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 58.49625 [[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 temperament]], which tempers out 3087/3125 and 10976/10935 in the 7-limit. | '''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. | ||
==Intervals== | ==Intervals== | ||
Revision as of 18:50, 11 April 2024
| ← 11edf | 12edf | 13edf → |
12EDF is the equal division of the just perfect fifth into 12 parts of 58.49625 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 dodecacot temperament, which tempers out 3087/3125 and 10976/10935 in the 7-limit.
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | exact 1/1 | ||
| 1 | 58.49625 | 28/27, 91/88, 88/85 | |
| 2 | 116.9925 | 15/14 | |
| 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 | |