13ed5/2: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''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]]. | '''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 == | == 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]]. | 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 in equal|13|5|2}} | == Harmonics == | ||
{{Harmonics in equal | |||
| steps = 13 | |||
| num = 5 | |||
| denom = 2 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 13 | |||
| num = 5 | |||
| denom = 2 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
== Intervals == | == Intervals == | ||
| Line 12: | Line 24: | ||
!# | !# | ||
!Cents | !Cents | ||
!Approximate ratios* | |||
!Jubilic[8] notation | !Jubilic[8] notation | ||
|- | |- | ||
|0 | |0 | ||
|0.000 | |0.000 | ||
| | |[[1/1]] | ||
|J | |||
|- | |- | ||
|1 | |1 | ||
|122.024 | |122.024 | ||
| | |[[14/13]], [[35/32]] | ||
|J&, K@ | |||
|- | |- | ||
|2 | |2 | ||
|244.048 | |244.048 | ||
| | |[[8/7]], [[28/25]] | ||
|K | |||
|- | |- | ||
|3 | |3 | ||
|366.072 | |366.072 | ||
| | |[[5/4]], [[16/13]], [[49/40]] | ||
|L | |||
|- | |- | ||
|4 | |4 | ||
|488.096 | |488.096 | ||
| | |[[32/25]], [[64/49]] | ||
|L&, M@ | |||
|- | |- | ||
|5 | |5 | ||
|610.120 | |610.120 | ||
| | |[[7/5]], [[10/7]] | ||
|M | |||
|- | |- | ||
|6 | |6 | ||
|732.144 | |732.144 | ||
| | |[[20/13]], [[25/16]], [[49/32]] | ||
|M&, N@ | |||
|- | |- | ||
|7 | |7 | ||
|854.168 | |854.168 | ||
| | |[[8/5]], [[13/8]] | ||
|N | |||
|- | |- | ||
|8 | |8 | ||
|976.192 | |976.192 | ||
| | |[[7/4]], [[25/14]] | ||
|O | |||
|- | |- | ||
|9 | |9 | ||
|1098.216 | |1098.216 | ||
| | |[[13/7]], [[64/35]] | ||
|O&, P@ | |||
|- | |- | ||
|10 | |10 | ||
|1220.240 | |1220.240 | ||
| | |[[2/1]], [[49/25]], 52/25 | ||
|P | |||
|- | |- | ||
|11 | |11 | ||
|1342.264 | |1342.264 | ||
| | |35/16 | ||
|Q | |||
|- | |- | ||
|12 | |12 | ||
|1464.288 | |1464.288 | ||
| | |[[16/7]] | ||
|Q&, J@ | |||
|- | |- | ||
|13 | |13 | ||
|1586.312 | |1586.312 | ||
| | |[[5/2]] | ||
|J | |||
|} | |} | ||
<nowiki>*</nowiki> Based on treating 13ed5/2 as a 5/2.5.7.13 subgroup temperament | |||