Insatinismic: Difference between revisions

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Insatinismic is a [[rank-5 temperament]] for the ~~add~~-29-19-limit that is a [[weak extension]] of [[5767168/5767125#Insanismic|insanismic]] and a detemperament of [[~~cassaschismic~~]]. It is not a member of any known temperament family or clan.

Insatinismic is a [[Catalog of rank-5 temperaments|rank-5 temperament]] for the [[19-limit]] and no-23 [[31-limit]] that is a [[weak extension]] of [[5767168/5767125#Insanismic|insanismic]] and a detemperament of [[septischismic]]. It is not a member of any known temperament family or clan.

Data below is given because infobox regtemp doesn't work with rank-5 temperaments:{{Databox|Temperament data|2=[[Subgroup]]: 2.3.5.7.11.13.17.19

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As a weak extension of insanismic, it does the following:

* The fifth generator is trisected for primes 11, 13 and 29, and can be instead taken to be ~1540/1539, or a redundant pair of 4096/4095~4225/4224 and 10241/10240. 10241/10240 is used to reached 17/16 and 19/16.

* The fifth generator is trisected for primes 11, 13 and 29, and can be instead taken to be ~1540/1539, or a redundant pair of 4096/4095~4225/4224 and 10241/10240. 10241/10240 is used to reached 17/16, 19/16 and 31/16.

=== Add-29,31 extension ===

Insatinismic is worse at extending to the no-23 31-limit, since it requires detempering from the suboptimal septischismic add-29,31 basis 53k & 217k & 311k, instead of 217 & 270 & 311. This adds the commas 176176/176175 and 178126/178125 into the list, where prime 29 has the most error out of all, around ~3x as much - still, just 0.003 cents. Prime 31 fits much better into the temperament.

== Notation ==

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-Insatinismic is a [[rank-5 temperament]] for the add-29-19-limit that is a [[weak extension]] of [[5767168/5767125#Insanismic|insanismic]] and a detemperament of [[cassaschismic]]. It is not a member of any known temperament family or clan.
+Insatinismic is a [[Catalog of rank-5 temperaments|rank-5 temperament]] for the [[19-limit]] and no-23 [[31-limit]] that is a [[weak extension]] of [[5767168/5767125#Insanismic|insanismic]] and a detemperament of [[septischismic]]. It is not a member of any known temperament family or clan.
 Data below is given because infobox regtemp doesn't work with rank-5 temperaments:{{Databox|Temperament data|2=[[Subgroup]]: 2.3.5.7.11.13.17.19
@@ Line 48: / Line 48: @@
 As a weak extension of insanismic, it does the following:
-* The fifth generator is trisected for primes 11, 13 and 29, and can be instead taken to be ~1540/1539, or a redundant pair of 4096/4095~4225/4224 and 10241/10240. 10241/10240 is used to reached 17/16 and 19/16.
+* The fifth generator is trisected for primes 11, 13 and 29, and can be instead taken to be ~1540/1539, or a redundant pair of 4096/4095~4225/4224 and 10241/10240. 10241/10240 is used to reached 17/16, 19/16 and 31/16.
+=== Add-29,31 extension ===
+Insatinismic is worse at extending to the no-23 31-limit, since it requires detempering from the suboptimal septischismic add-29,31 basis 53k & 217k & 311k, instead of 217 & 270 & 311. This adds the commas 176176/176175 and 178126/178125 into the list, where prime 29 has the most error out of all, around ~3x as much - still, just 0.003 cents. Prime 31 fits much better into the temperament.
 == Notation ==