2 36 71}}, {{val|0 -112 82 13 -88 -182}}]


Mapping: [{{val|1 11 -22 -7 37 19}}, {{val|0 -48 124 50 -171 -78}}]
POTE generator: ~84/65 = 443.7338


POTE generator: ~63/55 = 235.3738
{{Optimal ET sequence|legend=1|119f, 192, 311, 503, 814, 1125, 1939}}


Badness: 1.528
Badness: 1.410


=== 17-limit ===
=== 17-limit ===
Line 2,269: Line 2,301:
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Comma list: 2431/2430, 12376/12375, 2601/2600, 8624/8619, 2401/2400
Comma list: 12376/12375, 2401/2400, 14400/14399, 4225/4224, 11016/11011


Mapping: [{{val|1 11 -22 -7 37 19 -22}}, {{val|0 -48 124 50 -171 -78 133}}]
Mapping: [{{val|1 43 -28 -2 36 71 -34}}, {{val|0 -112 82 13 -88 -182 103}}]


POTE generator: ~63/55 = 235.3741
POTE generator: ~84/65 = 443.7340


{{Optimal ET sequence|legend=1|260, 311, 571, 882}}
{{Optimal ET sequence|legend=1|192, 311, 503, 814, 1939g, 2753dg}}


Badness: 1.212
Badness: 1.111


== Sweepaway (311 & 607) ==
== 311 & 509 ==


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11


Comma list: 2080/2079, 625/624, 3025/3024, 405769/405504
Comma list: 3025/3024, 2401/2400, 7168000/7144929


Mapping: [{{val|1 20 17 -6 12 44}}, {{val|0 -69 -55 33 -32 -151}}]
Mapping: [{{val|1 3 6 5 3}}, {{val|0 -40 -104 -62 13}}]


POTE generator: ~65/54 = 320.2613
POTE generator: ~6400/6237 = 42.4391


{{Optimal ET sequence|legend=1|15, 281f, 296, 311, 607, 918c}}
{{Optimal ET sequence|legend=1|85c, 113, 198, 311, 509, 820}}


Badness: 1.583
Badness: 1.926


=== 17-limit ===
=== 13-limit ===


Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13


Comma list: 2080/2079, 625/624, 1225/1224, 3025/3024, 270725/270336
Comma list: 2080/2079, 3025/3024, 4459/4455, 313600/312741


Mapping: [{{val|1 20 17 -6 12 44 -21}}, {{val|0 -69 -55 33 -32 -151 94}}]
Mapping: [{{val|1 3 6 5 3 6}}, {{val|0 -40 -104 -62 13 -65}}]


POTE generator: ~65/54 = 320.2617
POTE generator: ~40/39 = 42.4391


{{Optimal ET sequence|legend=1|15, 296, 311, 607, 918c}}
{{Optimal ET sequence|legend=1|85c, 113, 198, 311, 509, 820f}}


Badness: 1.503
Badness: 1.168


=== 19-limit ===
=== 17-limit ===


Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17


Commas: 2080/2079, 625/624, 1225/1224, 3025/3024, 1729/1728, 26775/26752
Comma list: 2080/2079, 1225/1224, 2431/2430, 2500/2499, 7616/7605


Mapping: [{{val|1 20 17 -6 12 44 -21 28}}, {{val|0 -69 -55 33 -32 -151 94 -89}}]
POTE generator: ~40/39 = 42.4389


POTE generator: ~65/54 = 320.2615
{{Optimal ET sequence|legend=1|113g, 198g, 311, 509, 820f}}


{{Optimal ET sequence|legend=1|15, 296, 311, 607, 918ch}}
Badness: 1.357


Badness: 1.274
== 311 & 571 ==
 
== 311 & 701 ==


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 2401/2400, 22478848/22460625, 1395654656/1395032625
Comma list: 3025/3024, 2401/2400, 294885080956928/294197433834375


Mapping: [{{val|1 -13 40 18 -17}}, {{val|0 72 -186 -75 101}}]
Mapping: [{{val|1 11 -22 -7 37}}, {{val|0 -48 124 50 -171}}]


POTE generator: ~405/352 = 243.0836
POTE generator: ~63/55 = 235.3736


{{Optimal ET sequence|legend=1|79c, 311, 701, 1012, 1323, 2335, 3658}}
{{Optimal ET sequence|legend=1|10, 18bcd, 21e, 23bc, 31, 41, 72, 167, 198, 239, 270, 342, 612, 954, 1566, 3101de, 3443de, 4055de, 4397cdee, 4667dee, 5009cddee}}


Badness: 2.442
Badness: 2.441


=== 13-limit ===
=== 13-limit ===
Line 2,339: Line 2,369:
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 4096/4095, 2401/2400, 6656/6655, 1574640/1574573
Comma list: 3025/3024, 2401/2400, 47432/47385, 114345/114244


Mapping: [{{val|1 -13 40 18 -17 -20}}, {{val|0 72 -186 -75 101 117}}]
Mapping: [{{val|1 11 -22 -7 37 19}}, {{val|0 -48 124 50 -171 -78}}]


POTE generator: ~405/352 = 243.0835
POTE generator: ~63/55 = 235.3738


{{Optimal ET sequence|legend=1|79c, 311, 701, 1012, 1323, 2335}}
Badness: 1.528


Badness: 1.383
=== 17-limit ===


== 311 & 1063 ==
Subgroup: 2.3.5.7.11.13.17


Subgroup: 2.3.5.7
Comma list: 2431/2430, 12376/12375, 2601/2600, 8624/8619, 2401/2400


Comma list: 2401/2400, 3367254360064/3363025078125
Mapping: [{{val|1 11 -22 -7 37 19 -22}}, {{val|0 -48 124 50 -171 -78 133}}]


Mapping: [{{val|1 11 -22 -7}}, {{val|0 -24 62 25}}]
POTE generator: ~63/55 = 235.3741


POTE generator: ~21/16 = 470.7489
{{Optimal ET sequence|legend=1|260, 311, 571, 882}}


{{Optimal ET sequence|legend=1|51, 79c, 130, 311, 441, 2776, 3217, 3658, 4099, 4540, 4981}}
Badness: 1.212


Badness: 1.127
== Sweepaway (311 & 607) ==


=== 11-limit ===
Subgroup: 2.3.5.7.11.13


Subgroup: 2.3.5.7.11
Comma list: 2080/2079, 625/624, 3025/3024, 405769/405504


Comma list: 2401/2400, 19712/19683, 9453125/9437184
Mapping: [{{val|1 20 17 -6 12 44}}, {{val|0 -69 -55 33 -32 -151}}]


Mapping: [{{val|1 11 -22 -7 98}}, {{val|0 -24 62 25 -241}}]
POTE generator: ~65/54 = 320.2613


POTE generator: ~21/16 = 470.7429
{{Optimal ET sequence|legend=1|15, 281f, 296, 311, 607, 918c}}


{{Optimal ET sequence|legend=1|130e, 181e, 311, 752, 1063}}
Badness: 1.583


Badness: 4.158
=== 17-limit ===


== 311 & 1193 ==
Subgroup: 2.3.5.7.11.13.17


Subgroup: 2.3.5.7
Comma list: 2080/2079, 625/624, 1225/1224, 3025/3024, 270725/270336


Comma list: 2401/2400, {{monzo|36 -16 -7 2}}
Mapping: [{{val|1 20 17 -6 12 44 -21}}, {{val|0 -69 -55 33 -32 -151 94}}]


Mapping: [{{val|1 11 -22 -7}}, {{val|0 -48 124 50}}]
POTE generator: ~65/54 = 320.2617


POTE generator: ~8/7 = 235.3744
{{Optimal ET sequence|legend=1|15, 296, 311, 607, 918c}}


{{Optimal ET sequence|legend=1|51, 79c, 130, 311, 441, 2776, 3217, 3658, 4099, 4540, 4981}}
Badness: 1.503


Badness: 1.127
=== 19-limit ===


=== 11-limit ===
Subgroup: 2.3.5.7.11.13.17.19


Subgroup: 2.3.5.7.11
Commas: 2080/2079, 625/624, 1225/1224, 3025/3024, 1729/1728, 26775/26752


Comma list: 3025/3024, 2401/2400, 3637837299712/3632067084375
Mapping: [{{val|1 20 17 -6 12 44 -21 28}}, {{val|0 -69 -55 33 -32 -151 94 -89}}]


Mapping: [{{val|1 11 -22 -7 37}}, {{val|0 -48 124 50 -171}}]
POTE generator: ~65/54 = 320.2615


POTE generator: ~55/48 = 235.3736
{{Optimal ET sequence|legend=1|15, 296, 311, 607, 918ch}}


{{Optimal ET sequence|legend=1|51e, 260, 311, 571, 882, 2075}}
Badness: 1.274


Badness: 2.441
== 311 & 701 ==


=== 13-limit ===
Subgroup: 2.3.5.7.11


Subgroup: 2.3.5.7.11.13
Comma list: 2401/2400, 22478848/22460625, 1395654656/1395032625


Comma list: 3025/3024, 4096/4095, 2401/2400, 492128/492075
Mapping: [{{val|1 -13 40 18 -17}}, {{val|0 72 -186 -75 101}}]


Mapping: [{{val|1 11 -22 -7 37 19}}, {{val|0 -48 124 50 -171 -78}}]
POTE generator: ~405/352 = 243.0836


POTE generator: ~55/48 = 235.3738
{{Optimal ET sequence|legend=1|79c, 311, 701, 1012, 1323, 2335, 3658}}


{{Optimal ET sequence|legend=1|51e, 260, 311, 571, 882, 2075f}}
Badness: 2.442


Badness: 1.528
=== 13-limit ===
 
== 311 & 1759 ==


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 3025/3024, 4225/4224, 4100625/4100096, 1664000/1663893
Comma list: 4096/4095, 2401/2400, 6656/6655, 1574640/1574573


Mapping: [{{val|1 -34 40 36 -71 -89}}, {{val|0 119 -126 -111 249 310}}]
Mapping: [{{val|1 -13 40 18 -17 -20}}, {{val|0 72 -186 -75 101 117}}]


POTE generator: ~315/256 = 358.8399
POTE generator: ~405/352 = 243.0835


{{Optimal ET sequence|legend=1|311, 826f, 1137, 1448, 4655cef, 6103cef, 7551ceeff, 8999cceeff}}
{{Optimal ET sequence|legend=1|79c, 311, 701, 1012, 1323, 2335}}


Badness: 1.405
Badness: 1.383


=== 17-limit ===
== 311 & 1063 ==


Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7


Comma list: 3025/3024, 2500/2499, 4225/4224, 56595/56576, 4100625/4100096
Comma list: 2401/2400, 3367254360064/3363025078125


Mapping: [{{val|1 -34 40 36 -71 -89 124}}, {{val|0 119 -126 -111 249 310 -401}}]
Mapping: [{{val|1 11 -22 -7}}, {{val|0 -24 62 25}}]


POTE generator: ~315/256 = 358.8402
POTE generator: ~21/16 = 470.7489


{{Optimal ET sequence|legend=1|311, 1137g, 1448, 1759}}
{{Optimal ET sequence|legend=1|51, 79c, 130, 311, 441, 2776, 3217, 3658, 4099, 4540, 4981}}


Badness: 1.903
Badness: 1.127


=== 19-limit ===
=== 11-limit ===


Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11


Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 1549184/1549125
Comma list: 2401/2400, 19712/19683, 9453125/9437184


Mapping: [{{val|1 -34 40 36 -71 -89 124 50}}, {{val|0 119 -126 -111 249 310 -401 -153}}]
Mapping: [{{val|1 11 -22 -7 98}}, {{val|0 -24 62 25 -241}}]


POTE generator: ~315/256 = 358.8402
POTE generator: ~21/16 = 470.7429


{{Optimal ET sequence|legend=1|311, 1137g, 1448, 1759}}
{{Optimal ET sequence|legend=1|130e, 181e, 311, 752, 1063}}


Badness: 1.418
Badness: 4.158


=== 23-limit ===
== 311 & 1193 ==


Subgroup: 2.3.5.7.11.13.17.19.23
Subgroup: 2.3.5.7


Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 76545/76544
Comma list: 2401/2400, {{monzo|36 -16 -7 2}}


Mapping: [{{val|1 -34 40 36 -71 -89 124 50 -81}}, {{val|0 119 -126 -111 249 310 -401 -153 286}}]
Mapping: [{{val|1 11 -22 -7}}, {{val|0 -48 124 50}}]


POTE generator: ~315/256 = 358.8402
POTE generator: ~8/7 = 235.3744


{{Optimal ET sequence|legend=1|311, 1137g, 1448, 1759}}
{{Optimal ET sequence|legend=1|51, 79c, 130, 311, 441, 2776, 3217, 3658, 4099, 4540, 4981}}


Badness: 1.239
Badness: 1.127


=== 29-limit ===
=== 11-limit ===


Subgroup: 2.3.5.7.11.13.17.19.23.29
Subgroup: 2.3.5.7.11


Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 5104/5103, 76545/76544
Comma list: 3025/3024, 2401/2400, 3637837299712/3632067084375


Mapping: [{{val|1 -34 40 36 -71 -89 124 50 -81 -101}}, {{val|0 119 -126 -111 249 310 -401 -153 286 354}}]
Mapping: [{{val|1 11 -22 -7 37}}, {{val|0 -48 124 50 -171}}]


POTE generator: ~315/256 = 358.8402
POTE generator: ~55/48 = 235.3736


Badness: 1.159
{{Optimal ET sequence|legend=1|51e, 260, 311, 571, 882, 2075}}


=== 31-limit ===
Badness: 2.441


Subgroup: 2.3.5.7.11.13.17.19.23.29.31
=== 13-limit ===


Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 5104/5103, 76545/76544, 6076/6075
Subgroup: 2.3.5.7.11.13


Mapping: [{{val|1 -34 40 36 -71 -89 124 50 -81 -101 -164}}, {{val|0 119 -126 -111 249 310 -401 -153 286 354 565}}]
Comma list: 3025/3024, 4096/4095, 2401/2400, 492128/492075


POTE generator: ~315/256 = 358.8403
Mapping: [{{val|1 11 -22 -7 37 19}}, {{val|0 -48 124 50 -171 -78}}]


Badness: 1.303
POTE generator: ~55/48 = 235.3738


=== 37-limit ===
{{Optimal ET sequence|legend=1|51e, 260, 311, 571, 882, 2075f}}


Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37
Badness: 1.528


Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 5104/5103, 76545/76544, 6076/6075, 5625/5624
== 311 & 1759 ==


Mapping: [{{val|1 -34 40 36 -71 -89 124 50 -81 -101 -164 39}}, {{val|0 119 -126 -111 249 310 -401 -153 286 354 565 -113}}]
Subgroup: 2.3.5.7.11.13


POTE generator: ~315/256 = 358.8402
Comma list: 3025/3024, 4225/4224, 4100625/4100096, 1664000/1663893


Badness: 1.301
Mapping: [{{val|1 -34 40 36 -71 -89}}, {{val|0 119 -126 -111 249 310}}]


=== 41-limit ===
POTE generator: ~315/256 = 358.8399


Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41
{{Optimal ET sequence|legend=1|311, 826f, 1137, 1448, 4655cef, 6103cef, 7551ceeff, 8999cceeff}}


Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 5104/5103, 76545/76544, 6076/6075, 5625/5624, 2625/2624
Badness: 1.405


Mapping: [{{val|1 -34 40 36 -71 -89 124 50 -81 -101 -164 39 116}}, {{val|0 119 -126 -111 249 310 -401 -153 286 354 565 -113 -370}}]
=== 17-limit ===


POTE generator: ~315/256 = 358.8403
Subgroup: 2.3.5.7.11.13.17


Badness: 1.360
Comma list: 3025/3024, 2500/2499, 4225/4224, 56595/56576, 4100625/4100096


== 373 & 509 ==
Mapping: [{{val|1 -34 40 36 -71 -89 124}}, {{val|0 119 -126 -111 249 310 -401}}]


Subgroup: 2.3.5.7.11.13
POTE generator: ~315/256 = 358.8402


Comma list: 3025/3024, 2401/2400, 40656/40625, 140625/140608
{{Optimal ET sequence|legend=1|311, 1137g, 1448, 1759}}


Mapping: [{{val|1 51 26 27 66 84}}, {{val|0 -192 -92 -94 -243 -312}}]
Badness: 1.903


POTE generator: ~1183/990 = 308.8441
=== 19-limit ===


{{Optimal ET sequence|legend=1|101bbcdeefff, 136ef, 237beff, 373, 882, 2137e}}
Subgroup: 2.3.5.7.11.13.17.19


Badness: 1.806
Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 1549184/1549125


== 373 & 727 ==
Mapping: [{{val|1 -34 40 36 -71 -89 124 50}}, {{val|0 119 -126 -111 249 310 -401 -153}}]


Subgroup: 2.3.5.7.11
POTE generator: ~315/256 = 358.8402


Comma list: 24057/24010, 137781/137500, 496125/495616
{{Optimal ET sequence|legend=1|311, 1137g, 1448, 1759}}


Mapping: [{{val|1 18 20 55 115}}, {{val|0 -39 -42 -124 -265}}]
Badness: 1.418


POTE generator: ~75/56 = 505.0903
=== 23-limit ===


{{Optimal ET sequence|legend=1|19e, 335dee, 354, 373, 727, 1100, 1827b}}
Subgroup: 2.3.5.7.11.13.17.19.23


Badness: 3.365
Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 76545/76544


=== 13-limit ===
Mapping: [{{val|1 -34 40 36 -71 -89 124 50 -81}}, {{val|0 119 -126 -111 249 310 -401 -153 286}}]


Subgroup: 2.3.5.7.11.13
POTE generator: ~315/256 = 358.8402


Comma list: 729/728, 1716/1715, 78975/78848, 34398/34375
{{Optimal ET sequence|legend=1|311, 1137g, 1448, 1759}}


Mapping: [{{val|1 18 20 55 115 50}}, {{val|0 -39 -42 -124 -265 -110}}]
Badness: 1.239


POTE generator: ~75/56 = 505.0903
=== 29-limit ===


{{Optimal ET sequence|legend=1|19e, 335dee, 354, 373, 727, 1100, 1827bf}}
Subgroup: 2.3.5.7.11.13.17.19.23.29


Badness: 1.677
Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 5104/5103, 76545/76544


== 379 & 577 ==
Mapping: [{{val|1 -34 40 36 -71 -89 124 50 -81 -101}}, {{val|0 119 -126 -111 249 310 -401 -153 286 354}}]


Subgroup: 2.5.7
POTE generator: ~315/256 = 358.8402


Comma list: {{monzo|40 -13 25}}
Badness: 1.159


Mapping: [{{val|1 20 12}}, {{val|0 -100 -52}}]
=== 31-limit ===


POTE generator: ~80/49 = 848.548
Subgroup: 2.3.5.7.11.13.17.19.23.29.31


{{Optimal ET sequence|legend=1|17c, 24c, 41, 99, 140, 239, 379, 1376, 1755, 2134, 6023, 8157, 10291d}}
Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 5104/5103, 76545/76544, 6076/6075


Badness: 0.785
Mapping: [{{val|1 -34 40 36 -71 -89 124 50 -81 -101 -164}}, {{val|0 119 -126 -111 249 310 -401 -153 286 354 565}}]


=== 11-limit ===
POTE generator: ~315/256 = 358.8403


Subgroup: 2.5.7.11
Badness: 1.303


Comma list: 102487/102400, {{monzo|28 11 -24 4}}
=== 37-limit ===


Mapping: [{{val|1 20 12 10}}, {{val|0 -100 -52 -37}}]
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37


POTE generator: ~133100/117649 = 212.1377
Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 5104/5103, 76545/76544, 6076/6075, 5625/5624


{{Optimal ET sequence|legend=1|17c, 164c, 181, 198, 379}}
Mapping: [{{val|1 -34 40 36 -71 -89 124 50 -81 -101 -164 39}}, {{val|0 119 -126 -111 249 310 -401 -153 286 354 565 -113}}]


Badness: 3.762
POTE generator: ~315/256 = 358.8402


== 487 & 691 ==
Badness: 1.301


Subgroup: 2.3.5.11.17.19
=== 41-limit ===


Comma list: 374000/373977, 500000/499851, 632225/632043, 116640/116603
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41


Mapping: [{{val|1 30 59 65 79 55}}, {{val|0 -187 -373 -405 -493 -334}}]
Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 5104/5103, 76545/76544, 6076/6075, 5625/5624, 2625/2624


POTE generator: ~10/9 = 182.3424
Mapping: [{{val|1 -34 40 36 -71 -89 124 50 -81 -101 -164 39 116}}, {{val|0 119 -126 -111 249 310 -401 -153 286 354 565 -113 -370}}]


{{Optimal ET sequence|legend=1|204cegh, 283ceggh, 487, 1178, 1665}}
POTE generator: ~315/256 = 358.8403


Badness: 1.522
Badness: 1.360


=== 31-limit ===
== 373 & 509 ==


Subgroup: 2.3.5.11.17.19.31
Subgroup: 2.3.5.7.11.13


Comma list: 6480/6479, 374000/373977, 500000/499851, 6138/6137, 242000/241893
Comma list: 3025/3024, 2401/2400, 40656/40625, 140625/140608


Mapping: [{{val|1 30 59 65 79 55 63}}, {{val|0 -187 -373 -405 -493 -334 -382}}]
Mapping: [{{val|1 51 26 27 66 84}}, {{val|0 -192 -92 -94 -243 -312}}]


POTE generator: ~10/9 = 182.3424
POTE generator: ~1183/990 = 308.8441


{{Optimal ET sequence|legend=1|204ceghk, 283cegghk, 487, 1178, 1665}}
{{Optimal ET sequence|legend=1|101bbcdeefff, 136ef, 237beff, 373, 882, 2137e}}


Badness: 1.045
Badness: 1.806
 
== 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


== Shortcrust (677 & 761) ==
Comma list: 729/728, 1716/1715, 78975/78848, 34398/34375


Subgroup: 2.3.5
Mapping: [{{val|1 18 20 55 115 50}}, {{val|0 -39 -42 -124 -265 -110}}]


Comma list: {{monzo|159 33 -91}}
POTE generator: ~75/56 = 505.0903


Mapping: [{{val|1 20 9}}, {{val|0 -91 -33}}]
{{Optimal ET sequence|legend=1|19e, 335dee, 354, 373, 727, 1100, 1827bf}}


POTE generator: ~48828125/42467328 = 242.8354
Badness: 1.677


{{Optimal ET sequence|legend=1|84, 341b, 425, 509, 593, 677, 1947, 2624, 8549c}}
== 379 & 577 ==
 
Subgroup: 2.5.7
 
Comma list: {{monzo|40 -13 25}}
 
Mapping: [{{val|1 20 12}}, {{val|0 -100 -52}}]
 
POTE generator: ~80/49 = 848.548
 
{{Optimal ET sequence|legend=1|17c, 24c, 41, 99, 140, 239, 379, 1376, 1755, 2134, 6023, 8157, 10291d}}
 
Badness: 0.785
 
=== 11-limit ===
 
Subgroup: 2.5.7.11
 
Comma list: 102487/102400, {{monzo|28 11 -24 4}}
 
Mapping: [{{val|1 20 12 10}}, {{val|0 -100 -52 -37}}]
 
POTE generator: ~133100/117649 = 212.1377
 
{{Optimal ET sequence|legend=1|17c, 164c, 181, 198, 379}}
 
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 ==
 
Subgroup: 2.3.5.11.17.19
 
Comma list: 374000/373977, 500000/499851, 632225/632043, 116640/116603
 
Mapping: [{{val|1 30 59 65 79 55}}, {{val|0 -187 -373 -405 -493 -334}}]
 
POTE generator: ~10/9 = 182.3424
 
{{Optimal ET sequence|legend=1|204cegh, 283ceggh, 487, 1178, 1665}}
 
Badness: 1.522
 
=== 31-limit ===
 
Subgroup: 2.3.5.11.17.19.31
 
Comma list: 6480/6479, 374000/373977, 500000/499851, 6138/6137, 242000/241893
 
Mapping: [{{val|1 30 59 65 79 55 63}}, {{val|0 -187 -373 -405 -493 -334 -382}}]
 
POTE generator: ~10/9 = 182.3424
 
{{Optimal ET sequence|legend=1|204ceghk, 283cegghk, 487, 1178, 1665}}
 
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) ==
 
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
Badness: 94.681
== 1063 & 5113 ==
Subgroup: 2.3.5.7.11
Comma list: 3294225/3294172, 781258401/781250000, 18889465931478580854784/18885534366318662109375
Mapping: [{{val|1 -256 320 338 560}}, {{val|0 853 -1052 -1110 -1843}}]
POTE generator: ~262144/212625 = 362.3704
{{Optimal ET sequence|legend=1|1063, 2987e, 4050, 5113, 9163}}
Badness: 8.800
== 3041 & 4349 ==
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 12376/12375, 10241/10240, 13377/13376, 89376/89375, 25025/25024, 617500/617463, 818125/818064
Mapping: [{{val|1 139 68 -35 -85 121 308 234 -177}}, {{val|0 -567 -271 156 365 -484 -1254 -948 749}}]
POTE generator: ~1287/1088 = 290.8255
{{Optimal ET sequence|legend=1|1308, 3041, 4349, 7390, 11739dg}}
Badness: 1.234
=== 29-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 12376/12375, 10241/10240, 13377/13376, 89376/89375, 25025/25024, 47125/47124, 25840/25839, 818125/818064
Mapping: [{{val|1 139 68 -35 -85 121 308 234 -177 143}}, {{val|0 -567 -271 156 365 -484 -1254 -948 749 -570}}]
POTE generator: ~1287/1088 = 290.8255
{{Optimal ET sequence|legend=1|270i, 1038gj, 1308, 2771i, 3041, 4349, 7390, 11739dgj}}
Badness: 1.103
=== 31-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23.29.31
Comma list: 12376/12375, 10241/10240, 13377/13376, 89376/89375, 25025/25024, 47125/47124, 13300/13299, 25840/25839, 818125/818064
Mapping: [{{val|1 139 68 -35 -85 121 308 234 -177 143 162}}, {{val|0 -567 -271 156 365 -484 -1254 -948 749 -570 -648}}]
POTE generator: ~1287/1088 = 290.8255
{{Optimal ET sequence|legend=1|270i, 1038gj, 1308, 2771i, 3041, 4349}}
Badness: 1.245
=== 37-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37
Comma list: 12376/12375, 10241/10240, 13377/13376, 89376/89375, 25025/25024, 47125/47124, 13300/13299, 25840/25839, 818125/818064, 395675/395604
Mapping: [{{val|1 139 68 -35 -85 121 308 234 -177 143 162 -4}}, {{val|0 -567 -271 156 365 -484 -1254 -948 749 -570 -648 38}}]
POTE generator: ~1287/1088 = 290.8255
{{Optimal ET sequence|legend=1|270i, 1038gj, 1308, 2771i, 3041, 4349, 7390}}
Badness: 1.197
=== 41-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41
Comma list: 12376/12375, 10241/10240, 13377/13376, 89376/89375, 25025/25024, 47125/47124, 13300/13299, 25840/25839, 818125/818064, 17425/17424, 395675/395604
Mapping: [{{val|1 139 68 -35 -85 121 308 234 -177 143 162 -4 -332}}, {{val|0 -567 -271 156 365 -484 -1254 -948 749 -570 -648 38 1392}}]
POTE generator: ~1287/1088 = 290.8255
{{Optimal ET sequence|legend=1|1308, 3041, 4349, 7390}}
Badness: 1.348
=== 43-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41.43
Comma list: 12376/12375, 10241/10240, 13377/13376, 89376/89375, 25025/25024, 47125/47124, 13300/13299, 25840/25839, 818125/818064, 17425/17424, 395675/395604, 111475/111456
Mapping: [{{val|1 139 68 -35 -85 121 308 234 -177 143 162 -4 -332 -409}}, {{val|0 -567 -271 156 365 -484 -1254 -948 749 -570 -648 38 1392 1710}}]
POTE generator: ~1287/1088 = 290.8255
{{Optimal ET sequence|legend=1|1308, 3041, 4349, 7390}}
Badness: 1.501
Retrieved from "https://en.xen.wiki/w/User:Francium/Miscellaneous_rank-2_temperaments"