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See [[Ragismic microtemperaments #Parakleismic]].
'''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.  


[[Category:Smart redirect]]
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]].
[[Category:Parakleismic]]
 
[[Category:Ragismic]]
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
 
== 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:Rank-2 temperaments]]
[[Category:Hemimean clan]]
[[Category:Ragismic microtemperaments]]
[[Category:Hemimage temperaments]]
[[Category:Canousmic temperaments]]
Retrieved from "https://en.xen.wiki/w/Parakleismic"