30ed7/4

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30ed7/4

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Prime factorization	2 × 3 × 5
Step size	32.2942¢
Octave	37\30ed7/4 (1194.89¢)
Twelfth	59\30ed7/4 (1905.36¢)
Consistency limit	6
Distinct consistency limit	3

30 equal divisions of 7/4 (abbreviated 30ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 30 equal parts of about 32.3 ¢ each. Each step represents a frequency ratio of (7/4)^1/30, or the 30th root of 7/4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	32.3
2	64.6	24/23, 25/24, 27/26
3	96.9	18/17, 19/18
4	129.2	15/14
5	161.5	23/21
6	193.8	19/17
7	226.1	8/7, 17/15
8	258.4	7/6, 22/19
9	290.6	13/11
10	322.9	6/5, 23/19
11	355.2	11/9, 27/22
12	387.5	5/4
13	419.8	23/18
14	452.1	22/17
15	484.4
16	516.7	23/17
17	549	26/19
18	581.3	7/5
19	613.6	10/7, 27/19
20	645.9	13/9
21	678.2
22	710.5	3/2
23	742.8	23/15, 26/17
24	775.1	25/16
25	807.4	8/5, 27/17
26	839.6
27	871.9
28	904.2	22/13
29	936.5	12/7, 19/11
30	968.8	7/4

Harmonics

Approximation of harmonics in 30ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-5.1	+3.4	-10.2	-9.0	-1.7	-10.2	-15.3	+6.8	-14.1	+14.6	-6.8
	Relative (%)	-15.8	+10.5	-31.7	-27.9	-5.3	-31.7	-47.5	+21.1	-43.7	+45.3	-21.1
Steps (reduced)		37 (7)	59 (29)	74 (14)	86 (26)	96 (6)	104 (14)	111 (21)	118 (28)	123 (3)	129 (9)	133 (13)

Approximation of harmonics in 30ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+16.1	-15.3	-5.6	+11.8	+3.8	+1.7	+5.0	+13.1	-6.8	+9.5	-2.8
	Relative (%)	+49.8	-47.5	-17.4	+36.6	+11.7	+5.2	+15.4	+40.4	-21.1	+29.5	-8.8
Steps (reduced)		138 (18)	141 (21)	145 (25)	149 (29)	152 (2)	155 (5)	158 (8)	161 (11)	163 (13)	166 (16)	168 (18)