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__FORCETOC__
{{interwiki
| de = Sensi
| en = Sensipent family
| es =
| ja =
}}


<span style="display: block; text-align: right;">[[de:Sensi]]</span>
= Sensipent =
[[Comma list]]: 78732/78125


=Sensipent=
[[Mapping]]: [{{val| 1 6 8 }}, {{val| 0 -7 -9 }}]
[[Comma|Comma]]: 78732/78125 = |2 9 -7&gt;


[[POTE_tuning|POTE generator]]: 162/125 = 443.058 cents
[[POTE generator]]: 162/125 = 443.058


[[Map|Map]]: [&lt;1 6 8|, &lt;0 -7 -9|]
{{Val list|legend=1| 8, 19, 46, 65, 539, 604c, 669c, 734c, 799c, 864c, 929c }}


[[EDO|EDO]]s: [[8edo|8]], [[19edo|19]], [[46edo|46]], [[65edo|65]], [[539edo|539]], [[604edo|604c]], [[669edo|669c]], [[734edo|734c]], [[799edo|799c]], [[864edo|864c]], [[929edo|929c]]
= Sensi =


=Sensi=
{{main| Sensi }}
{{main|Sensi}}
Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, 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 [[13-limit|13-limit]] sensi 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."


[[Comma|Commas]]: 126/125, 245/243
Sensi tempers out [[686/675]], [[245/243]] and [[4375/4374]] in addition to [[126/125]], 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 [[13-limit]] sensi 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 minimax
[[Comma list]]: 126/125, 245/243


[|1 0 0 0&gt;, |1/13 0 0 7/13&gt;, |5/13 0 0 9/13&gt;, |0 0 0 1&gt;]
[[Mapping]]: [{{val| 1 6 8 11 }}, {{val| 0 -7 -9 -13 }}]


[[Eigenmonzo|Eigenmonzos]]: 2, 7
Mapping generators: ~2, ~14/9


9-limit minimax
{{Multival|legend=1| 7 9 13 -2 1 5 }}


[|1 0 0 0&gt;, |2/5 14/5 -7/5 0&gt;,
[[POTE generator]]: ~9/7 = 443.383
|4/5 18/5 -9/5 0&gt;, |3/5 26/5 -13/5 0&gt;<nowiki>]</nowiki>


[[Eigenmonzo|Eigenmonzos]]: 2, 9/5
[[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


[[POTE_tuning|POTE generator]]: ~9/7 = 443.383
[[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 [[Algebraic_number|real root]] of x^5+x^4-4x^2+x-1, at 443.3783 cents.
{{Val list|legend=1| 19, 27, 46, 157d, 203cd, 249cdd, 295ccdd }}


[[Map|Map]]: [&lt;1 6 8 11|, &lt;0 -7 -9 -13|]
[[Badness]]: 0.0256
 
Wedgie: &lt;&lt;7 9 13 -2 1 5||
 
[[generator|Generators]]: 2, 14/9
 
[[EDO|EDO]]s: [[19edo|19]], [[27edo|27]], [[46edo|46]], [[157edo|157d]], [[203edo|203cd]], [[249edo|249cdd]], [[295edo|295ccdd]]
 
[[Badness|Badness]]: 0.0256


==Sensor==
==Sensor==
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[[Category:Theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Sensipent]]
[[Category:Sensipent]]
[[Category:Sensi]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Sensipent_family"