30ed5/2

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30ed5/2

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Prime factorization	2 × 3 × 5
Step size	52.8771¢
Octave	23\30ed5/2 (1216.17¢)
Twelfth	36\30ed5/2 (1903.58¢) (→6\5ed5/2)
Consistency limit	3
Distinct consistency limit	3

30 equal divisions of 5/2 (abbreviated 30ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 30 equal parts of about 52.9 ¢ each. Each step represents a frequency ratio of (5/2)^1/30, or the 30th root of 5/2.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	52.877
2	105.754	18/17
3	158.631	11/10, 12/11, 23/21
4	211.508	17/15, 25/22, 26/23
5	264.386	7/6
6	317.263	6/5
7	370.14	21/17, 26/21
8	423.017	14/11, 23/18
9	475.894
10	528.771	15/11, 23/17
11	581.648	7/5
12	634.525	13/9
13	687.403
14	740.28	23/15, 26/17
15	793.157	27/17
16	846.034	18/11
17	898.911
18	951.788	26/15
19	1004.665	25/14
20	1057.542	11/6
21	1110.42	17/9, 21/11
22	1163.297
23	1216.174
24	1269.051	23/11, 25/12, 27/13
25	1321.928	15/7
26	1374.805	11/5
27	1427.682	25/11
28	1480.559	26/11
29	1533.437	17/7
30	1586.314	5/2

Harmonics

Approximation of harmonics in 30ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+16.2	+1.6	-20.5	+16.2	+17.8	+15.3	-4.4	+3.2	-20.5	+26.0	-18.9
	Relative (%)	+30.6	+3.1	-38.8	+30.6	+33.7	+29.0	-8.2	+6.1	-38.8	+49.1	-35.8
Steps (reduced)		23 (23)	36 (6)	45 (15)	53 (23)	59 (29)	64 (4)	68 (8)	72 (12)	75 (15)	79 (19)	81 (21)

Approximation of harmonics in 30ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+1.2	-21.4	+17.8	+11.8	+12.6	+19.4	-21.3	-4.4	+16.9	-10.7	+18.1
	Relative (%)	+2.2	-40.5	+33.7	+22.4	+23.9	+36.7	-40.3	-8.2	+32.0	-20.3	+34.2
Steps (reduced)		84 (24)	86 (26)	89 (29)	91 (1)	93 (3)	95 (5)	96 (6)	98 (8)	100 (10)	101 (11)	103 (13)