249edo

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← 248edo249edo250edo →
Prime factorization 3 × 83
Step size 4.81928¢ 
Fifth 146\249 (703.614¢)
Semitones (A1:m2) 26:17 (125.3¢ : 81.93¢)
Dual sharp fifth 146\249 (703.614¢)
Dual flat fifth 145\249 (698.795¢)
Dual major 2nd 42\249 (202.41¢) (→14\83)
Consistency limit 3
Distinct consistency limit 3

249 equal divisions of the octave (abbreviated 249edo or 249ed2), also called 249-tone equal temperament (249tet) or 249 equal temperament (249et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 249 equal parts of about 4.82 ¢ each. Each step represents a frequency ratio of 21/249, or the 249th root of 2.

249edo is inconsistent in the 5-odd-limit and there are a number of mappings to be considered, in particular, a sharp tending mapping for the 2.3.5.7.17.19 subgroup, and a flat-tending mapping for the 2.9.5.7.11.13 subgroup.

In the 249bcee val, it is a tuning for the diesic temperament.

Odd harmonics

Approximation of odd harmonics in 249edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +1.66 -0.77 -0.15 -1.50 -1.92 -1.97 +0.89 +1.07 +1.28 +1.51 -1.77
Relative (%) +34.4 -16.0 -3.1 -31.1 -39.8 -40.9 +18.4 +22.2 +26.6 +31.3 -36.7
Steps
(reduced)
395
(146)
578
(80)
699
(201)
789
(42)
861
(114)
921
(174)
973
(226)
1018
(22)
1058
(62)
1094
(98)
1126
(130)