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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 == Tuning spectrum ==
-{| class="wikitable center-1 center-2"
+{| class="wikitable center-all left-4"
-! Eigenmonzo
+! EDO<br>generator
-! Generator
+! [[eigenmonzo|eigenmonzo<br>(unchanged interval)]]
-! Comments
+! generator<br>(¢)
+! comments
 |-
-| (16\61)
+| 16\61
+|
 | 314.754
 | Lower bound of 9-odd-limit diamond monotone
 |-
+|
 | 15/14
 | 314.930
 |
 |-
-| (21\80)
+| 21\80
+|
 | 315.000
 |
 |-
+|
 | 9/7
 | 315.009
 |
 |-
+|
 | 7/5
 | 315.118
 |
 |-
+|
 | 7/6
 | 315.142
 |
 |-
-| (26\99)
+| 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)
+| 31\118
+|
 | 315.254
 |
 |-
+|
 | 5/4
 | 315.263
 |
 |-
+|
 | 25/24
 | 315.289
 |
 |-
+|
 | 6/5
 | 315.641
 |
 |-
+|
 | 28/27
 | 315.740
 |
 |-
-| (5\19)
+| 5\19
+|
 | 315.789
 | Upper bound of 9-odd-limit diamond monotone
@@ Line 203: / Line 225: @@
 [[Category:Parakleismic| ]] <!-- main article -->
+[[Category:Rank-2 temperaments]]
 [[Category:Hemimean clan]]
 [[Category:Ragismic microtemperaments]]
 [[Category:Hemimage temperaments]]
 [[Category:Canousmic temperaments]]
-{{IoT}}