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Sensamagic clan: Difference between revisions

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= Bohpier =
= Bohpier =
Comma: 1220703125/1162261467
== 5-limit ==
[[Comma list]]: 1220703125/1162261467


POTE generator: ~27/25 = 146.476
[[Mapping]]: [<1 0 0|, <0 13 19|]


Map: [<1 0 0|, <0 13 19|]
[[POTE generator]]: ~27/25 = 146.476


EDOs: 8, 41, 131, 172, 213c
{{Val list|legend=1| 8, 41, 131, 172, 213c }}


Badness: 0.8605
[[Badness]]: 0.8605


== 7-limit ==
== 7-limit ==
[[Comma]]s: 245/243, 3125/3087
[[Comma list]]: 245/243, 3125/3087


[[POTE_tuning|POTE generator]]: ~27/25 = 146.474
[[Mapping]]: [<1 0 0 0|, <0 13 19 23|]


Map: [<1 0 0 0|, <0 13 19 23|]
{{Multival|legend=1| 13 19 23 0 0 0 }}


[[Wedgie]]: <<13 19 23 0 0 0||
[[POTE generator]]: ~27/25 = 146.474


EDOs: [[41edo|41]], [[49edo|49]], [[90edo|90]], [[131edo|131]]
{{Val list|legend=1| 41, 49, 90, 131 }}
 
EDTs: [[13edt|13]]


[[Badness]]: 0.0682
[[Badness]]: 0.0682


== 11-limit ==
== 11-limit ==
Commas: 100/99, 245/243, 1344/1331
Comma list: 100/99, 245/243, 1344/1331


POTE generator: ~12/11 = 146.545
POTE generator: ~12/11 = 146.545


Map: [<1 0 0 0 2|, <0 13 19 23 12|]
Mapping: [<1 0 0 0 2|, <0 13 19 23 12|]


EDOs: 41, 90e, 131e
{{Val list|legend=1| 41, 90e, 131e }}


Badness: 0.0339
Badness: 0.0339


== 13-limit ==
== 13-limit ==
Commas: 100/99, 144/143, 196/195, 275/273
Comma list: 100/99, 144/143, 196/195, 275/273


POTE generator: ~12/11 = 146.603
POTE generator: ~12/11 = 146.603


Map: [<1 0 0 0 2 2|, <0 13 19 23 12 14|]
Mapping: [<1 0 0 0 2 2|, <0 13 19 23 12 14|]


EDOs: 41, 90ef, 131ef, 221bdeff
{{Val list|legend=1| 41, 90ef, 131ef, 221bdeff }}


Badness: 0.0249
Badness: 0.0249
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* [http://micro.soonlabel.com/bophier/bophier-12equal-six-octaves.mp3 bophier-12equal-six-octaves.mp3]
* [http://micro.soonlabel.com/bophier/bophier-12equal-six-octaves.mp3 bophier-12equal-six-octaves.mp3]


= Sensa (Escaped) =
= Sensa aka escaped =
{{see also| Escapade family #Escaped }}
{{see also| Escapade family #Escaped }}


Commas: 245/243, 65625/65536
[[Comma list]]: 245/243, 65625/65536


POTE generator: ~28/27 = 55.122
[[Mapping]]: [<1 2 2 4|, <0 -9 7 -26|]


Map: [<1 2 2 4|, <0 -9 7 -26|]
{{Multival|legend=1| 9 -7 26 -32 16 80 }}


Wedgie: <<9 -7 26 -32 16 80||
[[POTE generator]]: ~28/27 = 55.122


EDOs: [[22edo|22]], [[43edo|43d]], [[65edo|65]], [[87edo|87]], [[109edo|109]], [[196edo|196]], [[283edo|283]]
{{Val list|legend=1| 22, 43d, 65, 87, 109, 196, 283 }}


Badness: 0.0887
[[Badness]]: 0.0887


== 11-limit ==
== 11-limit ==
Commas: 245/243, 385/384, 4000/3993
Comma list: 245/243, 385/384, 4000/3993
 
Mapping: [<1 2 2 4 3|, <0 -9 7 -26 10|]


POTE generator: ~28/27 = 55.126
POTE generator: ~28/27 = 55.126


Map: [<1 2 2 4 3|, <0 -9 7 -26 10|]
{{Val list|legend=1| 22, 43d, 65, 87, 109, 196, 283 }}
 
EDOs: 22, 43d, 65, 87, 109, 196, 283


Badness: 0.0358
Badness: 0.0358


== 13-limit ==
== 13-limit ==
Commas: 245/243, 352/351, 385/384, 625/624
Comma list: 245/243, 352/351, 385/384, 625/624
 
Mapping: [<1 2 2 4 3 2|, <0 -9 7 -26 10 37|]


POTE generator: ~28/27 = 55.138
POTE generator: ~28/27 = 55.138


Map: [<1 2 2 4 3 2|, <0 -9 7 -26 10 37|]
{{Val list|legend=1| 22, 65, 87, 109, 196, 283 }}
 
EDOs: 22, 65, 87, 109, 196, 283


Badness: 0.0317
Badness: 0.0317
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{{see also| Schismatic family }}
{{see also| Schismatic family }}


Commas: 245/243, 32805/32768
[[Comma list]]: 245/243, 32805/32768


POTE generator: ~128/105 = 351.049
[[Mapping]]: [<1 1 7 -1|, <0 2 -16 13|]


Map: [<1 1 7 -1|, <0 2 -16 13|]
{{Multival|legend=1| 2 -16 13 -30 15 75 }}


Wedgie: <<2 -16 13 -30 15 75||
[[POTE generator]]: ~128/105 = 351.049


EDOs: 17, 24, 41, 106d, 147d, 188cd, 335cd
{{Val list|legend=1| 17, 24, 41, 106d, 147d, 188cd, 335cd }}


Badness: 0.08015
[[Badness]]: 0.08015


== 11-limit ==
== 11-limit ==
Commas: 243/242, 245/242, 385/384
Comma list: 243/242, 245/242, 385/384
 
Mapping: [<1 1 7 -1 2|, <0 2 -16 13 5|]


POTE generator: ~11/9 = 351.014
POTE generator: ~11/9 = 351.014


Map: [<1 1 7 -1 2|, <0 2 -16 13 5|]
{{Val list|legend=1| 17, 24, 41, 106d, 147d }}
 
EDOs: 17, 24, 41, 106d, 147d


Badness: 0.0394
Badness: 0.0394


== 13-limit ==
== 13-limit ==
Commas: 105/104, 144/143, 243/242, 245/242
Comma list: 105/104, 144/143, 243/242, 245/242
 
Mapping: [<1 1 7 -1 2 4|, <0 2 -16 13 5 -1|]


POTE generator: ~11/9 = 351.025
POTE generator: ~11/9 = 351.025


Map: [<1 1 7 -1 2 4|, <0 2 -16 13 5 -1|]
{{Val list|legend=1| 17, 24, 41, 106df, 147df }}
 
EDOs: 17, 24, 41, 106df, 147df


Badness: 0.0310
Badness: 0.0310
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The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune.
The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune.


Commas: 245/243, 525/512
[[Comma list]]: 245/243, 525/512


POTE generator: ~45/32 = 567.720
[[Mapping]]: [<1 3 -1 8|, <0 -3 7 -11|]


Map: [<1 3 -1 8|, <0 -3 7 -11|]
{{Multival|legend=1| 3 -7 11 -18 9 45 }}


Wedgie: <<3 -7 11 -18 9 45||
[[POTE generator]]: ~45/32 = 567.720


EDOs: 17, 19, 36c, 55c, 74cd, 93cdd
{{Val list|legend=1| 17, 19, 36c, 55c, 74cd, 93cdd }}


Badness: 0.0737
[[Badness]]: 0.0737


= Cohemiripple =
= Cohemiripple =
{{see also| Ripple family }}
{{see also| Ripple family }}


Commas: 245/243, 1323/1250
[[Comma list]]: 245/243, 1323/1250


POTE generator: ~7/5 = 549.944
[[Mapping]]: [<1 7 11 12|, <0 -10 -16 -17|]


Map: [<1 7 11 12|, <0 -10 -16 -17|]
{{Multival|legend=1| 10 16 17 2 -1 -5 }}


Wedgie: <<10 16 17 2 -1 -5||
[[POTE generator]]: ~7/5 = 549.944


EDOs: 11cd, 13cd, 24
{{Val list|legend=1| 11cd, 13cd, 24 }}


Badness: 0.1902
[[Badness]]: 0.1902


== 11-limit ==
== 11-limit ==
Commas: 77/75, 243/242, 245/242
Comma list: 77/75, 243/242, 245/242
 
Mapping: [<1 7 11 12 17|, <0 -10 -16 -17 -25|]


POTE generator: ~7/5 = 549.945
POTE generator: ~7/5 = 549.945


Map: [<1 7 11 12 17|, <0 -10 -16 -17 -25|]
{{Val list|legend=1| 11cdee, 13cdee, 24 }}
 
EDOs: 11cdee, 13cdee, 24


Badness: 0.0827
Badness: 0.0827


== 13-limit ==
== 13-limit ==
Commas: 66/65, 77/75, 147/143, 243/242
Comma list: 66/65, 77/75, 147/143, 243/242
 
Mapping: [<1 7 11 12 17 14|, <0 -10 -16 -17 -25 -19|]


POTE generator: ~7/5 = 549.958
POTE generator: ~7/5 = 549.958


Map: [<1 7 11 12 17 14|, <0 -10 -16 -17 -25 -19|]
{{Val list|legend=1| 11cdeef, 13cdeef, 24 }}
 
EDOs: 11cdeef, 13cdeef, 24


Badness: 0.0499
Badness: 0.0499


= Superthird =
= Superthird =
Commas: 245/243, 78125/76832
[[Comma list]]: 245/243, 78125/76832


POTE generator: ~9/7 = 439.076
[[Mapping]]: [<1 13 15 25|, <0 -18 -20 -35|]


Map: [<1 13 15 25|, <0 -18 -20 -35|]
{{Multival|legend=1| 18 20 35 -10 5 25 }}


Wedgie: <<18 20 35 -10 5 25||
[[POTE generator]]: ~9/7 = 439.076


EDOs: 41, 317bc, 358bc, 399bc
{{Val list|legend=1| 41, 317bc, 358bc, 399bc }}


Badness: 0.1394
[[Badness]]: 0.1394


== 11-limit ==
== 11-limit ==
Commas: 100/99, 245/243, 78125/76832
Comma list: 100/99, 245/243, 78125/76832
 
Mapping: [<1 13 15 25 6|, <0 -18 -20 -35 -4|]


POTE generator: ~9/7 = 439.152
POTE generator: ~9/7 = 439.152


Map: [<1 13 15 25 6|, <0 -18 -20 -35 -4|]
{{Val list|legend=1| 41, 153be, 194be, 235bce }}
 
EDOs: 41, 153be, 194be, 235bce


Badness: 0.0709
Badness: 0.0709


== 13-limit ==
== 13-limit ==
Commas: 100/99, 144/143, 196/195, 1375/1352
Comma list: 100/99, 144/143, 196/195, 1375/1352
 
Mapping: [<1 13 15 25 6 24|, <0 -18 -20 -35 -4 -32|]


POTE generator: ~9/7 = 439.119
POTE generator: ~9/7 = 439.119


Map: [<1 13 15 25 6 24|, <0 -18 -20 -35 -4 -32|]
{{Val list|legend=1| 41 }}
 
EDOs: 41


Badness: 0.0528
Badness: 0.0528


= Magus =
= Magus =
Commas: 50331648/48828125
== 5-limit ==
[[Comma list]]: 50331648/48828125


POTE generator: ~5/4 = 391.225
[[Mapping]]: [<1 9 3|, <0 -11 -1|]


Map: [<1 9 3|, <0 -11 -1|]
[[POTE generator]]: ~5/4 = 391.225


EDOs: 40, 43, 46, 181c, 227c, 273c, 319c
{{Val list|legend=1| 40, 43, 46, 181c, 227c, 273c, 319c }}


Badness: 0.3602
[[Badness]]: 0.3602


== 7-limit ==
== 7-limit ==
Commas: 245/243, 28672/28125
[[Comma list]]: 245/243, 28672/28125


POTE generator: ~5/4 = 391.465
[[Mapping]]: [<1 9 3 21|, <0 -11 -1 -27|]


Map: [<1 9 3 21|, <0 -11 -1 -27|]
{{Multival|legend=1| 11 1 27 -24 12 60 }}


Wedgie: <<11 1 27 -24 12 60||
[[POTE generator]]: ~5/4 = 391.465


EDOs: 46, 95, 141bc, 187bc, 328bc
{{Val list|legend=1| 46, 95, 141bc, 187bc, 328bc }}


Badness: 0.1084
[[Badness]]: 0.1084


== 11-limit ==
== 11-limit ==
Commas: 176/175, 245/243, 1331/1323
Comma list: 176/175, 245/243, 1331/1323
 
Mapping: [<1 9 3 21 23|, <0 -11 -1 -27 -29|]


POTE generator: ~5/4 = 391.503
POTE generator: ~5/4 = 391.503


Map: [<1 9 3 21 23|, <0 -11 -1 -27 -29|]
{{Val list|legend=1| 46, 95, 141bc }}
 
EDOs: 46, 95, 141bc


Badness: 0.0451
Badness: 0.0451


== 13-limit ==
== 13-limit ==
Commas: 91/90, 176/175, 245/243, 1331/1323
Comma list: 91/90, 176/175, 245/243, 1331/1323
 
Mapping: [<1 9 3 21 23 1|, <0 -11 -1 -27 -29 4|]


POTE generator: ~5/4 = 391.366
POTE generator: ~5/4 = 391.366


Map: [<1 9 3 21 23 1|, <0 -11 -1 -27 -29 4|]
{{Val list|legend=1| 46, 233bcf, 279bcf }}
 
EDOs: 46, 233bcf, 279bcf


Badness: 0.0430
Badness: 0.0430


= Leapweek =
= Leapweek =
Commas: 245/243, 2097152/2066715
[[Comma list]]: 245/243, 2097152/2066715


POTE generator: ~3/2 = 704.536
[[Mapping]]: [<1 1 17 -6|, <0 1 -25 15|]


Map: [<1 1 17 -6|, <0 1 -25 15|]
[[POTE generator]]: ~3/2 = 704.536


EDOs: 17, 46, 109, 155, 264b, 419b
{{Val list|legend=1| 17, 46, 109, 155, 264b, 419b }}


Badness: 0.14058
[[Badness]]: 0.14058


== 11-limit ==
== 11-limit ==
Commas: 245/243, 385/384, 1331/1323
Comma list: 245/243, 385/384, 1331/1323
 
Mapping: [<1 1 17 -6 -3|, <0 1 -25 15 11|]


POTE generator: ~3/2 = 704.554
POTE generator: ~3/2 = 704.554


Map: [<1 1 17 -6 -3|, <0 1 -25 15 11|]
{{Val list|legend=1| 17, 46, 109, 264b, 373b, 637be }}
 
EDOs: 17, 46, 109, 264b, 373b, 637be


Badness: 0.0507
Badness: 0.0507


== 13-limit ==
== 13-limit ==
Commas: 169/168, 245/243, 352/351, 364/363
Comma list: 169/168, 245/243, 352/351, 364/363
 
Mapping: [<1 1 17 -6 -3 -1|, <0 1 -25 15 11 8|]


POTE generator: ~3/2 = 704.571
POTE generator: ~3/2 = 704.571


Map: [<1 1 17 -6 -3 -1|, <0 1 -25 15 11 8|]
{{Val list|legend=1| 17, 46, 63, 109, 218f, 373bf }}
 
EDOs: 17, 46, 63, 109, 218f, 373bf


Badness: 0.0327
Badness: 0.0327
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