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| '''Decic''' is a temperament for the 7, 11, 13, and 17 [[Harmonic limit|prime limits]]. It is a member of [[marvel temperaments]], [[cloudy clan]], and [[15/14 equal-step tuning|linus temperaments]]. It has a period of 1/10 octave and tempers out 225/224 and 16807/16384. The fifth of decic in size is a [[meantone]] fifth, but four of them are not used to reach the 5th harmonic. Instead, [[14/13]], [[15/14]] and [[16/15]] are equated to 1/10 of an octave, and from this it derives its name. Not only the meantone fifth (flat 3/2) or fourth (sharp 4/3), but also the [[magic]] major third (flat 5/4) can be used as a generator.
| | #redirect [[Marvel temperaments #Decic]] |
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| == Temperament data ==
| | [[Category:Rank-2 temperaments]] |
| <div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
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| <div style="line-height:1.6;">'''Decic temperament (10&50)'''</div>
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| <div class="mw-collapsible-content">
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| Subgroup: 2.3.5.7.11.13.17
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| [[Comma list]]: 105/104, 144/143, 170/169, 196/195, 221/220 | |
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| [[Mapping]]: [{{val| 10 16 23 28 35 37 41 }}, {{val| 0 1 -1 0 2 0 1 }}]
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| [[POTE generator]]s:
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| * 7-limit: ~3/2 = 698.69596
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| * 11-limit: ~3/2 = 696.79119
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| * 13-limit: ~3/2 = 696.99342
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| * 17-limit: ~3/2 = 697.08527
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| [[TOP tuning|TOP generator]]s:
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| * 7-limit: ~15/14 = 120.18411, ~3/2 = 699.76795
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| * 11-limit: ~15/14 = 120.14165, ~3/2 = 697.61366
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| * 13-limit: ~14/13 = 120.11775, ~3/2 = 697.67733
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| * 17-limit: ~14/13 = 120.12744, ~3/2 = 697.82559
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| [[Diamond monotone]] ranges:
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| * 7-odd-limit: ~3/2 = [680.00000, 720.00000] (34\60 to 6\10)
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| * 9-odd-limit: ~3/2 = [696.00000, 720.00000] (29\50 to 6\10)
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| * 11, 13, 15, and 17-odd-limit: ~3/2 = [696.00000, 700.00000] (29\50 to 35\60)
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| [[Diamond tradeoff]] ranges:
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| * 7 and 9-odd-limit: ~3/2 = [693.12909, 702.51219]
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| * 11, 13, and 15-odd-limit: ~3/2 = [689.36294, 702.51219]
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| * 17-odd-limit: ~3/2 = [689.36294, 704.95541]
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| Diamond monotone and tradeoff ranges:
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| * 7-odd-limit: ~3/2 = [693.12909, 702.51219]
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| * 9-odd-limit: ~3/2 = [696.00000, 702.51219]
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| * 11, 13, 15, and 17-odd-limit: ~3/2 = [696.00000, 700.00000]
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| [[Optimal GPV sequence]]s:
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| * 7-limit: {{Vals| 10, 30b, 40, 50, 60, 110d, 170cdd }}
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| * 11 and 13-limit: {{Vals| 10, 30be, 40, 50 }}
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| * 17-limit: {{Vals| 10, 30beg, 40, 50 }}
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| [[Badness]]:
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| * 7-limit: 0.089135
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| * 11-limit: 0.063900
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| * 13-limit: 0.036880
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| * 17-limit: 0.025064
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| </div></div>
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| == Scales ==
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| * [[Decic50]]
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| [[Category:Cloudy clan]]
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| [[Category:Marvel temperaments]] | | [[Category:Marvel temperaments]] |
| [[Category:Decic| ]]<!-- main article -->
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| {{IoT}}
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