Sensipent family: Difference between revisions
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Temperaments discussed elsewhere include: | Temperaments discussed elsewhere include: | ||
* ''[[Catafourth]]'' → [[Breedsmic temperaments #Catafourth|Breedsmic temperaments]] (+2401/2400) | * ''[[Catafourth]]'' → [[Breedsmic temperaments #Catafourth|Breedsmic temperaments]] (+2401/2400) | ||
* ''[[Browser]]'' → [[Mirkwai clan #Browser|Mirkwai clan]] (+16875/16807) | * ''[[Browser]]'' → [[Mirkwai clan #Browser|Mirkwai clan]] (+16875/16807) | ||
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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 | 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. | ||
=== Septimal sensi === | === Septimal sensi === | ||
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Badness: 0.023504 | Badness: 0.023504 | ||
== Subpental == | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 3136/3125, 19683/19600 | |||
{{Mapping|legend=1| 1 6 8 17 | 0 -14 -18 -45 }} | |||
{{Multival|legend=1| 14 18 45 -4 32 54 }} | |||
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~56/45 = 378.467 | |||
{{Optimal ET sequence|legend=1| 19, 111, 130, 929c, 1059c, 1189bc, 1319bc }} | |||
[[Badness]]: 0.054303 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 540/539, 3136/3125, 8019/8000 | |||
Mapping: {{mapping| 1 6 8 17 -6 | 0 -14 -18 -45 30 }} | |||
Optimal tuning (POTE): ~2 = 1\1, ~56/45 = 378.440 | |||
{{Optimal ET sequence|legend=1| 19, 111, 130, 241, 371ce, 501cde, 872cde }} | |||
Badness: 0.045352 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 351/350, 540/539, 676/675, 3136/3125 | |||
Mapping: {{mapping| 1 6 8 17 -6 16 | 0 -14 -18 -45 30 -39 }} | |||
Optimal tuning (POTE): ~2 = 1\1, ~56/45 = 378.437 | |||
{{Optimal ET sequence|legend=1| 19, 111, 130, 241, 371ce }} | |||
Badness: 0.023940 | |||
== Heinz == | == Heinz == | ||