49ed7/3

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49ed7/3

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Prime factorization	72
Step size	29.9361¢
Octave	40\49ed7/3 (1197.45¢) (semiconvergent)
Twelfth	64\49ed7/3 (1915.91¢)
Consistency limit	2
Distinct consistency limit	2

49 equal divisions of 7/3 (abbreviated 49ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 49 equal parts of about 29.9 ¢ each. Each step represents a frequency ratio of (7/3)^1/49, or the 49th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	29.9
2	59.9	29/28, 30/29, 31/30
3	89.8	20/19
4	119.7	15/14, 31/29
5	149.7	12/11, 25/23
6	179.6	31/28
7	209.6	26/23
8	239.5	23/20
9	269.4	7/6
10	299.4	19/16
11	329.3	23/19, 29/24
12	359.2	16/13
13	389.2	5/4
14	419.1	14/11
15	449	13/10, 22/17
16	479	25/19, 29/22
17	508.9
18	538.9	15/11, 26/19
19	568.8	32/23
20	598.7	17/12, 24/17, 31/22
21	628.7	23/16
22	658.6	19/13, 22/15
23	688.5
24	718.5
25	748.4	17/11, 20/13
26	778.3	11/7
27	808.3	8/5
28	838.2	13/8
29	868.1	28/17
30	898.1	32/19
31	928	12/7, 29/17
32	958
33	987.9	23/13, 30/17
34	1017.8
35	1047.8	11/6
36	1077.7	28/15
37	1107.6	19/10
38	1137.6	25/13, 29/15
39	1167.5
40	1197.4	2/1
41	1227.4
42	1257.3	29/14, 31/15
43	1287.3
44	1317.2	15/7
45	1347.1	24/11
46	1377.1	31/14
47	1407
48	1436.9	23/10
49	1466.9	7/3

Harmonics

Approximation of harmonics in 49ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.6	+14.0	-5.1	-2.3	+11.4	+14.0	-7.7	-2.0	-4.8	+9.8	+8.8
	Relative (%)	-8.5	+46.6	-17.1	-7.5	+38.1	+46.6	-25.6	-6.7	-16.1	+32.8	+29.6
Steps (reduced)		40 (40)	64 (15)	80 (31)	93 (44)	104 (6)	113 (15)	120 (22)	127 (29)	133 (35)	139 (41)	144 (46)

Approximation of harmonics in 49ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-10.0	+11.4	+11.7	-10.2	+4.6	-4.6	-8.4	-7.4	-2.0	+7.3	-9.8
	Relative (%)	-33.3	+38.1	+39.1	-34.1	+15.3	-15.3	-28.0	-24.6	-6.7	+24.2	-32.8
Steps (reduced)		148 (1)	153 (6)	157 (10)	160 (13)	164 (17)	167 (20)	170 (23)	173 (26)	176 (29)	179 (32)	181 (34)