Septischismic: Difference between revisions
Shift the 13-limit comma basis to the 11-limit in the infobox as the latter is nullity-2. Reduce decimal places to 2 since the infobox is meant to only give a general impression |
Restore dual name (community request) |
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| Odd limit 1 = 11 | Mistuning 1 = 0.588 | Complexity 1 = ? | | Odd limit 1 = 11 | Mistuning 1 = 0.588 | Complexity 1 = ? | ||
}} | }} | ||
'''Septischismic''' is a [[rank-3 temperament]] that expands [[gary]]'s [[chain of fifths]] into the full [[7-limit]] by adding an independent [[generator]] for the [[5/1|5th]] [[harmonic]]. It is therefore a member of the [[septischismic family]]. The [[11-limit]] version, sometimes called '''cassaschismic''', inherits gary's mapping for [[11/1|11]], making it a member of the [[olympic clan]]. | '''Septischismic''', alternatively called '''garischismic''' in the 7-limit, is a [[rank-3 temperament]] that expands [[gary]]'s [[chain of fifths]] into the full [[7-limit]] by adding an independent [[generator]] for the [[5/1|5th]] [[harmonic]]. It is therefore a member of the [[septischismic family]]. The [[11-limit]] version, sometimes called '''cassaschismic''', inherits gary's mapping for [[11/1|11]], making it a member of the [[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|major minthma]] and many other important commas around that size. [[Tempering out]] this aberschisma results in [[cassandra]], so septischismic is a rank-3 [[detemperament]] of it, modifying its mapping by ±1 aberschisma to reach primes 5, 13, and 19. | 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|major minthma]] and many other important commas around that size. [[Tempering out]] this aberschisma results in [[cassandra]], so septischismic is a rank-3 [[detemperament]] of it, modifying its mapping by ±1 aberschisma to reach primes 5, 13, and 19. | ||
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There are two natural strong extensions available to add primes 17, 29 and 31, but they are more complex and in the case of 29 and 31, accrue considerably more error into the temperament than the rest of primes. | There are two natural strong extensions available to add primes 17, 29 and 31, but they are more complex and in the case of 29 and 31, accrue considerably more error into the temperament than the rest of primes. | ||
See [[Septischismic family #Septischismic]] for technical data and extensions. | See [[Septischismic family #Septischismic a.k.a. garischismic]] for technical data and extensions. | ||
== Interval lattice == | == Interval lattice == | ||