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Created page with "'''Division of the just perfect fifth into 41 equal parts''' (41EDF) is related to 70 edo, but with the 3/2 rather than the 2/1 being just. The octave is abo..." Tags: Mobile edit Mobile web edit |
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'''[[EDF|Division of the just perfect fifth]] into 41 equal parts''' (41EDF) is related to [[70edo | {{Infobox ET}} | ||
'''[[EDF|Division of the just perfect fifth]] into 41 equal parts''' (41EDF) is related to [[70edo]], but with the [[3/2]] rather than the [[2/1]] being [[just]]. The [[octave]] is [[Octave shrinking|compressed]] by about 1.5402 [[cents]] and the step size is about 17.1209 cents. | |||
Unlike 70edo, it is only consistent up to the 7-[[integer-limit]], with discrepancy for the 8th harmonic (three octaves). | |||
Lookalikes: [[70edo]], [[111edt]] | Lookalikes: [[70edo]], [[111edt]] | ||
== Harmonics == | |||
{{Harmonics in equal|41|3|2|intervals=prime}} | |||
{{Harmonics in equal|41|3|2|intervals=prime|start=12|collapsed=yes}} | |||
{{stub}} | |||
Latest revision as of 19:22, 1 August 2025
| ← 40edf | 41edf | 42edf → |
Division of the just perfect fifth into 41 equal parts (41EDF) is related to 70edo, but with the 3/2 rather than the 2/1 being just. The octave is compressed by about 1.5402 cents and the step size is about 17.1209 cents.
Unlike 70edo, it is only consistent up to the 7-integer-limit, with discrepancy for the 8th harmonic (three octaves).
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.54 | -1.54 | +4.39 | +3.98 | -8.07 | -6.23 | -8.39 | +4.50 | -0.96 | -8.49 | -4.10 |
| Relative (%) | -9.0 | -9.0 | +25.6 | +23.3 | -47.1 | -36.4 | -49.0 | +26.3 | -5.6 | -49.6 | -23.9 | |
| Steps (reduced) |
70 (29) |
111 (29) |
163 (40) |
197 (33) |
242 (37) |
259 (13) |
286 (40) |
298 (11) |
317 (30) |
340 (12) |
347 (19) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.23 | +8.38 | -5.59 | -5.49 | -8.04 | -5.38 | +5.39 | -2.94 | -0.61 | +2.66 | +2.88 |
| Relative (%) | -13.0 | +48.9 | -32.7 | -32.1 | -47.0 | -31.4 | +31.5 | -17.2 | -3.6 | +15.5 | +16.8 | |
| Steps (reduced) |
365 (37) |
376 (7) |
380 (11) |
389 (20) |
401 (32) |
412 (2) |
416 (6) |
425 (15) |
431 (21) |
434 (24) |
442 (32) | |
|
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