36ed12

← 35ed12

36ed12

37ed12 →

Prime factorization	22 × 32
Step size	119.499 ¢
Octave	10\36ed12 (1194.99 ¢) (→ 5\18ed12)
Twelfth	16\36ed12 (1911.98 ¢) (→ 4\9ed12)
Consistency limit	9
Distinct consistency limit	5
Special properties	Highly composite

36 equal divisions of the 12th harmonic (abbreviated 36ed12) is a nonoctave tuning system that divides the interval of 12/1 into 36 equal parts of about 119 ¢ each. Each step represents a frequency ratio of 12^1/36, or the 36th root of 12.

Interval table

Steps	Cents	Approximate ratios
0	0	1/1
1	119.5	15/14, 16/15, 29/27
2	239	8/7, 23/20
3	358.5	16/13, 21/17, 27/22
4	478	21/16, 29/22
5	597.5	17/12, 24/17
6	717
7	836.5	13/8, 21/13
8	956	26/15
9	1075.5	13/7, 28/15
10	1195	2/1
11	1314.5	15/7
12	1434	16/7, 23/10
13	1553.5	22/9, 27/11
14	1673	21/8, 29/11
15	1792.5
16	1912
17	2031.5	29/9
18	2151
19	2270.5	26/7
20	2390
21	2509.5	17/4
22	2629
23	2748.5
24	2868	21/4
25	2987.5	28/5
26	3107	6/1
27	3226.5
28	3346
29	3465.5
30	3585
31	3704.5	17/2
32	3824
33	3943.5
34	4063	21/2
35	4182.5
36	4302	12/1

Harmonics

Approximation of harmonics in 36ed12

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-5.0	+10.0	-10.0	-37.8	+5.0	-22.9	-15.0	+20.0	-42.9	+31.1	+0.0
	Relative (%)	-4.2	+8.4	-8.4	-31.7	+4.2	-19.1	-12.6	+16.8	-35.9	+26.1	+0.0
Steps (reduced)		10 (10)	16 (16)	20 (20)	23 (23)	26 (26)	28 (28)	30 (30)	32 (32)	33 (33)	35 (35)	36 (0)