2549edo

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2549edo

2550edo →

Prime factorization	2549 (prime)
Step size	0.470773 ¢
Fifth	1491\2549 (701.922 ¢)
Semitones (A1:m2)	241:192 (113.5 ¢ : 90.39 ¢)
Consistency limit	7
Distinct consistency limit	7

2549 equal divisions of the octave (abbreviated 2549edo or 2549ed2), also called 2549-tone equal temperament (2549tet) or 2549 equal temperament (2549et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2549 equal parts of about 0.471 ¢ each. Each step represents a frequency ratio of 2^1/2549, or the 2549th root of 2.

Theory

2549edo is consistent to the 7-odd-limit, tempering out 43046721/43025920, [28 7 -12 -4⟩ and [-14 4 -10 11⟩. It is strong in the 2.3.7.11.17.19.29 subgroup, tempering out 5832/5831, 23409/23408, 69632/69629, 2910897/2910208, 19267919/19267584 and 424589/424536. Using the 2.3.7.11.17.19.41 subgroup, it tempers out 8569/8568.

Prime harmonics

Approximation of prime harmonics in 2549edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.033	+0.191	+0.025	-0.043	-0.198	+0.027	+0.015	+0.207	+0.003	-0.116
	Relative (%)	+0.0	-6.9	+40.5	+5.2	-9.1	-42.1	+5.7	+3.3	+44.1	+0.6	-24.6
Steps (reduced)		2549 (0)	4040 (1491)	5919 (821)	7156 (2058)	8818 (1171)	9432 (1785)	10419 (223)	10828 (632)	11531 (1335)	12383 (2187)	12628 (2432)

Subsets and supersets

2549edo is the 373rd prime edo. 5098edo, which doubles it, gives a good correction to the harmonic 5.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[-4040 2549⟩	[⟨2549 4040]]	0.0103	0.0103	2.19

Music

Francium

• "Cats Play Soccer" from Microtonal Six-Dimensional Cats (2025) – Spotify | Bandcamp | YouTube