Parakleismic: Difference between revisions

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'''Parakleismic''' is the microtemperament tempering out the [[parakleisma]] in the 5-limit. This article also assumes the canonical mapping for 7, which means tempering out [[3136/3125]] and [[4375/4374]] in the 7-limit.

Parakleismic is much ~~alike~~ [[catakleismic]] but a good tuning has the generator ([[6/5]]) flat, instead of sharp, than the just version. The sixth generator step is half a [[syntonic comma]] flat of the harmonic 3. Consequently, the 12th generator step is mapped to [[10/9]] instead of [[9/8]], and the 13th generator step is mapped to [[4/3]] instead of [[27/20]].

Parakleismic is much like [[catakleismic]] but a good tuning has the generator ([[6/5]]) flat, instead of sharp, than the just version. The sixth generator step is half a [[syntonic comma]] flat of the harmonic 3. Consequently, the 12th generator step is mapped to [[10/9]] instead of [[9/8]], and the 13th generator step is mapped to [[4/3]] instead of [[27/20]].

Extensions for harmonic 11 includes ''undecimal parakleismic'', mapping it to +36 steps, ''paralytic'', to -82 steps, ''parkleismic'', to -63 steps, and ''paradigmic'', to +17 steps.

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== Tuning spectrum ==

{| class="wikitable center-all"

{| class="wikitable center-all left-4"

! ET generator

! EDO generator

! [[eigenmonzo|eigenmonzo (unchanged interval]])

! [[eigenmonzo|eigenmonzo (unchanged interval)]]

! generator (¢)

! comments

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|}

~~[[Category:Temperaments]]~~

[[Category:Parakleismic| ]]

[[Category:Rank-2 temperaments]]

[[Category:Hemimean clan]]

[[Category:Ragismic microtemperaments]]

[[Category:Hemimage temperaments]]

[[Category:Canousmic temperaments]]

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 '''Parakleismic''' is the microtemperament tempering out the [[parakleisma]] in the 5-limit. This article also assumes the canonical mapping for 7, which means tempering out [[3136/3125]] and [[4375/4374]] in the 7-limit.
-Parakleismic is much alike [[catakleismic]] but a good tuning has the generator ([[6/5]]) flat, instead of sharp, than the just version. The sixth generator step is half a [[syntonic comma]] flat of the harmonic 3. Consequently, the 12th generator step is mapped to [[10/9]] instead of [[9/8]], and the 13th generator step is mapped to [[4/3]] instead of [[27/20]].
+Parakleismic is much like [[catakleismic]] but a good tuning has the generator ([[6/5]]) flat, instead of sharp, than the just version. The sixth generator step is half a [[syntonic comma]] flat of the harmonic 3. Consequently, the 12th generator step is mapped to [[10/9]] instead of [[9/8]], and the 13th generator step is mapped to [[4/3]] instead of [[27/20]].
 Extensions for harmonic 11 includes ''undecimal parakleismic'', mapping it to +36 steps, ''paralytic'', to -82 steps, ''parkleismic'', to -63 steps, and ''paradigmic'', to +17 steps.
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 == Tuning spectrum ==
-{| class="wikitable center-all"
+{| class="wikitable center-all left-4"
-! ET<br>generator
+! EDO<br>generator
-! [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
+! [[eigenmonzo|eigenmonzo<br>(unchanged interval)]]
 ! generator<br>(¢)
 ! comments
@@ Line 224: / Line 224: @@
 |}
-[[Category:Temperaments]]
 [[Category:Parakleismic| ]] <!-- main article -->
+[[Category:Rank-2 temperaments]]
 [[Category:Hemimean clan]]
 [[Category:Ragismic microtemperaments]]
 [[Category:Hemimage temperaments]]
 [[Category:Canousmic temperaments]]