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


Sensi tempers out [[245/243]], [[686/675]] 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 cale]]s of size 11, 19 and 27 are available.  
Sensi tempers out [[245/243]], [[686/675]] 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 scale]]s of size 11, 19 and 27 are available.  


=== Septimal sensi ===
=== Septimal sensi ===
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[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit]]: ~9/7 = {{monzo| 2/13 0 0 1/13 }}  
* [[7-odd-limit]]: ~9/7 = {{monzo| 2/13 0 0 1/13 }}  
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.7
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7
* [[9-odd-limit]]: ~9/7 = {{monzo| 1/5 2/5 -1/5 0 }}
* [[9-odd-limit]]: ~9/7 = {{monzo| 1/5 2/5 -1/5 0 }}
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.9/5
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/5


[[Tuning ranges of regular temperaments|Tuning ranges]]:  
[[Tuning ranges of regular temperaments|Tuning ranges]]:  
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Badness: 0.022908
Badness: 0.022908
=== Sensis ===
Subgroup: 2.3.5.7.11
Comma list: 56/55, 100/99, 245/243
Mapping: {{mapping| 1 6 8 11 6 | 0 -7 -9 -13 -4 }}
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.962
{{Optimal ET sequence|legend=1| 8d, 19, 27e, 73ee }}
Badness: 0.028680
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 78/77, 91/90, 100/99
Mapping: {{mapping| 1 6 8 11 6 10 | 0 -7 -9 -13 -4 -10 }}
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.945
{{Optimal ET sequence|legend=1| 19, 27e, 46e, 73ee }}
Badness: 0.020017


=== Sensus ===
=== Sensus ===
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Badness: 0.016238
Badness: 0.016238
=== Sensis ===
Subgroup: 2.3.5.7.11
Comma list: 56/55, 100/99, 245/243
Mapping: {{mapping| 1 6 8 11 6 | 0 -7 -9 -13 -4 }}
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.962
{{Optimal ET sequence|legend=1| 8d, 19, 27e, 73ee }}
Badness: 0.028680
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 78/77, 91/90, 100/99
Mapping: {{mapping| 1 6 8 11 6 10 | 0 -7 -9 -13 -4 -10 }}
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 443.945
{{Optimal ET sequence|legend=1| 19, 27e, 46e, 73ee }}
Badness: 0.020017


=== Sensa ===
=== Sensa ===
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Badness: 0.023258
Badness: 0.023258


=== Hemisensi ===
=== Bisensi ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 126/125, 243/242, 245/242
Comma list: 121/120, 126/125, 245/243


Mapping: {{mapping| 1 13 17 24 32 | 0 -14 -18 -26 -35 }}
Mapping: {{mapping| 2 5 7 9 9 | 0 -7 -9 -13 -8 }}


: mapping generators: ~2, ~44/25
: mapping generators: ~99/70, ~11/10


Optimal tuning (POTE): ~2 = 1\1, ~25/22 = 221.605
Optimal tuning (POTE): ~99/70 = 1\2, ~11/10 = 156.692


{{Optimal ET sequence|legend=1| 27e, 38d, 65, 157de, 222cde }}
{{Optimal ET sequence|legend=1| 8d, …, 38d, 46, 176dde, 222cdde, 268cddee }}


Badness: 0.048714
Badness: 0.041723


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 91/90, 126/125, 169/168, 243/242
Comma list: 91/90, 121/120, 126/125, 169/168


Mapping: {{mapping| 1 13 17 24 32 30 | 0 -14 -18 -26 -35 -30 }}
Mapping: {{mapping| 2 5 7 9 9 10 | 0 -7 -9 -13 -8 -10 }}


Optimal tuning (POTE): ~2 = 1\1, ~25/22 = 221.556
Optimal tuning (POTE): ~55/39 = 1\2, ~11/10 = 156.725


{{Optimal ET sequence|legend=1| 27e, 38df, 65f }}
{{Optimal ET sequence|legend=1| 8d, …, 38df, 46 }}


Badness: 0.033016
Badness: 0.026339


=== Bisensi ===
=== Hemisensi ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 121/120, 126/125, 245/243
Comma list: 126/125, 243/242, 245/242


Mapping: {{mapping| 2 5 7 9 9 | 0 -7 -9 -13 -8 }}
Mapping: {{mapping| 1 13 17 24 32 | 0 -14 -18 -26 -35 }}


: mapping generators: ~99/70, ~11/10
: mapping generators: ~2, ~44/25


Optimal tuning (POTE): ~99/70 = 1\2, ~11/10 = 156.692
Optimal tuning (POTE): ~2 = 1\1, ~25/22 = 221.605


{{Optimal ET sequence|legend=1| 8d, …, 38d, 46, 176dde, 222cdde, 268cddee }}
{{Optimal ET sequence|legend=1| 27e, 38d, 65, 157de, 222cde }}


Badness: 0.041723
Badness: 0.048714


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 91/90, 121/120, 126/125, 169/168
Comma list: 91/90, 126/125, 169/168, 243/242


Mapping: {{mapping| 2 5 7 9 9 10 | 0 -7 -9 -13 -8 -10 }}
Mapping: {{mapping| 1 13 17 24 32 30 | 0 -14 -18 -26 -35 -30 }}


Optimal tuning (POTE): ~55/39 = 1\2, ~11/10 = 156.725
Optimal tuning (POTE): ~2 = 1\1, ~25/22 = 221.556


{{Optimal ET sequence|legend=1| 8d, …, 38df, 46 }}
{{Optimal ET sequence|legend=1| 27e, 38df, 65f }}


Badness: 0.026339
Badness: 0.033016


== Sensei ==
== Sensei ==
Retrieved from "https://en.xen.wiki/w/Sensipent_family"