49ed4

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49ed4

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Prime factorization	72
Step size	48.9796¢
Octave	25\49ed4 (1224.49¢)
Twelfth	39\49ed4 (1910.2¢)
Consistency limit	1
Distinct consistency limit	1

49 equal divisions of the 4th harmonic (abbreviated 49ed4) is a nonoctave tuning system that divides the interval of 4/1 into 49 equal parts of about 49 ¢ each. Each step represents a frequency ratio of 4^1/49, or the 49th root of 4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	49
2	98
3	146.9	25/23
4	195.9	19/17
5	244.9	15/13
6	293.9	13/11
7	342.9	11/9
8	391.8
9	440.8
10	489.8
11	538.8	15/11
12	587.8	7/5
13	636.7	13/9
14	685.7
15	734.7	23/15, 29/19
16	783.7	11/7
17	832.7	21/13
18	881.6	5/3
19	930.6
20	979.6
21	1028.6
22	1077.6
23	1126.5	25/13
24	1175.5
25	1224.5
26	1273.5	23/11
27	1322.4	15/7
28	1371.4
29	1420.4	25/11
30	1469.4	7/3
31	1518.4
32	1567.3
33	1616.3
34	1665.3
35	1714.3	27/10
36	1763.3	25/9
37	1812.2
38	1861.2
39	1910.2
40	1959.2
41	2008.2
42	2057.1	23/7
43	2106.1
44	2155.1
45	2204.1	25/7
46	2253.1	11/3
47	2302
48	2351
49	2400

Harmonics

Approximation of harmonics in 49ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+24.5	+8.2	+0.0	+5.5	-16.2	+10.8	+24.5	+16.5	-19.0	+11.9	+8.2
	Relative (%)	+50.0	+16.8	+0.0	+11.3	-33.2	+22.0	+50.0	+33.7	-38.7	+24.4	+16.8
Steps (reduced)		25 (25)	39 (39)	49 (0)	57 (8)	63 (14)	69 (20)	74 (25)	78 (29)	81 (32)	85 (36)	88 (39)

Approximation of harmonics in 49ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+16.6	-13.7	+13.8	+0.0	-7.0	-8.0	-3.6	+5.5	+19.0	-12.5	+8.5
	Relative (%)	+33.9	-28.0	+28.1	+0.0	-14.3	-16.3	-7.4	+11.3	+38.8	-25.6	+17.3
Steps (reduced)		91 (42)	93 (44)	96 (47)	98 (0)	100 (2)	102 (4)	104 (6)	106 (8)	108 (10)	109 (11)	111 (13)