Cassaschismic: Difference between revisions

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'''Cassaschismic''' is a [[rank-3 temperament|rank-3]] [[regular temperament|temperament]] that expands the [[chain of fifths]] of [[gary]] into the full [[11-limit]] by adding an independent [[generator]] for the [[5/1|5th]] [[harmonic]]. It is therefore a member of the [[garischismic family]] and [[olympic clan]].

By moving the generators around, the generator for 5 can be used for [[13/1|13]] and [[19/1|19]]. It can also be taken to be a generic ~~3~5c~~ aberschisma, which represents the [[schisma]], the [[aberschisma]], the [[undevicesimal schisma]], and many other important commas around that size. [[Tempering out]] this tiny interval results in [[cassandra]], so cassaschismic may be viewed as a rank-3 [[detemperament]] thereof, modifying its mapping by ±1 aberschisma step to reach the rest of primes.

By moving the generators around, the generator for 5 can be used for [[13/1|13]] and [[19/1|19]]. It can also be taken to be a 3–5{{c}} generic aberschisma, which represents the [[schisma]], the [[aberschisma]], the [[undevicesimal schisma]], and many other important commas around that size. [[Tempering out]] this tiny interval results in [[cassandra]], so cassaschismic may be viewed as a rank-3 [[detemperament]] thereof, modifying its mapping by ±1 aberschisma step to reach the rest of primes.

Other ~~subsets~~ include [[~~gariwizmic~~]], [[~~cotoneum~~]], [[newt~~]], [[vulture]], [[heptacot~~]], [[satin]], [[~~witcher~~]]; ~~which~~ instead of tempering out the aberschisma, find it deep in the generator chain.

Other rank-2 temperaments of cassaschismic include [[cotoneum]], [[gariwizmic]], [[newt]], [[satin]], and [[vulture]]; these temperaments, instead of tempering out the aberschisma, find it deep in the generator chain.

It is [[support]]ed by notable [[equal temperament]]s such as {{EDOs| 217, 270, 311, and 364 }}, where the aberschisma step is well represented by one edostep. It is also trivially supported by edos of cassandra, these being [[41edo|41]], [[53edo|53]], [[94edo|94]], and of course, [[12edo]] through the 12e [[val]], where both the comma step and the aberschisma step are tempered out, so it can be used in any of those forms as well.

Cassaschismic is [[support]]ed by notable [[equal temperament]]s such as {{EDOs| 217, 270, 311, and 364 }}, where the aberschisma step is well represented by one edostep. It is also trivially supported by edos of cassandra, these being [[41edo|41]], [[53edo|53]], [[94edo|94]], and of course, [[12edo]] through the 12e [[val]], where both the comma step and the aberschisma step are tempered out, so it can be used in any of those forms as well.

See [[Garischismic family #Cassaschismic]] for technical data.

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 '''Cassaschismic''' is a [[rank-3 temperament|rank-3]] [[regular temperament|temperament]] that expands the [[chain of fifths]] of [[gary]] into the full [[11-limit]] by adding an independent [[generator]] for the [[5/1|5th]] [[harmonic]]. It is therefore a member of the [[garischismic family]] and [[olympic clan]].
-By moving the generators around, the generator for 5 can be used for [[13/1|13]] and [[19/1|19]]. It can also be taken to be a generic 3~5c aberschisma, which represents the [[schisma]], the [[aberschisma]], the [[undevicesimal schisma]], and many other important commas around that size. [[Tempering out]] this tiny interval results in [[cassandra]], so cassaschismic may be viewed as a rank-3 [[detemperament]] thereof, modifying its mapping by ±1 aberschisma step to reach the rest of primes.
+By moving the generators around, the generator for 5 can be used for [[13/1|13]] and [[19/1|19]]. It can also be taken to be a 3–5{{c}} generic aberschisma, which represents the [[schisma]], the [[aberschisma]], the [[undevicesimal schisma]], and many other important commas around that size. [[Tempering out]] this tiny interval results in [[cassandra]], so cassaschismic may be viewed as a rank-3 [[detemperament]] thereof, modifying its mapping by ±1 aberschisma step to reach the rest of primes.
-Other subsets include [[gariwizmic]], [[cotoneum]], [[newt]], [[vulture]], [[heptacot]], [[satin]], [[witcher]]; which instead of tempering out the aberschisma, find it deep in the generator chain.
+Other rank-2 temperaments of cassaschismic include [[cotoneum]], [[gariwizmic]], [[newt]], [[satin]], and [[vulture]]; these temperaments, instead of tempering out the aberschisma, find it deep in the generator chain.
-It is [[support]]ed by notable [[equal temperament]]s such as {{EDOs| 217, 270, 311, and 364 }}, where the aberschisma step is well represented by one edostep. It is also trivially supported by edos of cassandra, these being [[41edo|41]], [[53edo|53]], [[94edo|94]], and of course, [[12edo]] through the 12e [[val]], where both the comma step and the aberschisma step are tempered out, so it can be used in any of those forms as well.
+Cassaschismic is [[support]]ed by notable [[equal temperament]]s such as {{EDOs| 217, 270, 311, and 364 }}, where the aberschisma step is well represented by one edostep. It is also trivially supported by edos of cassandra, these being [[41edo|41]], [[53edo|53]], [[94edo|94]], and of course, [[12edo]] through the 12e [[val]], where both the comma step and the aberschisma step are tempered out, so it can be used in any of those forms as well.
 See [[Garischismic family #Cassaschismic]] for technical data.