55edf: Difference between revisions
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'''[[EDF|Division of the just perfect fifth]] into 55 equal parts''' (55EDF) is related to [[94edo | '''[[EDF|Division of the just perfect fifth]] into 55 equal parts''' (55EDF) is related to [[94edo]], but with the 3/2 rather than the 2/1 being [[just]]. The octave is [[Octave shrinking|compressed]] by about 0.2951 [[cents]] and the step size is about 12.7628 cents. | ||
It is [[consistent]] to the 24-[[integer limit]] (''which is contained within, but is not the same as, the [[23-odd-limit]]''). Its lookalikes include [[94edo]] and [[149edt]]. | |||
== Harmonics == | |||
{{Harmonics in equal|55|3|2}} | |||
{{Harmonics in equal|55|3|2|columns=12|collapsed=1|start=12}} | |||
{{todo|expand}} | |||
Latest revision as of 19:23, 1 August 2025
| ← 54edf | 55edf | 56edf → |
(semiconvergent)
(semiconvergent)
Division of the just perfect fifth into 55 equal parts (55EDF) is related to 94edo, but with the 3/2 rather than the 2/1 being just. The octave is compressed by about 0.2951 cents and the step size is about 12.7628 cents.
It is consistent to the 24-integer limit (which is contained within, but is not the same as, the 23-odd-limit). Its lookalikes include 94edo and 149edt.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.30 | -0.30 | -0.59 | -4.02 | -0.59 | +0.56 | -0.89 | -0.59 | -4.31 | -3.40 | -0.89 |
| Relative (%) | -2.3 | -2.3 | -4.6 | -31.5 | -4.6 | +4.4 | -6.9 | -4.6 | -33.8 | -26.7 | -6.9 | |
| Steps (reduced) |
94 (39) |
149 (39) |
188 (23) |
218 (53) |
243 (23) |
264 (44) |
282 (7) |
298 (23) |
312 (37) |
325 (50) |
337 (7) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.93 | +0.26 | -4.31 | -1.18 | -4.03 | -0.89 | -5.15 | -4.61 | +0.26 | -3.70 | -4.08 | -1.18 |
| Relative (%) | +7.3 | +2.1 | -33.8 | -9.2 | -31.6 | -6.9 | -40.3 | -36.1 | +2.1 | -29.0 | -31.9 | -9.2 | |
| Steps (reduced) |
348 (18) |
358 (28) |
367 (37) |
376 (46) |
384 (54) |
392 (7) |
399 (14) |
406 (21) |
413 (28) |
419 (34) |
425 (40) |
431 (46) | |