Catakleismic: Difference between revisions

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The '''catakleismic''' temperament is one of the best [[7-limit]] extensions of [[hanson]], the 5-limit temperament tempering out the [[15625/15552|kleisma]] (15625/15552), though it is naturally viewed as a 2.3.5.7.13 temperament, first extending hanson to include the harmonic 13 (called '''cata'''), and then to include 7.

In addition to the kleisma, catakleismic tempers the [[marvel comma]] (225/224), equating the interval of [[25/24]] (which is already equated to [[26/25]] and [[27/26]] in the 2.3.5.13 subgroup interpretation of kleismic) to [[28/27]]. This forces a flatter interpretation of 25/24, which is found 4 [[6/5]] generators up, and therefore a flatter interpretation of the generator, which confines reasonable catakleismic tunings to the portion of the kleismic tuning spectrum. between [[19edo]] and [[34edo]]; in fact, catakleismic is the 19 & 34d temperament in the 7-limit. It can additionally be defined by tempering out the marvel comma and the [[ragisma]] (4375/4374), which finds [[7/6]] at the square of [[27/25]], which is found at the square of 25/24. Therefore the 7th harmonic appears 22 generators up the chain.

In addition to the kleisma, catakleismic tempers the [[marvel comma]] (225/224), equating the interval of [[25/24]] (which is already equated to [[26/25]] and [[27/26]] in the 2.3.5.13 subgroup interpretation of kleismic) to [[28/27]]. This forces a flatter interpretation of 25/24, which is found 4 [[6/5]] generators up, and therefore a flatter interpretation of the generator, which confines reasonable catakleismic tunings to the portion of the kleismic tuning spectrum between [[19edo]] and [[34edo]]; in fact, catakleismic is the 19 & 34d temperament in the 7-limit. It can additionally be defined by tempering out the marvel comma and the [[ragisma]] (4375/4374), which finds [[7/6]] at the square of [[27/25]], which is found at the square of 25/24. Therefore the 7th harmonic appears 22 generators up the chain.

Various reasonable extensions exist for harmonic 11. These are ''undecimal catakleismic'', mapping 11 to -21 generator steps, ''cataclysmic'', to +32 steps, ''catalytic'', to +51 steps, and cataleptic, to -2 steps.

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 The '''catakleismic''' temperament is one of the best [[7-limit]] extensions of [[hanson]], the 5-limit temperament tempering out the [[15625/15552|kleisma]] (15625/15552), though it is naturally viewed as a 2.3.5.7.13 temperament, first extending hanson to include the harmonic 13 (called '''cata'''), and then to include 7.
-In addition to the kleisma, catakleismic tempers the [[marvel comma]] (225/224), equating the interval of [[25/24]] (which is already equated to [[26/25]] and [[27/26]] in the 2.3.5.13 subgroup interpretation of kleismic) to [[28/27]]. This forces a flatter interpretation of 25/24, which is found 4 [[6/5]] generators up, and therefore a flatter interpretation of the generator, which confines reasonable catakleismic tunings to the portion of the kleismic tuning spectrum. between [[19edo]] and [[34edo]]; in fact, catakleismic is the 19 & 34d temperament in the 7-limit. It can additionally be defined by tempering out the marvel comma and the [[ragisma]] (4375/4374), which finds [[7/6]] at the square of [[27/25]], which is found at the square of 25/24. Therefore the 7th harmonic appears 22 generators up the chain.
+In addition to the kleisma, catakleismic tempers the [[marvel comma]] (225/224), equating the interval of [[25/24]] (which is already equated to [[26/25]] and [[27/26]] in the 2.3.5.13 subgroup interpretation of kleismic) to [[28/27]]. This forces a flatter interpretation of 25/24, which is found 4 [[6/5]] generators up, and therefore a flatter interpretation of the generator, which confines reasonable catakleismic tunings to the portion of the kleismic tuning spectrum between [[19edo]] and [[34edo]]; in fact, catakleismic is the 19 & 34d temperament in the 7-limit. It can additionally be defined by tempering out the marvel comma and the [[ragisma]] (4375/4374), which finds [[7/6]] at the square of [[27/25]], which is found at the square of 25/24. Therefore the 7th harmonic appears 22 generators up the chain.
 Various reasonable extensions exist for harmonic 11. These are ''undecimal catakleismic'', mapping 11 to -21 generator steps, ''cataclysmic'', to +32 steps, ''catalytic'', to +51 steps, and cataleptic, to -2 steps.