Parakleismic: Difference between revisions

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-#REDIRECT [[Ragismic microtemperaments #Parakleismic]]
+'''Parakleismic''' is the microtemperament tempering out the [[parakleisma]] in the 5-limit, and [[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]].
+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.
+See [[Ragismic microtemperaments #Parakleismic]] for technical data.
+== Interval chain ==
+{| class="wikitable center-1 right-2"
+! #
+! Cents*
+! Approximate Ratios
+|-
+| 0
+| 0.0
+| '''1/1'''
+|-
+| 1
+| 315.2
+| 6/5
+|-
+| 2
+| 630.4
+| 36/25
+|-
+| 3
+| 945.5
+| 140/81
+|-
+| 4
+| 60.7
+| 28/27
+|-
+| 5
+| 375.9
+| 56/45
+|-
+| 6
+| 691.1
+| 112/75
+|-
+| 7
+| 1006.3
+| 25/14
+|-
+| 8
+| 121.4
+| 15/14
+|-
+| 9
+| 436.6
+| 9/7
+|-
+| 10
+| 751.8
+| 54/35
+|-
+| 11
+| 1067.0
+| 50/27
+|-
+| 12
+| 182.2
+| 10/9
+|-
+| 13
+| 497.4
+| '''4/3'''
+|-
+| 14
+| 812.5
+| '''8/5'''
+|-
+| 15
+| 1127.7
+| 48/25
+|-
+| 16
+| 242.9
+| 144/125
+|-
+| 17
+| 558.1
+| 112/81
+|-
+| 18
+| 873.7
+| 224/135
+|-
+| 19
+| 1188.4
+| 125/63, 448/225, 486/245
+|-
+| 20
+| 303.6
+| 25/21
+|-
+| 21
+| 618.8
+| 10/7
+|-
+| 22
+| 934.0
+| 12/7
+|-
+| 23
+| 49.2
+| 36/35
+|}
+<nowiki>*</nowiki> in 7-limit POTE tuning
+[[Category:Temperament]]
+[[Category:Parakleismic| ]] <!-- main article -->
+[[Category:Hemimean]]
 [[Category:Ragismic microtemperaments]]
-[[Category:Temperament]]
+[[Category:Hemimage]]