Parakleismic: Difference between revisions

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-'''Parakleismic''' is the microtemperament tempering out the [[parakleisma]] in the 5-limit, and [[3136/3125]] and [[4375/4374]] in the 7-limit.
+'''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 flat, instead of sharp, than the just version. The sixth generator step is half a [[syntonic comma]] flat of the harmonic 3. The 12th step is mapped to [[10/9]] instead of [[9/8]], and the 13th 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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 |}
 <nowiki>*</nowiki> in 7-limit POTE tuning
+== Tuning spectrum ==
+{| class="wikitable center-all left-4"
+! EDO<br>generator
+! [[eigenmonzo|eigenmonzo<br>(unchanged interval)]]
+! generator<br>(¢)
+! comments
+|-
+| 16\61
+|
+| 314.754
+| Lower bound of 9-odd-limit diamond monotone
+|-
+|
+| 15/14
+| 314.930
+|
+|-
+| 21\80
+|
+| 315.000
+|
+|-
+|
+| 9/7
+| 315.009
+|
+|-
+|
+| 7/5
+| 315.118
+|
+|-
+|
+| 7/6
+| 315.142
+|
+|-
+| 26\99
+|
+| 315.152
+|
+|-
+|
+| 21/20
+| 315.163
+|
+|-
+|
+| 49/48
+| 315.163
+|
+|-
+|
+| 36/35
+| 315.164
+|
+|-
+|
+| 8/7
+| 315.176
+| 7-odd-limit minimax (error = 1.217¢)
+|-
+|
+| 80/63
+| 315.183
+| 9-odd-limit minimax (error = 1.345¢)
+|-
+|
+| 10/9
+| 315.200
+|
+|-
+|
+| 4/3
+| 315.234
+|
+|-
+|
+| 16/15
+| 315.249
+| 5-odd-limit minimax (error = 0.196¢)
+|-
+| 31\118
+|
+| 315.254
+|
+|-
+|
+| 5/4
+| 315.263
+|
+|-
+|
+| 25/24
+| 315.289
+|
+|-
+|
+| 6/5
+| 315.641
+|
+|-
+|
+| 28/27
+| 315.740
+|
+|-
+| 5\19
+|
+| 315.789
+| Upper bound of 9-odd-limit diamond monotone
+|}
 [[Category:Parakleismic| ]] <!-- main article -->
-[[Category:Hemimean]]
+[[Category:Rank-2 temperaments]]
+[[Category:Hemimean clan]]
 [[Category:Ragismic microtemperaments]]
 [[Category:Hemimage temperaments]]
 [[Category:Canousmic temperaments]]
-{{IoT}}