21ed5/2: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''21ed5/2''' is the equal division of the [[5/2]] interval into 21 parts of approximately 75.539 [[cent]]s each. It roughly corresponds to [[16edo]]. | |||
== Theory == | |||
From a no-threes point of view, 21ed5/2 tempers out [[50/49]] in the 7-limit (being a jubilic system similar to [[13ed5/2]]), [[625/616]] and [[176/175]] in the 11-limit, and 143/140, 715/686 and [[847/845]] in the 13-limit. It is not particularly excellent as a no-threes system with the 5/4 and 7/4 being noticeably off, but can work for 5/2-equivalent jubilic. | |||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 21 | |||
| num = 5 | |||
| denom = 2 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 21 | |||
| num = 5 | |||
| denom = 2 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
== Interval table == | |||
{|class="wikitable" | |||
|- | |||
!Steps | |||
!Cents | |||
![[5L 3s (5/2-equivalent)|Jubilic[8]]] notation | |||
!Approximate ratios* | |||
|- | |||
|0 | |||
|0.000 | |||
|J | |||
|[[1/1]] | |||
|- | |||
|1 | |||
|75.539 | |||
|J& | |||
|[[26/25]] | |||
|- | |||
|2 | |||
|151.078 | |||
|K@ | |||
|[[35/32]] | |||
|- | |||
|3 | |||
|226.616 | |||
|K | |||
|[[8/7]], [[28/25]] | |||
|- | |||
|4 | |||
|302.155 | |||
|K&, L@ | |||
|[[13/11]], [[77/64]] | |||
|- | |||
|5 | |||
|377.694 | |||
|L | |||
|[[5/4]], [[11/9]], [[16/13]], [[49/40]] | |||
|- | |||
|6 | |||
|453.233 | |||
|L& | |||
|[[13/10]], [[32/25]] | |||
|- | |||
|7 | |||
|528.771 | |||
|M@ | |||
|[[11/8]], [[35/26]] | |||
|- | |||
|8 | |||
|604.310 | |||
|M | |||
|[[7/5]], [[10/7]] | |||
|- | |||
|9 | |||
|679.849 | |||
|M& | |||
|[[16/11]], [[52/35]] | |||
|- | |||
|10 | |||
|755.388 | |||
|N@ | |||
|[[11/7]], [[20/13]], [[25/16]], [[49/32]] | |||
|- | |||
|11 | |||
|830.926 | |||
|N | |||
|[[8/5]], [[13/8]] | |||
|- | |||
|12 | |||
|906.465 | |||
|N&, O@ | |||
|[[22/13]], [[55/32]] | |||
|- | |||
|13 | |||
|982.004 | |||
|O | |||
|[[7/4]], [[25/14]] | |||
|- | |||
|14 | |||
|1057.543 | |||
|O& | |||
|[[13/7]], [[20/11]] | |||
|- | |||
|15 | |||
|1133.081 | |||
|P@ | |||
|[[25/13]] | |||
|- | |||
|16 | |||
|1208.620 | |||
|P | |||
|[[2/1]] | |||
|- | |||
|17 | |||
|1284.159 | |||
|P&, Q@ | |||
|[[52/25]] | |||
|- | |||
|18 | |||
|1359.698 | |||
|Q | |||
|[[11/5]] | |||
|- | |||
|19 | |||
|1435.236 | |||
|Q& | |||
|[[16/7]] | |||
|- | |||
|20 | |||
|1510.775 | |||
|J@ | |||
|[[26/11]] | |||
|- | |||
|21 | |||
|1586.314 | |||
|J | |||
|[[5/2]] | |||
|} | |||
<nowiki>*</nowiki> Based on treating 21ed5/2 as a no-threes 13-limit temperament | |||