102557edo
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Prime factorization
73 × 13 × 23
Step size
0.0117008¢
Fifth
59992\102557 (701.955¢)
Semitones (A1:m2)
9716:7711 (113.7¢ : 90.22¢)
Consistency limit
39
Distinct consistency limit
39
Special properties
| ← 102556edo | 102557edo | 102558edo → |
102557 equal divisions of the octave (abbreviated 102557edo or 102557ed2), also called 102557-tone equal temperament (102557tet) or 102557 equal temperament (102557et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 102557 equal parts of about 0.0117 ¢ each. Each step represents a frequency ratio of 21/102557, or the 102557th root of 2.
102557edo is notable for being a good high-limit system, and specializes in the 17-limit with a lower relative error than any smaller equal temperaments. It is consistent to the 39-odd-limit and is the first non-trivial edo to be consistent in the 32-odd-prime-sum-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00000 | +0.00001 | +0.00024 | +0.00118 | +0.00084 | +0.00004 | +0.00086 | +0.00349 | +0.00066 | +0.00050 | +0.00572 | +0.00107 | -0.00539 | -0.00508 | +0.00036 |
| Relative (%) | +0.0 | +0.1 | +2.0 | +10.1 | +7.1 | +0.4 | +7.3 | +29.8 | +5.6 | +4.3 | +48.9 | +9.1 | -46.1 | -43.4 | +3.1 | |
| Steps (reduced) |
102557 (0) |
162549 (59992) |
238130 (33016) |
287914 (82800) |
354789 (47118) |
379506 (71835) |
419198 (8970) |
435655 (25427) |
463923 (53695) |
498220 (87992) |
508088 (97860) |
534266 (21481) |
549454 (36669) |
556501 (43716) |
569662 (56877) | |