513edo
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Prime factorization
33 × 19
Step size
2.33918¢
Fifth
300\513 (701.754¢) (→100\171)
Semitones (A1:m2)
48:39 (112.3¢ : 91.23¢)
Consistency limit
11
Distinct consistency limit
11
| ← 512edo | 513edo | 514edo → |
513 equal divisions of the octave (abbreviated 513edo or 513ed2), also called 513-tone equal temperament (513tet) or 513 equal temperament (513et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 513 equal parts of about 2.34 ¢ each. Each step represents a frequency ratio of 21/513, or the 513th root of 2.
513edo divides the steps of 171edo into three. It is consistent to the 11-odd-limit, tempering out 4000/3993, 12005/11979, and 46656/46585 using the patent val. Using the alternative 513e val, 35937/35840, 42592/42525, and 166375/165888 are tempered out in the 11-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.20 | -0.35 | -0.40 | +0.73 | -0.76 | +0.31 | -0.44 | +0.97 | -0.34 | +1.16 |
| Relative (%) | +0.0 | -8.6 | -14.9 | -17.3 | +31.2 | -32.6 | +13.2 | -18.7 | +41.3 | -14.4 | +49.7 | |
| Steps (reduced) |
513 (0) |
813 (300) |
1191 (165) |
1440 (414) |
1775 (236) |
1898 (359) |
2097 (45) |
2179 (127) |
2321 (269) |
2492 (440) |
2542 (490) | |
Subsets and supersets
Since 513 factors into 33 × 19, 513edo has subset edos 3, 9, 19, 27, 57, and 171.