Sensamagic clan: Difference between revisions

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 == Extensions ==
-For full 7-limit extensions, we have bohpier, sensa/escaped, salsa, pycnic, cohemiripple, superthird, magus and leapweek discussed below, as well as [[Father family #Father|father]], [[Dicot family #Sidi|sidi]], [[Meantone family #Godzilla|godzilla]], [[Porcupine family #Hedgehog|hedgehog]], [[Archytas clan #Superpyth|superpyth]], [[Sensipent family #Sensi|sensi]], [[Augmented family #Hemiaug|hemiaug]], [[Magic family #magic|magic]], [[Gamelismic clan#Rodan|rodan]], [[Tetracot family #Octacot|octacot]], [[Diaschismic family #Shrutar|shrutar]], and [[Kleismic family #Clyde|clyde]] discussed elsewhere.
+For full 7-limit extensions, we have sensi, bohpier, sensa/escaped, salsa, pycnic, cohemiripple, superthird, magus and leapweek discussed below, as well as [[Father family #Father|father]], [[Dicot family #Sidi|sidi]], [[Meantone family #Godzilla|godzilla]], [[Porcupine family #Hedgehog|hedgehog]], [[Archytas clan #Superpyth|superpyth]], [[Augmented family #Hemiaug|hemiaug]], [[Magic family #magic|magic]], [[Gamelismic clan#Rodan|rodan]], [[Tetracot family #Octacot|octacot]], [[Diaschismic family #Shrutar|shrutar]], and [[Kleismic family #Clyde|clyde]] discussed elsewhere.
 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]].
+= Sensi =
+{{main| Sensi }}
+{{see also| Sensipent family #Sensi }}
+Sensi tempers out [[126/125]], [[686/675]] and [[4375/4374]] in addition to [[245/243]], and can be described as the 19&amp;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."
+== 7-limit ==
+Subgroup: 2.3.5.7
+[[Comma list]]: 126/125, 245/243
+[[Mapping]]: [{{val| 1 6 8 11 }}, {{val| 0 -7 -9 -13 }}]
+Mapping generators: ~2, ~14/9
+{{Multival|legend=1| 7 9 13 -2 1 5 }}
+[[POTE generator]]: ~9/7 = 443.383
+[[Minimax tuning]]:
+* [[7-odd-limit]]
+: [{{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: 2, 7
+* [[9-odd-limit]]
+: [{{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: 2, 9/5
+[[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.
+{{Val list|legend=1| 19, 27, 46, 157d, 203cd, 249cdd, 295ccdd }}
+[[Badness]]: 0.0256
+=== Sensation ===
+Subgroup: 2.3.5.7.13
+Comma list: 91/90, 126/125, 169/168
+Sval mapping: [{{val| 1 6 8 11 10 }}, {{val| 0 -7 -9 -13 -10 }}]
+Gencom mapping: [{{val| 1 6 8 11 0 10 }}, {{val| 0 -7 -9 -13 0 -10 }}]
+Gencom: [2 9/7; 91/90 126/125 169/168]
+POTE generator: ~9/7 = 443.322
+{{Val list|legend=1| 19, 27, 46, 111de, 157de }}
+== Sensor ==
+Subgroup: 2.3.5.7.11
+Comma list: 126/125, 245/243, 385/384
+Mapping: [{{val| 1 6 8 11 -6 }}, {{val| 0 -7 -9 -13 15 }}]
+POTE generator: ~9/7 = 443.294
+{{Val list|legend=1| 19, 27, 46, 111d, 157d, 268cdd }}
+Badness: 0.0379
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 91/90, 126/125, 169/168, 385/384
+Mapping: [{{val| 1 6 8 11 -6 10 }}, {{val| 0 -7 -9 -13 15 -10 }}]
+POTE generator: ~9/7 = 443.321
+{{Val list|legend=1| 19, 27, 46, 111df, 157df }}
+Badness: 0.0256
+== Sensis ==
+Subgroup: 2.3.5.7.11
+Comma list: 56/55, 100/99, 245/243
+Mapping: [{{val| 1 6 8 11 6 }}, {{val| 0 -7 -9 -13 -4 }}]
+POTE generator: ~9/7 = 443.962
+{{Val list|legend=1| 19, 27e, 73ee }}
+Badness: 0.0287
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 56/55, 78/77, 91/90, 100/99
+Mapping: [{{val| 1 6 8 11 6 10 }}, {{val| 0 -7 -9 -13 -4 -10 }}]
+POTE generator: ~9/7 = 443.945
+{{Val list|legend=1| 19, 27e, 46e, 73ee }}
+Badness: 0.0200
+== Sensus ==
+Subgroup: 2.3.5.7.11
+Comma list: 126/125, 176/175, 245/243
+Mapping: [{{val| 1 6 8 11 23 }}, {{val| 0 -7 -9 -13 -31 }}]
+POTE generator: ~9/7 = 443.626
+{{Val list|legend=1| 19e, 27e, 46, 119c, 165c }}
+Badness: 0.0295
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 91/90, 126/125, 169/168, 352/351
+Mapping: [{{val| 1 6 8 11 23 10 }}, {{val| 0 -7 -9 -13 -31 -10 }}]
+POTE generator: ~9/7 = 443.559
+{{Val list|legend=1| 19e, 27e, 46, 165cf, 211bccf, 257bccff, 303bccdff }}
+Badness: 0.0208
+== Sensa ==
+Subgroup: 2.3.5.7.11
+Comma list: 55/54, 77/75, 99/98
+Mapping: [{{val| 1 6 8 11 11 }}, {{val| 0 -7 -9 -13 -12 }}]
+POTE generator: ~9/7 = 443.518
+{{Val list|legend=1| 19e, 27, 46ee }}
+Badness: 0.0368
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 55/54, 66/65, 77/75, 143/140
+Mapping: [{{val| 1 6 8 11 11 10 }}, {{val| 0 -7 -9 -13 -12 -11 }}]
+POTE generator: ~9/7 = 443.506
+{{Val list|legend=1| 19e, 27, 46ee }}
+Badness: 0.0233
+== Hemisensi ==
+Subgroup: 2.3.5.7.11
+Comma list: 126/125, 243/242, 245/242
+Mapping: [{{val| 1 13 17 24 32 }}, {{val| 0 -14 -18 -26 -35 }}]
+POTE generator: ~25/22 = 221.605
+{{Val list|legend=1| 27e, 65, 157de, 222cde }}
+Badness: 0.0487
 = Bohpier =