Parakleismic: Difference between revisions
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<nowiki>*</nowiki> in 7-limit POTE tuning | <nowiki>*</nowiki> in 7-limit POTE tuning | ||
[[Category:Parakleismic| ]] <!-- main article --> | [[Category:Parakleismic| ]] <!-- main article --> | ||
[[Category:Hemimean]] | [[Category:Hemimean]] | ||
[[Category:Ragismic microtemperaments]] | [[Category:Ragismic microtemperaments]] | ||
[[Category:Hemimage]] | [[Category:Hemimage temperaments]] | ||
[[Category:Canousmic temperaments]] | |||
{{IoT}} | |||
Revision as of 16:05, 8 June 2021
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
| # | 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 |
* in 7-limit POTE tuning Template:IoT