36ed7/3

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36ed7/3

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Prime factorization	22 × 32
Step size	40.7464¢
Octave	29\36ed7/3 (1181.65¢)
Twelfth	47\36ed7/3 (1915.08¢)
Consistency limit	2
Distinct consistency limit	2
Special properties	Highly composite

36 equal divisions of 7/3 (abbreviated 36ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 36 equal parts of about 40.7⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/36, or the 36th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	40.7
2	81.5	23/22
3	122.2	14/13, 15/14
4	163
5	203.7	28/25
6	244.5	15/13
7	285.2	13/11
8	326	23/19
9	366.7
10	407.5	19/15, 29/23
11	448.2	22/17
12	489
13	529.7	15/11, 19/14, 23/17
14	570.4	18/13
15	611.2
16	651.9	19/13
17	692.7
18	733.4	23/15, 26/17, 29/19
19	774.2
20	814.9
21	855.7	18/11, 23/14
22	896.4
23	937.2
24	977.9
25	1018.7
26	1059.4
27	1100.2
28	1140.9	29/15
29	1181.6
30	1222.4
31	1263.1	25/12, 29/14
32	1303.9
33	1344.6	13/6
34	1385.4	29/13
35	1426.1
36	1466.9	7/3

Harmonics

Approximation of harmonics in 36ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-18.4	+13.1	+4.0	-15.6	-5.2	+13.1	-14.3	-14.5	+6.8	+4.8	+17.2
	Relative (%)	-45.0	+32.2	+9.9	-38.2	-12.8	+32.2	-35.1	-35.6	+16.8	+11.8	+42.1
Steps (reduced)		29 (29)	47 (11)	59 (23)	68 (32)	76 (4)	83 (11)	88 (16)	93 (21)	98 (26)	102 (30)	106 (34)

Approximation of harmonics in 36ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+0.8	-5.2	-2.4	+8.1	-15.4	+7.9	-4.2	-11.5	-14.5	-13.5	-9.0
	Relative (%)	+2.0	-12.8	-6.0	+19.8	-37.8	+19.4	-10.3	-28.3	-35.6	-33.2	-22.1
Steps (reduced)		109 (1)	112 (4)	115 (7)	118 (10)	120 (12)	123 (15)	125 (17)	127 (19)	129 (21)	131 (23)	133 (25)