12edf: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''12EDF''' is the [[EDF|equal division of the just perfect fifth]] into 12 parts of 58. | '''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]] (similar to every second step of [[41edo]]). 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]]. | |||
==Harmonics== | |||
{{Harmonics in equal|12|3|2}} | |||
{{Harmonics in equal|12|3|2|start=12|collapsed=1}} | |||
==Intervals== | ==Intervals== | ||
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|- | |- | ||
| | 1 | | | 1 | ||
| | 58. | | | 58.49625 | ||
| | 91/88, 88/85 | | | [[28/27]], 91/88, 88/85 | ||
| | | | | | ||
|- | |- | ||
| Line 25: | Line 31: | ||
|- | |- | ||
| | 3 | | | 3 | ||
| | 175. | | | 175.48875 | ||
| | [[21/19]] | | | [[10/9]], [[21/19]] | ||
| | | | | | ||
|- | |- | ||
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|- | |- | ||
| | 5 | | | 5 | ||
| | 292. | | | 292.48125 | ||
| | 45/38 | | | 45/38 | ||
| | | | | | ||
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|- | |- | ||
| | 7 | | | 7 | ||
| | 409. | | | 409.47375 | ||
| | [[19/15]] | | | [[19/15]], [[63/50]] | ||
| | | | | | ||
|- | |- | ||
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|- | |- | ||
| | 9 | | | 9 | ||
| | 526. | | | 526.46625 | ||
| | [[19/14]] | | | [[19/14]] | ||
| | | | | | ||
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| | 11 | | | 11 | ||
| | 643.4588 | | | 643.4588 | ||
| |13/9 | | | [[13/9]] | ||
| | | | | | ||
|- | |- | ||
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|} | |} | ||
{{todo|expand}} | |||