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{{see also| Sensamagic clan #Sensi }}
{{see also| Sensamagic clan #Sensi }}


Sensi tempers out [[686/675]], [[245/243]] and [[4375/4374]] in addition to [[126/125]], and can be described as the 19&27 temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 2.3.5.7.13 sensi (sensation) tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo|46EDO]] is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available. The name "sensi" is a play on the words "semi-" and "sixth."
Sensi tempers out [[686/675]], [[245/243]] and [[4375/4374]] in addition to [[126/125]], and can be described as the 19&27 temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 2.3.5.7.13 sensi (sensation) tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available. The name "sensi" is a play on the words "semi-" and "sixth."


=== Septimal sensi ===
=== Septimal sensi ===
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[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit]]
* [[7-odd-limit]]: ~9/7 = {{monzo| 2/13 0 0 1/13 }}  
: [{{monzo| 1 0 0 0 }}, {{monzo| 1/13 0 0 7/13 }}, {{monzo| 5/13 0 0 9/13 }}, {{monzo| 0 0 0 1 }}]
: [[Eigenmonzo]]s (unchanged intervals): 2, 7
: [[Eigenmonzo]]s (unchanged intervals): 2, 7
* [[9-odd-limit]]
* [[9-odd-limit]]: ~9/7 = {{monzo| 1/5 2/5 -1/5 0 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 2/5 14/5 -7/5 0 }}, {{monzo| 4/5 18/5 -9/5 0 }}, {{monzo| 3/5 26/5 -13/5 0 }}]
: [[Eigenmonzo]]s (unchanged intervals): 2, 9/5
: [[Eigenmonzo]]s (unchanged intervals): 2, 9/5
[[Tuning ranges of regular temperaments|Tuning ranges]]:
* 7-odd-limit [[diamond monotone]]: ~9/7 = [442.105, 450.000] (7\19 to 3\8)
* 9-odd-limit diamond monotone: ~9/7 = [442.105, 444.444] (7\19 to 10\27)
* 7-odd-limit [[diamond tradeoff]]: ~9/7 = [442.179, 445.628]
* 9-odd-limit diamond tradeoff: ~9/7 = [435.084, 445.628]
* 7-odd-limit diamond monotone and tradeoff: ~9/7 = [442.179, 445.628]
* 9-odd-limit diamond monotone and tradeoff: ~9/7 = [442.105, 444.444]


[[Algebraic generator]]: The real root of ''x''<sup>5</sup> + ''x''<sup>4</sup> - 4''x''<sup>2</sup> + ''x'' - 1, at 443.3783 cents.
[[Algebraic generator]]: The real root of ''x''<sup>5</sup> + ''x''<sup>4</sup> - 4''x''<sup>2</sup> + ''x'' - 1, at 443.3783 cents.
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POTE generator: ~9/7 = 443.322
POTE generator: ~9/7 = 443.322


Vals: {{Val list| 19, 27, 46, 111de, 157de }}
Optimal GPV sequence: {{Val list| 19, 27, 46, 111de, 157de }}


=== Sensor ===
=== Sensor ===
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POTE generator: ~9/7 = 443.294
POTE generator: ~9/7 = 443.294


Vals: {{Val list| 19, 27, 46, 111d, 157d, 268cdd }}
Optimal GPV sequence: {{Val list| 19, 27, 46, 111d, 157d, 268cdd }}


Badness: 0.037942
Badness: 0.037942
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POTE generator: ~9/7 = 443.321
POTE generator: ~9/7 = 443.321


Vals: {{Val list| 19, 27, 46, 111df, 157df }}
Optimal GPV sequence: {{Val list| 19, 27, 46, 111df, 157df }}


Badness: 0.025575
Badness: 0.025575
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Comma list: 91/90, 126/125, 154/153, 169/168, 256/255
Mapping: [{{val| 1 -1 -1 -2 9 0 10 }}, {{val| 0 7 9 13 -15 10 -16 }}]
POTE generator: ~9/7 = 443.365
Optimal GPV sequence: {{Val list| 19, 27, 46, 157df, 203cdff, 249cddff }}
Badness: 0.022908


=== Sensis ===
=== Sensis ===
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POTE generator: ~9/7 = 443.962
POTE generator: ~9/7 = 443.962


Vals: {{Val list| 8d, 19, 27e, 73ee }}
Optimal GPV sequence: {{Val list| 8d, 19, 27e, 73ee }}


Badness: 0.028680
Badness: 0.028680
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POTE generator: ~9/7 = 443.945
POTE generator: ~9/7 = 443.945


Vals: {{Val list| 19, 27e, 46e, 73ee }}
Optimal GPV sequence: {{Val list| 19, 27e, 46e, 73ee }}


Badness: 0.020017
Badness: 0.020017
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POTE generator: ~9/7 = 443.626
POTE generator: ~9/7 = 443.626


Vals: {{Val list| 19e, 27e, 46, 119c, 165c }}
Optimal GPV sequence: {{Val list| 19e, 27e, 46, 119c, 165c }}


Badness: 0.029486
Badness: 0.029486
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POTE generator: ~9/7 = 443.559
POTE generator: ~9/7 = 443.559


Vals: {{Val list| 19e, 27e, 46, 165cf, 211bccf, 257bccff, 303bccdff }}
Optimal GPV sequence: {{Val list| 19e, 27e, 46, 165cf, 211bccf, 257bccff, 303bccdff }}


Badness: 0.020789
Badness: 0.020789
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POTE generator: ~9/7 = 443.518
POTE generator: ~9/7 = 443.518


Vals: {{Val list| 19e, 27, 46ee }}
Optimal GPV sequence: {{Val list| 19e, 27, 46ee }}


Badness: 0.036835
Badness: 0.036835
Line 173: Line 192:
POTE generator: ~9/7 = 443.506
POTE generator: ~9/7 = 443.506


Vals: {{Val list| 19e, 27, 46ee }}
Optimal GPV sequence: {{Val list| 19e, 27, 46ee }}


Badness: 0.023258
Badness: 0.023258
Line 186: Line 205:
POTE generator: ~25/22 = 221.605
POTE generator: ~25/22 = 221.605


Vals: {{Val list| 27e, 65, 157de, 222cde }}
Optimal GPV sequence: {{Val list| 27e, 65, 157de, 222cde }}


Badness: 0.048714
Badness: 0.048714
Line 229: Line 248:
POTE generator: ~35/32 = 156.883
POTE generator: ~35/32 = 156.883


Vals: {{Val list| 46, 84, 130, 306, 436ce }}
Optimal GPV sequence: {{Val list| 46, 84, 130, 306, 436ce }}


Badness: 0.037132
Badness: 0.037132
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POTE generator: ~35/32 = 156.904
POTE generator: ~35/32 = 156.904


Vals: {{Val list| 46, 84, 130, 566ce, 596cef }}
Optimal GPV sequence: {{Val list| 46, 84, 130, 566ce, 596cef }}


Badness: 0.023504
Badness: 0.023504
Line 268: Line 287:
POTE generator: ~11/8 = 547.631
POTE generator: ~11/8 = 547.631


Vals: {{Val list| 46, 103, 149, 252e, 401bdee }}
Optimal GPV sequence: {{Val list| 46, 103, 149, 252e, 401bdee }}


Badness: 0.042412
Badness: 0.042412
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POTE generator: ~11/8 = 547.629
POTE generator: ~11/8 = 547.629


Vals: {{Val list| 46, 103, 149, 252ef, 401bdeef }}
Optimal GPV sequence: {{Val list| 46, 103, 149, 252ef, 401bdeef }}


Badness: 0.025779
Badness: 0.025779
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POTE generator: ~11/8 = 547.635
POTE generator: ~11/8 = 547.635


Vals: {{Val list| 46, 103, 149, 252ef, 401bdeef }}
Optimal GPV sequence: {{Val list| 46, 103, 149, 252ef, 401bdeef }}


Badness: 0.018479
Badness: 0.018479
Line 307: Line 326:
POTE generator: ~11/8 = 547.614
POTE generator: ~11/8 = 547.614


Vals: {{Val list| 46, 103h, 149h, 252efhh }}
Optimal GPV sequence: {{Val list| 46, 103h, 149h, 252efhh }}


Badness: 0.019005
Badness: 0.019005
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