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"

! ET ~~generator~~

! Edo Generator

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

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

! ~~generator~~ (¢)

! Generator (¢)

! ~~comments~~

! Comments

|-

| 16\61

@@ Line 1: / Line 1: @@
 '''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.
@@ Line 113: / Line 113: @@
 == Tuning spectrum ==
 {| class="wikitable center-all"
-! ET<br>generator
+! Edo<br>Generator
-! [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
+! [[Eigenmonzo|Eigenmonzo<br>(unchanged interval)]]
-! generator<br>(¢)
+! Generator<br>(¢)
-! comments
+! Comments
 |-
 | 16\61