Decic: Difference between revisions
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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. | |||
== Temperament data == | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">'''Decic temperament (10&50)'''</div> | |||
<div class="mw-collapsible-content"> | |||
Subgroup: 2.3.5.7.11.13.17 | |||
[[Comma list]]: 105/104, 144/143, 170/169, 196/195, 221/220 | |||
[[Mapping]]: [{{val| 10 16 23 28 35 37 41 }}, {{val| 0 1 -1 0 2 0 1 }}] | |||
[[POTE generator]]s: | |||
* 7-limit: ~3/2 = 698.69596 | |||
* 11-limit: ~3/2 = 696.79119 | |||
* 13-limit: ~3/2 = 696.99342 | |||
* 17-limit: ~3/2 = 697.08527 | |||
[[TOP tuning|TOP generator]]s: | |||
* 7-limit: ~15/14 = 120.18411, ~3/2 = 699.76795 | |||
* 11-limit: ~15/14 = 120.14165, ~3/2 = 697.61366 | |||
* 13-limit: ~14/13 = 120.11775, ~3/2 = 697.67733 | |||
* 17-limit: ~14/13 = 120.12744, ~3/2 = 697.82559 | |||
[[Diamond monotone]] ranges: | |||
* 7-odd-limit: ~3/2 = [680.00000, 720.00000] (34\60 to 6\10) | |||
* 9-odd-limit: ~3/2 = [696.00000, 720.00000] (29\50 to 6\10) | |||
* 11, 13, 15, and 17-odd-limit: ~3/2 = [696.00000, 700.00000] (29\50 to 35\60) | |||
[[Diamond tradeoff]] ranges: | |||
* 7 and 9-odd-limit: ~3/2 = [693.12909, 702.51219] | |||
* 11, 13, and 15-odd-limit: ~3/2 = [689.36294, 702.51219] | |||
* 17-odd-limit: ~3/2 = [689.36294, 704.95541] | |||
Diamond monotone and tradeoff ranges: | |||
* 7-odd-limit: ~3/2 = [693.12909, 702.51219] | |||
* 9-odd-limit: ~3/2 = [696.00000, 702.51219] | |||
* 11, 13, 15, and 17-odd-limit: ~3/2 = [696.00000, 700.00000] | |||
[[Optimal GPV sequence]]s: | |||
* 7-limit: {{Vals| 10, 30b, 40, 50, 60, 110d, 170cdd }} | |||
* 11 and 13-limit: {{Vals| 10, 30be, 40, 50 }} | |||
* 17-limit: {{Vals| 10, 30beg, 40, 50 }} | |||
[[Badness]]: | |||
* 7-limit: 0.089135 | |||
* 11-limit: 0.063900 | |||
* 13-limit: 0.036880 | |||
* 17-limit: 0.025064 | |||
</div></div> | |||
[[Category:Cloudy clan]] | [[Category:Cloudy clan]] | ||
[[Category:Marvel temperaments]] | |||
[[Category:Decic| ]]<!-- main article --> | |||
{{IoT}} | {{IoT}} | ||