13ed5/2: Difference between revisions
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'''13ed5/2''' is the equal division of the [[5/2]] interval into 13 parts of 122.024 [[cent]]s each. It roughly corresponds to [[10edo]], and their [[patent val]]s match up until the 7-limit. | |||
== Theory == | |||
Like 10edo, 13ed5/2 tempers out [[50/49]] in the no-threes 7-limit, [[support]]ing 5/2-equivalent jubilic temperament with a generator of ~[[7/5]]. In this regard, it could be considered a "no-threes cousin" of [[12edo]] and [[13edt]], having the basic tuning for the octatonic scale of 5/2-equivalent jubilic ([[5L 3s (5/2-equivalent)|5L 3s⟨5/2⟩]]). It also tempers out [[56/55]] in the 11-limit and [[26/25]], [[52/49]] and [[65/64]] in the 13-limit. | |||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 13 | |||
| num = 5 | |||
| denom = 2 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 13 | |||
| num = 5 | |||
| denom = 2 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
== Intervals == | |||
{|class="wikitable article-table" | |||
|- | |||
!# | |||
!Cents | |||
!Approximate ratios* | |||
!Jubilic[8] notation | |||
|- | |||
|0 | |||
|0.000 | |||
|[[1/1]] | |||
|J | |||
|- | |||
|1 | |||
|122.024 | |||
|[[14/13]], [[35/32]] | |||
|J&, K@ | |||
|- | |||
|2 | |||
|244.048 | |||
|[[8/7]], [[28/25]] | |||
|K | |||
|- | |||
|3 | |||
|366.072 | |||
|[[5/4]], [[16/13]], [[49/40]] | |||
|L | |||
|- | |||
|4 | |||
|488.096 | |||
|[[32/25]], [[64/49]] | |||
|L&, M@ | |||
|- | |||
|5 | |||
|610.120 | |||
|[[7/5]], [[10/7]] | |||
|M | |||
|- | |||
|6 | |||
|732.144 | |||
|[[20/13]], [[25/16]], [[49/32]] | |||
|M&, N@ | |||
|- | |||
|7 | |||
|854.168 | |||
|[[8/5]], [[13/8]] | |||
|N | |||
|- | |||
|8 | |||
|976.192 | |||
|[[7/4]], [[25/14]] | |||
|O | |||
|- | |||
|9 | |||
|1098.216 | |||
|[[13/7]], [[64/35]] | |||
|O&, P@ | |||
|- | |||
|10 | |||
|1220.240 | |||
|[[2/1]], [[49/25]], 52/25 | |||
|P | |||
|- | |||
|11 | |||
|1342.264 | |||
|35/16 | |||
|Q | |||
|- | |||
|12 | |||
|1464.288 | |||
|[[16/7]] | |||
|Q&, J@ | |||
|- | |||
|13 | |||
|1586.312 | |||
|[[5/2]] | |||
|J | |||
|} | |||
<nowiki>*</nowiki> Based on treating 13ed5/2 as a 5/2.5.7.13 subgroup temperament | |||