21ed5/2: Difference between revisions
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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. | 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 == | ||
{{Harmonics in equal|21|5|2}} | {{Harmonics in equal | ||
| steps = 21 | |||
| num = 5 | |||
| denom = 2 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 21 | |||
| num = 5 | |||
| denom = 2 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
== Interval table == | == Interval table == | ||
| Line 31: | Line 42: | ||
|- | |- | ||
|3 | |3 | ||
| | |226.616 | ||
| | |K | ||
|[[8/7]], [[28/25]] | |[[8/7]], [[28/25]] | ||
|- | |- | ||
|4 | |4 | ||
| | |302.155 | ||
| | |K&, L@ | ||
|[[13/11]], [[77/64]] | |[[13/11]], [[77/64]] | ||
|- | |- | ||
|5 | |5 | ||
| | |377.694 | ||
| | |L | ||
|[[5/4]], [[11/9]], [[16/13]], [[49/40]] | |[[5/4]], [[11/9]], [[16/13]], [[49/40]] | ||
|- | |- | ||
|6 | |6 | ||
| | |453.233 | ||
| | |L& | ||
|[[13/10]], [[32/25]] | |[[13/10]], [[32/25]] | ||
|- | |- | ||
|7 | |7 | ||
| | |528.771 | ||
| | |M@ | ||
|[[11/8]], [[35/26]] | |[[11/8]], [[35/26]] | ||
|- | |- | ||
|8 | |8 | ||
| | |604.310 | ||
| | |M | ||
|[[7/5]], [[10/7]] | |[[7/5]], [[10/7]] | ||
|- | |- | ||
|9 | |9 | ||
| | |679.849 | ||
| | |M& | ||
|[[16/11]], [[52/35]] | |[[16/11]], [[52/35]] | ||
|- | |- | ||
|10 | |10 | ||
| | |755.388 | ||
| | |N@ | ||
|[[11/7]], [[20/13]], [[25/16]], [[49/32]] | |[[11/7]], [[20/13]], [[25/16]], [[49/32]] | ||
|- | |- | ||
|11 | |11 | ||
| | |830.926 | ||
| | |N | ||
|[[8/5]], [[13/8]] | |[[8/5]], [[13/8]] | ||
|- | |- | ||
|12 | |12 | ||
| | |906.465 | ||
| | |N&, O@ | ||
|[[22/13]], [[55/32]] | |[[22/13]], [[55/32]] | ||
|- | |- | ||
|13 | |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 | <nowiki>*</nowiki> Based on treating 21ed5/2 as a no-threes 13-limit temperament | ||