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{{Technical data page}}
{{Technical data page}}
The '''sensamagic clan''' tempers out the sensamagic comma, [[245/243]], a triprime [[comma]] with no factors of 2, {{val| 0 -5 1 2 }} to be exact. Tempering out 245/243 alone in the full 7-limit leads to a [[Planar temperament|rank-3 temperament]], [[sensamagic]], for which [[283edo]] is the [[optimal patent val]].
The '''sensamagic clan''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the sensamagic comma, [[245/243]], a triprime [[comma]] with no factors of 2, {{val| 0 -5 1 2 }} to be exact.  
 
Tempering out 245/243 alone in the full 7-limit leads to a [[rank-3 temperament]], [[sensamagic]], for which [[283edo]] is the [[optimal patent val]].


== BPS ==
== BPS ==
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{{Mapping|legend=2| 1 1 2 | 0 -2 1 }}
{{Mapping|legend=2| 1 1 2 | 0 -2 1 }}
: mapping generators: ~3, ~9/7


: sval mapping generators: ~3, ~9/7
[[Optimal tuning]] ([[POTE]]): ~3 = 1901.9550{{c}}, ~9/7 = 440.4881{{c}}
 
[[Optimal tuning]] ([[POTE]]): ~3 = 1901.9550, ~9/7 = 440.4881


[[Optimal ET sequence]]: [[4edt|b4]], [[9edt|b9]], [[13edt|b13]], [[56edt|b56]], [[69edt|b69]], [[82edt|b82]], [[95edt|b95]]
[[Optimal ET sequence]]: [[4edt|b4]], [[9edt|b9]], [[13edt|b13]], [[56edt|b56]], [[69edt|b69]], [[82edt|b82]], [[95edt|b95]]
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{{Mapping|legend=1| 1 0 0 0 | 0 13 19 23 }}
{{Mapping|legend=1| 1 0 0 0 | 0 13 19 23 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~27/25 = 146.474
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~27/25 = 146.474{{c}}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
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{{Optimal ET sequence|legend=1| 41, 131, 172, 213c }}
{{Optimal ET sequence|legend=1| 41, 131, 172, 213c }}


[[Badness]]: 0.068237
[[Badness]] (Smith): 0.068237


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 0 0 0 2 | 0 13 19 23 12 }}
Mapping: {{mapping| 1 0 0 0 2 | 0 13 19 23 12 }}


Optimal tuning (POTE): ~2 = 1200.000, ~12/11 = 146.545
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 146.545{{c}}


Minimax tuning:  
Minimax tuning:  
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{{Optimal ET sequence|legend=0| 41, 90e, 131e }}
{{Optimal ET sequence|legend=0| 41, 90e, 131e }}


Badness: 0.033949
Badness (Smith): 0.033949


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 1 0 0 0 2 2 | 0 13 19 23 12 14 }}
Mapping: {{mapping| 1 0 0 0 2 2 | 0 13 19 23 12 14 }}


Optimal tuning (POTE): ~2 = 1200.000, ~12/11 = 146.603
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 146.603{{c}}


Minimax tuning:  
Minimax tuning:  
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{{Optimal ET sequence|legend=0| 41, 90ef, 131ef, 221bdeff }}
{{Optimal ET sequence|legend=0| 41, 90ef, 131ef, 221bdeff }}


Badness: 0.024864
Badness (Smith): 0.024864


=== Triboh ===
=== Triboh ===
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Mapping: {{mapping| 1 0 0 0 0 | 0 39 57 69 85 }}
Mapping: {{mapping| 1 0 0 0 0 | 0 39 57 69 85 }}


Optimal tuning (POTE): ~2 = 1200.000, ~77/75 = 48.828
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~77/75 = 48.828{{c}}


{{Optimal ET sequence|legend=0| 49, 123ce, 172 }}
{{Optimal ET sequence|legend=0| 49, 123ce, 172 }}


Badness: 0.162592
Badness (Smith): 0.162592


==== 13-limit ====
==== 13-limit ====
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Mapping: {{mapping| 1 0 0 0 0 0 | 0 39 57 69 85 91 }}
Mapping: {{mapping| 1 0 0 0 0 0 | 0 39 57 69 85 91 }}


Optimal tuning (POTE): ~2 = 1200.000, ~77/75 = 48.822
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~77/75 = 48.822{{c}}


{{Optimal ET sequence|legend=0| 49f, 123ce, 172f, 295ce, 467bccef }}
{{Optimal ET sequence|legend=0| 49f, 123ce, 172f, 295ce, 467bccef }}


Badness: 0.082158
Badness (Smith): 0.082158


== Salsa ==
== Salsa ==
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{{Mapping|legend=1| 1 1 7 -1 | 0 2 -16 13 }}
{{Mapping|legend=1| 1 1 7 -1 | 0 2 -16 13 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~128/105 = 351.049
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~128/105 = 351.049{{c}}


{{Optimal ET sequence|legend=1| 17, 24, 41, 106d, 147d, 188cd, 335cd }}
{{Optimal ET sequence|legend=1| 17, 24, 41, 106d, 147d, 188cd, 335cd }}


[[Badness]]: 0.080152
[[Badness]] (Smith): 0.080152


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 1 7 -1 2 | 0 2 -16 13 5 }}
Mapping: {{mapping| 1 1 7 -1 2 | 0 2 -16 13 5 }}


Optimal tuning (POTE): ~2 = 1200.000, ~11/9 = 351.014
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/9 = 351.014{{c}}


{{Optimal ET sequence|legend=0| 17, 24, 41, 106d, 147d }}
{{Optimal ET sequence|legend=0| 17, 24, 41, 106d, 147d }}


Badness: 0.039444
Badness (Smith): 0.039444


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 1 7 -1 2 4 | 0 2 -16 13 5 -1 }}
Mapping: {{mapping| 1 1 7 -1 2 4 | 0 2 -16 13 5 -1 }}


Optimal tuning (POTE): ~2 = 1200.000, ~11/9 = 351.025
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/9 = 351.025{{c}}


{{Optimal ET sequence|legend=0| 17, 24, 41, 106df, 147df }}
{{Optimal ET sequence|legend=0| 17, 24, 41, 106df, 147df }}


Badness: 0.030793
Badness (Smith): 0.030793


== Pycnic ==
== Pycnic ==
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{{Mapping|legend=1| 1 3 -1 8 | 0 -3 7 -11 }}
{{Mapping|legend=1| 1 3 -1 8 | 0 -3 7 -11 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~45/32 = 567.720
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~45/32 = 567.720{{c}}


{{Optimal ET sequence|legend=1| 17, 19, 55c, 74cd, 93cdd }}
{{Optimal ET sequence|legend=1| 17, 19, 55c, 74cd, 93cdd }}


[[Badness]]: 0.073735
[[Badness]] (Smith): 0.073735


== Superthird ==
== Superthird ==
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{{Mapping|legend=1| 1 -5 -5 -10 | 0 18 20 35 }}
{{Mapping|legend=1| 1 -5 -5 -10 | 0 18 20 35 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~9/7 = 439.076
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~9/7 = 439.076{{c}}


{{Optimal ET sequence|legend=1| 11cd, 30d, 41, 317bcc, 358bcc, 399bcc }}
{{Optimal ET sequence|legend=1| 11cd, 30d, 41, 317bcc, 358bcc, 399bcc }}


[[Badness]]: 0.139379
[[Badness]] (Smith): 0.139379


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 -5 -5 -10 2 | 0 18 20 35 4 }}
Mapping: {{mapping| 1 -5 -5 -10 2 | 0 18 20 35 4 }}


Optimal tuning (POTE): ~2 = 1200.000, ~9/7 = 439.152
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~9/7 = 439.152{{c}}


{{Optimal ET sequence|legend=0| 11cd, 30d, 41, 153be, 194be, 235bcee }}
{{Optimal ET sequence|legend=0| 11cd, 30d, 41, 153be, 194be, 235bcee }}


Badness: 0.070917
Badness (Smith): 0.070917


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 -5 -5 -10 2 -8 | 0 18 20 35 4 32 }}
Mapping: {{mapping| 1 -5 -5 -10 2 -8 | 0 18 20 35 4 32 }}


Optimal tuning (POTE): ~2 = 1200.000, ~9/7 = 439.119
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~9/7 = 439.119{{c}}


{{Optimal ET sequence|legend=0| 11cdf, 30df, 41 }}
{{Optimal ET sequence|legend=0| 11cdf, 30df, 41 }}


Badness: 0.052835
Badness (Smith): 0.052835


== Superenneadecal ==
== Superenneadecal ==
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{{Mapping|legend=1| 19 0 14 -7 | 0 1 1 2 }}
{{Mapping|legend=1| 19 0 14 -7 | 0 1 1 2 }}


[[Optimal tuning]] ([[POTE]]): ~392/375 = 63.158, ~3/2 = 704.166
[[Optimal tuning]] ([[POTE]]): ~392/375 = 63.158{{c}}, ~3/2 = 704.166{{c}}


{{Optimal ET sequence|legend=1| 19, 76bcd, 95, 114, 133, 247b, 380bcd }}
{{Optimal ET sequence|legend=1| 19, 76bcd, 95, 114, 133, 247b, 380bcd }}


[[Badness]]: 0.132311
[[Badness]] (Smith): 0.132311


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 19 0 14 -7 96 | 0 1 1 2 -1 }}
Mapping: {{mapping| 19 0 14 -7 96 | 0 1 1 2 -1 }}


Optimal tuning (POTE): ~33/32 = 63.158, ~3/2 = 705.667
Optimal tuning (POTE): ~33/32 = 63.158{{c}}, ~3/2 = 705.667{{c}}


{{Optimal ET sequence|legend=0| 19, 76bcd, 95, 114e }}
{{Optimal ET sequence|legend=0| 19, 76bcd, 95, 114e }}


Badness: 0.101496
Badness (Smith): 0.101496


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 19 0 14 -7 96 10 | 0 1 1 2 -1 2 }}
Mapping: {{mapping| 19 0 14 -7 96 10 | 0 1 1 2 -1 2 }}


Optimal tuning (POTE): ~33/32 = 63.158, ~3/2 = 705.801
Optimal tuning (POTE): ~33/32 = 63.158{{c}}, ~3/2 = 705.801{{c}}


{{Optimal ET sequence|legend=0| 19, 76bcdf, 95, 114e }}
{{Optimal ET sequence|legend=0| 19, 76bcdf, 95, 114e }}


Badness: 0.053197
Badness (Smith): 0.053197


== Magus ==
== Magus ==
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{{Mapping|legend=1| 1 -2 2 -6 | 0 11 1 27 }}
{{Mapping|legend=1| 1 -2 2 -6 | 0 11 1 27 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~5/4 = 391.465
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~5/4 = 391.465{{c}}


{{Optimal ET sequence|legend=1| 46, 95, 141bc, 187bc, 328bbcc }}
{{Optimal ET sequence|legend=1| 46, 95, 141bc, 187bc, 328bbcc }}


[[Badness]]: 0.108417
[[Badness]] (Smith): 0.108417


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 -2 2 -6 -6 | 0 11 1 27 29 }}
Mapping: {{mapping| 1 -2 2 -6 -6 | 0 11 1 27 29 }}


Optimal tuning (POTE): ~2 = 1200.000, ~5/4 = 391.503
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~5/4 = 391.503{{c}}


{{Optimal ET sequence|legend=0| 46, 95, 141bc }}
{{Optimal ET sequence|legend=0| 46, 95, 141bc }}


Badness: 0.045108
Badness (Smith): 0.045108


=== 13-limit ===
=== 13-limit ===
Line 314: Line 315:
Mapping: {{mapping| 1 -2 2 -6 -6 5 | 0 11 1 27 29 -4 }}
Mapping: {{mapping| 1 -2 2 -6 -6 5 | 0 11 1 27 29 -4 }}


Optimal tuning (POTE): ~2 = 1200.000, ~5/4 = 391.366
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~5/4 = 391.366{{c}}


{{Optimal ET sequence|legend=0| 46, 233bcff, 279bccff }}
{{Optimal ET sequence|legend=0| 46, 233bcff, 279bccff }}


Badness: 0.043024
Badness (Smith): 0.043024


== Leapweek ==
== Leapweek ==
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{{Mapping|legend=1| 1 0 42 -21 | 0 1 -25 15 }}
{{Mapping|legend=1| 1 0 42 -21 | 0 1 -25 15 }}
: mapping generators: ~2, ~3
: mapping generators: ~2, ~3


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~3/2 = 704.536
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 704.536{{c}}


{{Optimal ET sequence|legend=1| 17, 29c, 46, 109, 155, 264b, 419b }}
{{Optimal ET sequence|legend=1| 17, 29c, 46, 109, 155, 264b, 419b }}


[[Badness]]: 0.140577
[[Badness]] (Smith): 0.140577


=== 11-limit ===
=== 11-limit ===
Line 344: Line 344:
Mapping: {{mapping| 1 0 42 -21 -14 | 0 1 -25 15 11 }}
Mapping: {{mapping| 1 0 42 -21 -14 | 0 1 -25 15 11 }}


Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 704.554
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 704.554{{c}}


{{Optimal ET sequence|legend=0| 17, 29c, 46, 109, 264b, 373b, 637bbe }}
{{Optimal ET sequence|legend=0| 17, 29c, 46, 109, 264b, 373b, 637bbe }}


Badness: 0.050679
Badness (Smith): 0.050679


=== 13-limit ===
=== 13-limit ===
Line 357: Line 357:
Mapping: {{mapping| 1 0 42 -21 -14 -9 | 0 1 -25 15 11 8 }}
Mapping: {{mapping| 1 0 42 -21 -14 -9 | 0 1 -25 15 11 8 }}


Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 704.571
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 704.571{{c}}


{{Optimal ET sequence|legend=0| 17, 29c, 46, 63, 109 }}
{{Optimal ET sequence|legend=0| 17, 29c, 46, 63, 109 }}


Badness: 0.032727
Badness (Smith): 0.032727


==== 17-limit ====
==== 17-limit ====
Line 370: Line 370:
Mapping: {{mapping| 1 0 42 -21 -14 -9 -34 | 0 1 -25 15 11 8 24 }}
Mapping: {{mapping| 1 0 42 -21 -14 -9 -34 | 0 1 -25 15 11 8 24 }}


Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 704.540
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 704.540{{c}}


{{Optimal ET sequence|legend=0| 17g, 29cg, 46, 109, 155f, 264bfg }}
{{Optimal ET sequence|legend=0| 17g, 29cg, 46, 109, 155f, 264bfg }}


Badness: 0.026243
Badness (Smith): 0.026243


==== Leapweeker ====
==== Leapweeker ====
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Mapping: {{mapping| 1 0 42 -21 -14 -9 39 | 0 1 -25 15 11 8 -22 }}
Mapping: {{mapping| 1 0 42 -21 -14 -9 39 | 0 1 -25 15 11 8 -22 }}


Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 704.537
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 704.537{{c}}


{{Optimal ET sequence|legend=0| 17, 29c, 46, 109g, 155fg, 264bfgg }}
{{Optimal ET sequence|legend=0| 17, 29c, 46, 109g, 155fg, 264bfgg }}


Badness: 0.026774
Badness (Smith): 0.026774


[[Category:Temperament clans]]
[[Category:Temperament clans]]
Retrieved from "https://en.xen.wiki/w/Sensamagic_clan"