306edo

← 305edo

306edo

307edo →

Prime factorization	2 × 32 × 17
Step size	3.92157 ¢
Fifth	179\306 (701.961 ¢) (convergent)
Semitones (A1:m2)	29:23 (113.7 ¢ : 90.2 ¢)
Consistency limit	5
Distinct consistency limit	5

306 equal divisions of the octave (abbreviated 306edo or 306ed2), also called 306-tone equal temperament (306tet) or 306 equal temperament (306et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 306 equal parts of about 3.92 ¢ each. Each step represents a frequency ratio of 2^1/306, or the 306th root of 2.

306edo provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the patent val tempers out 78732/78125 (sensipent comma), whereas the alternative 306c val tempers out 32805/32768 (schisma). In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after 31\53 and before 389\665 in the sequence of continued fraction approximations to to log₂(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as 612edo.

306edo provides an excellent approximation of Valotti temperament due to its representation of the Pythagorean comma as 6 steps.

Prime harmonics

Approximation of prime harmonics in 306edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.006	+1.922	-0.198	+1.623	-1.312	+0.927	+0.526	-0.823	+1.795	+0.062
	Relative (%)	+0.0	+0.1	+49.0	-5.1	+41.4	-33.5	+23.6	+13.4	-21.0	+45.8	+1.6
Steps (reduced)		306 (0)	485 (179)	711 (99)	859 (247)	1059 (141)	1132 (214)	1251 (27)	1300 (76)	1384 (160)	1487 (263)	1516 (292)

Subsets and supersets

Since 306 factors into 2 × 3² × 17, 306edo has subset edos 2, 3, 6, 9, 17, 18, 34, 51, 102, and 153. 612edo, which doubles it, provides corrections for the 5th, 11th, and 29th harmonics.