52edf
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Prime factorization
22 × 13
Step size
13.4991¢
Octave
89\52edf (1201.42¢)
Twelfth
141\52edf (1903.38¢)
Consistency limit
4
Distinct consistency limit
4
| ← 51edf | 52edf | 53edf → |
Division of the just perfect fifth into 52 equal parts (52EDF) is related to 89edo, but with the 3/2 rather than the 2/1 being just. The octave is about 1.4230 cents stretched and the step size is about 13.4991 cents.
Unlike 89edo, it is only consistent up to the 4-integer-limit, with discrepancy for the 5th harmonic.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.42 | +1.42 | -5.49 | +5.96 | +6.42 | +0.69 | -4.77 | +5.16 | -1.62 | +2.05 | -5.42 |
| Relative (%) | +10.5 | +10.5 | -40.7 | +44.1 | +47.5 | +5.1 | -35.3 | +38.2 | -12.0 | +15.2 | -40.1 | |
| Steps (reduced) |
89 (37) |
141 (37) |
206 (50) |
250 (42) |
308 (48) |
329 (17) |
363 (51) |
378 (14) |
402 (38) |
432 (16) |
440 (24) | |