49edf: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''49EDF''' is the [[EDF|equal division of the just perfect fifth]] into 49 parts of 14.3256 [[ | '''49EDF''' is the [[EDF|equal division of the just perfect fifth]] into 49 parts of 14.3256 [[cents]] each, corresponding to 83.7661 [[edo]] (similar to every fourth step of [[335edo]]). | ||
It is related to the [[temperament]] which [[tempers out]] |71 27 -49> in the [[5-limit]], which is supported by {{EDOs|83, 84, 167, 251, 335, 419, 503, and 586}} EDOs. | |||
Lookalikes: [[84edo]], [[133edt]] | Lookalikes: [[84edo]], [[133edt]] | ||
== Harmonics == | |||
[[Subgroup]]s 49edf performs well on include the no-5s [[31-limit]], the [[Dual-n|dual-5]] 31-limit, and any subsets thereof. | |||
{{Harmonics in equal|49|3|2|intervals=prime|columns=7}} | |||
{{Harmonics in equal|49|3|2|intervals=prime|columns=7|start=8|title=(contd.)}} | |||
{{todo|expand}} | |||
[[Category:Edf]] | [[Category:Edf]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 04:21, 18 December 2024
| ← 48edf | 49edf | 50edf → |
49EDF is the equal division of the just perfect fifth into 49 parts of 14.3256 cents each, corresponding to 83.7661 edo (similar to every fourth step of 335edo).
It is related to the temperament which tempers out |71 27 -49> in the 5-limit, which is supported by 83, 84, 167, 251, 335, 419, 503, and 586 EDOs.
Harmonics
Subgroups 49edf performs well on include the no-5s 31-limit, the dual-5 31-limit, and any subsets thereof.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | |
|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.35 | +3.35 | -7.14 | -2.31 | +3.11 | +0.41 | -5.60 |
| Relative (%) | +23.4 | +23.4 | -49.9 | -16.1 | +21.7 | +2.9 | -39.1 | |
| Steps (reduced) |
84 (35) |
133 (35) |
194 (47) |
235 (39) |
290 (45) |
310 (16) |
342 (48) | |
| Harmonic | 19 | 23 | 29 | 31 | 37 | 41 | 43 | |
|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.40 | +1.13 | +0.95 | +0.09 | -5.38 | +3.14 | +6.64 |
| Relative (%) | +16.8 | +7.9 | +6.6 | +0.7 | -37.5 | +21.9 | +46.3 | |
| Steps (reduced) |
356 (13) |
379 (36) |
407 (15) |
415 (23) |
436 (44) |
449 (8) |
455 (14) | |