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| '''Superkleismic temperament''' is temperament for the 7, 11, and 13 [[Harmonic limit|prime limits]]. It is a member of [[shibboleth family]], [[gamelismic clan]], [[keemic temperaments]], and [[octagar temperaments]]. The minor-third generator of superkleismic is ~6.3 cents sharp of [[6/5]], even wider than [[Kleismic family|kleismic]] minor third (~317 cents), and from this it derives its name. The two mappings unite at [[15edo]]. While not as simple or accurate as kleismic in the 5-limit, it comes into it's own as a 7&11 limit temperament, approximating both simply and accurately in good tunings. Discarding the 3&5 and concentrating purely on that subgroup gets you [[orgone]]. [[41edo]] is a good tuning for superkleismic, with a minor-third generator of 11\41, and MOS of 11, 15, or 26 notes are available. | | '''Superkleismic''' is a [[regular temperament]] defined in the [[7-limit|7-]], [[11-limit|11-]], and [[13-limit]]. It is a member of [[shibboleth family]] as well as of the [[gamelismic clan]]. The minor-third generator of superkleismic is ~6.3 cents sharp of [[6/5]], even wider than the [[Kleismic family|kleismic]] minor third (~317 cents), and from this it derives its name. The two mappings unite at [[15edo]]. While not as simple or accurate as kleismic in the 5-limit, it comes into its own as a 7- and 11-limit temperament, approximating both simply and accurately in good tunings. Discarding the harmonics 3 and 5 and concentrating purely on that subgroup gets you [[orgone]]. [[41edo]] is a good tuning for superkleismic, with a minor-third generator of 11\41, and [[mos]]ses of 11, 15, or 26 notes are available. |
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| == Temperament data ==
| | See [[Shibboleth family #Superkleismic]] for more technical data. |
| <div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
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| <div style="line-height:1.6;">'''Superkleismic temperament (15 & 26)'''</div>
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| <div class="mw-collapsible-content">
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| Subgroup: 2.3.5.7.11.13
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| [[Comma list]]: 100/99, 105/104, 144/143, 245/242 | |
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| [[Mapping]]: [{{val| 1 4 5 2 4 8 }}, {{val| 0 -9 -10 3 -2 -16 }}]
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| [[POTE generator]]:
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| * 7-limit: ~6/5 = 321.93010
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| * 11-limit: ~6/5 = 321.84656
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| * 13-limit: ~6/5 = 321.99387
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| [[TOP tuning|TOP generator]]s:
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| * 7-limit: ~2 = 1200.76801, ~6/5 = 322.13613
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| * 11-limit: ~2 = 1200.17605, ~6/5 = 321.89378
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| * 13-limit: ~2 = 1200.03800, ~6/5 = 322.00406
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| [[Diamond monotone]] ranges:
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| * 5-odd-limit: ~6/5 = [315.78947, 327.27273] (5\19 to 3\11)
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| * 7, 9, 11, and 13-odd-limit: ~6/5 = [320.00000, 323.07692] (4\15 to 7\26)
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| * 15-odd-limit: ~6/5 = 321.95122 (11\41)
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| [[Diamond tradeoff]] ranges:
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| * 5-odd-limit: ~6/5 = [315.64129, 322.00500]
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| * 7 and 9-odd-limit: ~6/5 = [315.64129, 322.94197]
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| * 11, 13, and 15-odd-limit: ~6/5 = [315.64129, 324.34103]
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| Diamond monotone and tradeoff ranges:
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| * 5-odd-limit: ~6/5 = [315.78947, 322.00500]
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| * 7 and 9-odd-limit: ~6/5 = [320.00000, 322.94197]
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| * 11 and 13-odd-limit: ~6/5 = [320.00000, 323.07692]
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| * 15-odd-limit: ~6/5 = 321.95122
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| [[Optimal ET sequence]]s:
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| * 7-limit: {{Optimal ET sequence| 11c, 15, 26, 41 }}
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| * 11-limit: {{Optimal ET sequence| 11c, 15, 26, 41, 179cde, 220cde, 261ccdee }}
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| * 13-limit: {{Optimal ET sequence| 11cf, 15, 26, 41 }}
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| [[Badness]]:
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| * 7-limit: 0.047932
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| * 11-limit: 0.025659
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| * 13-limit: 0.021478
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| </div></div>
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| == Interval chain == | | == Interval chain == |
| {| class="wikitable center-1 right-2" | | {| class="wikitable center-1 right-2" |
| ! Number of <br>minor third | | ! # |
| ! Cents <br>value* | | ! Cents<br>Value* |
| ! Approximate Ratios | | ! Approximate Ratios |
| |- | | |- |
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| Gencom mapping: [{{val| 1 4 5 2 4 8 }}, {{val| 0 -9 -10 3 -2 -16 }}] | | Gencom mapping: [{{val| 1 4 5 2 4 8 }}, {{val| 0 -9 -10 3 -2 -16 }}] |
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| {| class="wikitable center-all" | | {| class="wikitable center-1 right-2" |
| |- | | |- |
| ! [[eigenmonzo|eigenmonzo<br>(unchanged-interval)]] | | ! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]] |
| ! minor third<br>(¢) | | ! Generator<br>(¢) |
| ! comments | | ! Comments |
| |- | | |- |
| | 6/5 | | | 6/5 |
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| |} | | |} |
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| == Scales ==
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| * [[Shibboleth7]] - [[4L 3s]] scale
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| * [[Shibboleth11]] - [[4L 7s]] scale
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| * [[Shibboleth15]] - [[11L 4s]] scale
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| [[Category:Temperaments]] | | [[Category:Temperaments]] |
| [[Category:Shibboleth family]] | | [[Category:Shibboleth family]] |
| [[Category:Gamelismic clan]] | | [[Category:Gamelismic clan]] |
| | [[Category:Keemic temperaments]] |