Sensipent family: Difference between revisions

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=== Sensible ===

An extension of sensipent to prime 11 of dubious canonicity (but significantly higher accuracy than [[sensi]]) interprets the generator as [[165/128]]~[[128/99]] by tempering [[8019/8000|S9/S10]] so that [[11/8]] is reached as ([[10/9]])3. This extension is very strong as supported by the [[optimal ET sequence]] going very far and as supported by another observation: that it is equivalent to tempering the [[semiporwellisma]] which ~~as it~~ is equal to [[961/960|S31]] * [[1024/1023|S32]]2 (thus forming the S-expression-based comma list)~~, which by the~~ equivalence of the aforementioned [[lopsided comma]] also implies that this temperament equates ([[33/32]])2 with [[16/15]] as well as that a natural extension to prime 31 exists through {S31, S32}, which we will see is very accurate, but this itself suggests that an extension to prime 17 is reasonably accurate through tempering [[1089/1088|S33]] so that a slightly sharp ~[[22/17]] is equated with the generator.

An extension of sensipent to prime 11 of dubious canonicity (but significantly higher accuracy than [[sensi]]) interprets the generator as [[165/128]]~[[128/99]] by tempering [[8019/8000|S9/S10]] so that [[11/8]] is reached as ([[10/9]])3. This extension is very strong as supported by the [[optimal ET sequence]] going very far and as supported by another observation: that it is equivalent to tempering the [[semiporwellisma]] which is equal to [[961/960|S31]] * [[1024/1023|S32]]2 (thus forming the S-expression-based comma list). The equivalence of the aforementioned [[lopsided comma]] also implies that this temperament equates ([[33/32]])2 with [[16/15]] as well as that a natural extension to prime 31 exists through {S31, S32}, which we will see is very accurate, but this itself suggests that an extension to prime 17 is reasonably accurate through tempering [[1089/1088|S33]] so that a slightly sharp ~[[22/17]] is equated with the generator.

[[Subgroup]]: 2.3.5.11

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 === Sensible ===
-An extension of sensipent  to prime 11 of dubious canonicity (but significantly higher accuracy than [[sensi]]) interprets the generator as [[165/128]]~[[128/99]] by tempering [[8019/8000|S9/S10]] so that [[11/8]] is reached as ([[10/9]])<sup>3</sup>. This extension is very strong as supported by the [[optimal ET sequence]] going very far and as supported by another observation: that it is equivalent to tempering the [[semiporwellisma]] which as it is equal to [[961/960|S31]] * [[1024/1023|S32]]<sup>2</sup> (thus forming the S-expression-based comma list), which by the equivalence of the aforementioned [[lopsided comma]] also implies that this temperament equates ([[33/32]])<sup>2</sup> with [[16/15]] as well as that a natural extension to prime 31 exists through {S31, S32}, which we will see is very accurate, but this itself suggests that an extension to prime 17 is reasonably accurate through tempering [[1089/1088|S33]] so that a slightly sharp ~[[22/17]] is equated with the generator.
+An extension of sensipent  to prime 11 of dubious canonicity (but significantly higher accuracy than [[sensi]]) interprets the generator as [[165/128]]~[[128/99]] by tempering [[8019/8000|S9/S10]] so that [[11/8]] is reached as ([[10/9]])<sup>3</sup>. This extension is very strong as supported by the [[optimal ET sequence]] going very far and as supported by another observation: that it is equivalent to tempering the [[semiporwellisma]] which is equal to [[961/960|S31]] * [[1024/1023|S32]]<sup>2</sup> (thus forming the S-expression-based comma list). The equivalence of the aforementioned [[lopsided comma]] also implies that this temperament equates ([[33/32]])<sup>2</sup> with [[16/15]] as well as that a natural extension to prime 31 exists through {S31, S32}, which we will see is very accurate, but this itself suggests that an extension to prime 17 is reasonably accurate through tempering [[1089/1088|S33]] so that a slightly sharp ~[[22/17]] is equated with the generator.
 [[Subgroup]]: 2.3.5.11