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	48.98
2	97.959
3	146.939	25/23
4	195.918	19/17
5	244.898	15/13
6	293.878	13/11
7	342.857	11/9
8	391.837
9	440.816
10	489.796
11	538.776	15/11
12	587.755	7/5
13	636.735	13/9
14	685.714
15	734.694	23/15, 29/19
16	783.673	11/7
17	832.653	21/13
18	881.633	5/3
19	930.612
20	979.592
21	1028.571
22	1077.551
23	1126.531	25/13
24	1175.51
25	1224.49
26	1273.469	23/11
27	1322.449	15/7
28	1371.429
29	1420.408	25/11
30	1469.388	7/3
31	1518.367
32	1567.347
33	1616.327
34	1665.306
35	1714.286	27/10
36	1763.265	25/9
37	1812.245
38	1861.224
39	1910.204
40	1959.184
41	2008.163
42	2057.143	23/7
43	2106.122
44	2155.102
45	2204.082	25/7
46	2253.061	11/3
47	2302.041
48	2351.02
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)