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{{Infobox ET}} | |||
'''12EDF''' is the [[EDF|equal division of the just perfect fifth]] into 12 parts of 58.49625 [[cent|cents]] each, corresponding to 20.5141 [[edo]]. This is similar to every second step of [[41edo]], and thus to the fretting of one string on the [[Kite Guitar]]. It is an intersection of [[3edf]]~[[5edo]] and [[4edf]]~[[7edo]] relations, and could pass as both [[20edo]] and [[21edo]], with both relations nearly breaking down by this point. It is related to the [[Tetracot family#Dodecacot|dodecacot temperament]], which tempers out 3087/3125 and 10976/10935 in the 7-limit. | |||
It is a strong [[half-prime subgroup|3/2.5/2.7/2 subgroup]] system, a fact first noted by [[User:CompactStar|CompactStar]], tempering out the commas [[10976/10935]] and [[3125/3087]], although the representation of [[11/2]] is more questionable. [[24edf]] (effectively 41edo) provides a correction for 11/2. It contains the [[macrodiatonic and microdiatonic scales|microdiatonic]] scale that corresponds to 12edo's [[5L 2s|diatonic scale]] with [[2/1]] compressed to [[3/2]]. | |||
1 | ==Harmonics== | ||
{{Harmonics in equal|12|3|2}} | |||
{{Harmonics in equal|12|3|2|start=12|collapsed=1}} | |||
2 | ==Intervals== | ||
{| class="wikitable" | |||
3 | |- | ||
! | degree | |||
4 | ! | cents value | ||
! | corresponding <br>JI intervals | |||
5 | ! | comments | ||
|- | |||
6 | ! colspan="2" | 0 | ||
| | '''exact [[1/1]]''' | |||
7 | | | | ||
|- | |||
8 | | | 1 | ||
| | 58.49625 | |||
9 | | | [[28/27]], 91/88, 88/85 | ||
| | | |||
10 | |- | ||
| | 2 | |||
11 | | | 116.9925 | ||
| | [[15/14]] | |||
12 | | | | ||
|- | |||
| | 3 | |||
| | 175.48875 | |||
| | [[10/9]], [[21/19]] | |||
| | | |||
|- | |||
| | 4 | |||
| | 233.9850 | |||
| | [[8/7]] | |||
| | | |||
|- | |||
| | 5 | |||
| | 292.48125 | |||
| | 45/38 | |||
| | | |||
|- | |||
| | 6 | |||
| | 350.9775 | |||
| | [[11/9]], [[27/22]] | |||
| | | |||
|- | |||
| | 7 | |||
| | 409.47375 | |||
| | [[19/15]], [[63/50]] | |||
| | | |||
|- | |||
| | 8 | |||
| | 467.9700 | |||
| | [[21/16]] | |||
| | | |||
|- | |||
| | 9 | |||
| | 526.46625 | |||
| | [[19/14]] | |||
| | | |||
|- | |||
| | 10 | |||
| | 584.9625 | |||
| | [[7/5]] | |||
| | | |||
|- | |||
| | 11 | |||
| | 643.4588 | |||
| | [[13/9]] | |||
| | | |||
|- | |||
| | 12 | |||
| | 701.9550 | |||
| | '''exact [[3/2]]''' | |||
| | just perfect fifth | |||
|- | |||
|13 | |||
|760.45125 | |||
|273/176, 132/85 | |||
| | |||
|- | |||
|14 | |||
|818.9475 | |||
|8/5 | |||
| | |||
|- | |||
|15 | |||
|877.44375 | |||
|63/38 | |||
| | |||
|- | |||
|16 | |||
|935.94 | |||
|12/7 | |||
| | |||
|- | |||
|17 | |||
|994.43625 | |||
|135/76 | |||
| | |||
|- | |||
|18 | |||
|1052.9325 | |||
|11/6, 81/44 | |||
| | |||
|- | |||
|19 | |||
|1111.42875 | |||
|19/10 | |||
| | |||
|- | |||
|20 | |||
|1169.925 | |||
|63/32 | |||
| | |||
|- | |||
|21 | |||
|1228.42125 | |||
|57/28 | |||
| | |||
|- | |||
|22 | |||
|1286.9175 | |||
|21/10 | |||
| | |||
|- | |||
|23 | |||
|1345.41375 | |||
|13/6 | |||
| | |||
|- | |||
|24 | |||
|1403.91 | |||
|'''exact''' 9/4 | |||
| | |||
|} | |||
{{todo|expand}} | |||