30ed5/4

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30ed5/4

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Prime factorization	2 × 3 × 5
Step size	12.8771¢
Octave	93\30ed5/4 (1197.57¢) (→31\10ed5/4)
Twelfth	148\30ed5/4 (1905.81¢) (→74\15ed5/4)
Consistency limit	3
Distinct consistency limit	3

30 equal divisions of 5/4 (abbreviated 30ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 30 equal parts of about 12.9 ¢ each. Each step represents a frequency ratio of (5/4)^1/30, or the 30th root of 5/4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	12.9
2	25.8
3	38.6
4	51.5
5	64.4	24/23, 25/24
6	77.3	26/25
7	90.1	19/18
8	103	16/15, 18/17
9	115.9	15/14
10	128.8	14/13
11	141.6	13/12
12	154.5	12/11, 23/21
13	167.4	11/10
14	180.3	21/19
15	193.2	19/17
16	206	26/23
17	218.9	17/15, 25/22
18	231.8
19	244.7	15/13, 22/19
20	257.5
21	270.4	7/6
22	283.3	27/23
23	296.2	13/11
24	309.1
25	321.9	6/5
26	334.8	17/14, 23/19
27	347.7
28	360.6	26/21
29	373.4	21/17
30	386.3	5/4

Harmonics

Approximation of harmonics in 30ed5/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.43	+3.86	-4.85	-4.85	+1.43	+4.98	+5.59	-5.16	+5.59	-4.88	-1.00
	Relative (%)	-18.9	+30.0	-37.7	-37.7	+11.1	+38.7	+43.4	-40.1	+43.4	-37.9	-7.7
Steps (reduced)		93 (3)	148 (28)	186 (6)	216 (6)	241 (1)	262 (22)	280 (10)	295 (25)	310 (10)	322 (22)	334 (4)

Approximation of harmonics in 30ed5/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.08	+2.55	-1.00	+3.17	+1.23	+5.29	+1.83	+3.17	-4.04	+5.57	+5.87
	Relative (%)	+16.2	+19.8	-7.7	+24.6	+9.5	+41.1	+14.2	+24.6	-31.4	+43.2	+45.6
Steps (reduced)		345 (15)	355 (25)	364 (4)	373 (13)	381 (21)	389 (29)	396 (6)	403 (13)	409 (19)	416 (26)	422 (2)