1749edo
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Prime factorization
3 × 11 × 53
Step size
0.686106¢
Fifth
1023\1749 (701.887¢) (→31\53)
Semitones (A1:m2)
165:132 (113.2¢ : 90.57¢)
Consistency limit
9
Distinct consistency limit
9
| ← 1748edo | 1749edo | 1750edo → |
1749 equal divisions of the octave (abbreviated 1749edo or 1749ed2), also called 1749-tone equal temperament (1749tet) or 1749 equal temperament (1749et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1749 equal parts of about 0.686 ¢ each. Each step represents a frequency ratio of 21/1749, or the 1749th root of 2.
Theory
This EDO has a consistency level of only 9, nevertheless, it's well-behaved in the 2.3.5.7.13.17 subgroup.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | -0.068 | -0.036 | -0.044 | +0.312 | -0.047 | +0.019 | +0.257 | +0.199 | +0.268 | +0.076 |
| relative (%) | +0 | -10 | -5 | -6 | +45 | -7 | +3 | +37 | +29 | +39 | +11 | |
| Steps (reduced) |
1749 (0) |
2772 (1023) |
4061 (563) |
4910 (1412) |
6051 (804) |
6472 (1225) |
7149 (153) |
7430 (434) |
7912 (916) |
8497 (1501) |
8665 (1669) | |