36ed7/4

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36ed7/4

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Prime factorization	22 × 32
Step size	26.9118¢
Octave	45\36ed7/4 (1211.03¢) (→5\4ed7/4)
Twelfth	71\36ed7/4 (1910.74¢)
Consistency limit	3
Distinct consistency limit	3
Special properties	Highly composite

36 equal divisions of 7/4 (abbreviated 36ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 36 equal parts of about 26.9⁠ ⁠¢ each. Each step represents a frequency ratio of (7/4)^1/36, or the 36th root of 7/4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	26.9
2	53.8	29/28
3	80.7	22/21, 23/22
4	107.6
5	134.6	14/13, 27/25
6	161.5	23/21
7	188.4	10/9, 19/17, 28/25, 29/26
8	215.3	26/23
9	242.2
10	269.1
11	296	13/11
12	322.9	6/5
13	349.9
14	376.8	26/21
15	403.7	29/23
16	430.6
17	457.5	17/13
18	484.4	29/22
19	511.3
20	538.2
21	565.1	25/18, 29/21
22	592.1
23	619
24	645.9
25	672.8
26	699.7	3/2
27	726.6
28	753.5	17/11
29	780.4	11/7
30	807.4
31	834.3	21/13
32	861.2	23/14
33	888.1	5/3
34	915	22/13
35	941.9	19/11
36	968.8

Harmonics

Approximation of harmonics in 36ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+11.0	+8.8	-4.8	+12.5	-7.1	-4.8	+6.2	-9.3	-3.4	-6.9	+3.9
	Relative (%)	+41.0	+32.6	-18.0	+46.5	-26.4	-18.0	+23.0	-34.7	-12.5	-25.6	+14.6
Steps (reduced)		45 (9)	71 (35)	89 (17)	104 (32)	115 (7)	125 (17)	134 (26)	141 (33)	148 (4)	154 (10)	160 (16)

Approximation of harmonics in 36ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-0.1	+6.2	-5.6	-9.7	-7.0	+1.7	-11.2	+7.7	+3.9	+4.1	+7.9
	Relative (%)	-0.3	+23.0	-20.8	-36.0	-26.0	+6.3	-41.5	+28.5	+14.6	+15.4	+29.4
Steps (reduced)		165 (21)	170 (26)	174 (30)	178 (34)	182 (2)	186 (6)	189 (9)	193 (13)	196 (16)	199 (19)	202 (22)