# 1749edo

 ← 1748edo 1749edo 1750edo →
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 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.

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 (%) +0.0 -9.9 -5.2 -6.4 +45.4 -6.9 +2.7 +37.5 +29.0 +39.1 +11.1
Steps
(reduced)
1749
(0)
2772
(1023)
4061
(563)
4910
(1412)
6051
(804)
6472
(1225)
7149
(153)
7430
(434)
7912
(916)
8497
(1501)
8665
(1669)