1749edo

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← 1748edo1749edo1750edo →
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

1749 equal divisions of the octave (abbreviated 1749edo), or 1749-tone equal temperament (1749tet), 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 of 1749edo 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.


Approximation of prime harmonics in 1749edo
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)