249edo

← 248edo

249edo

250edo →

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 2^1/249, 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.

It is part of the optimal ET sequence for the diesic and undecimal magic temperaments.

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)