49edf: Difference between revisions
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Created page with "'''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 ste..." Tags: Mobile edit Mobile web edit |
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{{Infobox ET}} | |||
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49edf corresponds to 83.7661[[edo]], similar to every fourth step of [[335edo]]. It is related to the [[temperament]] which [[tempering out|tempers out]] {{monzo| 71 27 -49 }} in the [[5-limit]], which is supported by {{EDOs| 83-, 84-, 167-, 251-, 335-, 419-, 503-, and 586edo }}. | |||
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|collapsed=true|title=Approximation of prime harmonics in 49edf (continued)}} | |||
{{Todo|expand}} | |||
Latest revision as of 17:19, 17 January 2025
| ← 48edf | 49edf | 50edf → |
49 equal divisions of the perfect fifth (abbreviated 49edf or 49ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 49 equal parts of about 14.3 ¢ each. Each step represents a frequency ratio of (3/2)1/49, or the 49th root of 3/2.
49edf corresponds to 83.7661edo, 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 586edo.
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) | |