Cassaschismic: Difference between revisions

Line 11:

| Odd limit 1 = 11 | Mistuning 1 = 0.588 | Complexity 1 = ?

}}

'''Cassaschismic''' is a [[rank-3 ~~temperament|rank-3]] [[regular temperament|~~temperament]] that expands [[gary]]'s [[chain of fifths]] 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]].

'''Cassaschismic''' is a [[rank-3 temperament]] that expands [[gary]]'s [[chain of fifths]] 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]].

The generator for 5 can be used for [[13/1|13]] and [[19/1|19]]. By moving the generators around, it can also be taken to be a ~4.5{{c}} generic aberschisma, which represents the [[schisma]], the [[aberschisma]], the [[undevicesimal schisma]], the [[352/351|minor minthma]] and many other important commas around that size. [[Tempering out]] this aberschisma results in [[cassandra]], so cassaschismic is a rank-3 [[detemperament]] of it, modifying its mapping by ±1 aberschisma to reach primes 5, 13, and 19.

@@ Line 11: / Line 11: @@
 | Odd limit 1 = 11 | Mistuning 1 = 0.588 | Complexity 1 = ?
 }}
-'''Cassaschismic''' is a [[rank-3 temperament|rank-3]] [[regular temperament|temperament]] that expands [[gary]]'s [[chain of fifths]] 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]].
+'''Cassaschismic''' is a [[rank-3 temperament]] that expands [[gary]]'s [[chain of fifths]] 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]].
 The generator for 5 can be used for [[13/1|13]] and [[19/1|19]]. By moving the generators around, it can also be taken to be a ~4.5{{c}} generic aberschisma, which represents the [[schisma]], the [[aberschisma]], the [[undevicesimal schisma]], the [[352/351|minor minthma]] and many other important commas around that size. [[Tempering out]] this aberschisma results in [[cassandra]], so cassaschismic is a rank-3 [[detemperament]] of it, modifying its mapping by ±1 aberschisma to reach primes 5, 13, and 19.