1236edo

← 1235edo

1236edo

1237edo →

Prime factorization	22 × 3 × 103
Step size	0.970874¢
Fifth	723\1236 (701.942¢) (→241\412)
Semitones (A1:m2)	117:93 (113.6¢ : 90.29¢)
Consistency limit	17
Distinct consistency limit	17
Special properties	Zeta peak

1236 equal divisions of the octave (abbreviated 1236edo or 1236ed2), also called 1236-tone equal temperament (1236tet) or 1236 equal temperament (1236et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1236 equal parts of about 0.971 ¢ each. Each step represents a frequency ratio of 2^1/1236, or the 1236th root of 2.

1236edo is a zeta peak edo, though not zeta integral nor zeta gap. It is a strong 17-limit system and distinctly consistent through the 17-odd-limit, with a 17-limit comma basis of {2601/2600, 4096/4095, 5832/5831, 6656/6655, 9801/9800, 105644/105625}.

Prime harmonics

Approximation of prime harmonics in 1236edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.013	+0.094	+0.106	+0.138	+0.249	-0.101	-0.426	-0.119	-0.451	-0.375
	Relative (%)	+0.0	-1.4	+9.7	+10.9	+14.3	+25.7	-10.4	-43.8	-12.3	-46.5	-38.7
Steps (reduced)		1236 (0)	1959 (723)	2870 (398)	3470 (998)	4276 (568)	4574 (866)	5052 (108)	5250 (306)	5591 (647)	6004 (1060)	6123 (1179)

Subsets and supersets

Since 1236 factors into 2² × 3 × 103, 1236edo has subset edos 2, 3, 6, 12, 103, 206, 309, and 618. It is divisible by 12, and is an atomic system.