73ed4

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73ed4

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Prime factorization	73 (prime)
Step size	32.8767¢
Octave	37\73ed4 (1216.44¢)
Twelfth	58\73ed4 (1906.85¢)
Consistency limit	1
Distinct consistency limit	1

73 equal divisions of the 4th harmonic (abbreviated 73ed4) is a nonoctave tuning system that divides the interval of 4/1 into 73 equal parts of about 32.9⁠ ⁠¢ each. Each step represents a frequency ratio of 4^1/73, or the 73rd root of 4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	32.9
2	65.8	26/25, 27/26, 28/27
3	98.6	35/33, 37/35
4	131.5	14/13, 27/25
5	164.4
6	197.3	28/25, 37/33
7	230.1
8	263
9	295.9
10	328.8	23/19, 35/29
11	361.6
12	394.5
13	427.4
14	460.3
15	493.2
16	526	19/14, 23/17
17	558.9	29/21
18	591.8	31/22, 38/27
19	624.7	33/23
20	657.5	19/13
21	690.4
22	723.3	35/23, 38/25
23	756.2	17/11
24	789
25	821.9	37/23
26	854.8
27	887.7	5/3
28	920.5
29	953.4	26/15, 33/19
30	986.3	23/13
31	1019.2	9/5
32	1052.1
33	1084.9
34	1117.8	21/11
35	1150.7	33/17, 37/19
36	1183.6
37	1216.4
38	1249.3	35/17
39	1282.2
40	1315.1
41	1347.9	37/17
42	1380.8
43	1413.7	34/15
44	1446.6
45	1479.5
46	1512.3
47	1545.2	22/9
48	1578.1
49	1611	33/13, 38/15
50	1643.8
51	1676.7	29/11
52	1709.6
53	1742.5
54	1775.3
55	1808.2	37/13
56	1841.1
57	1874
58	1906.8
59	1939.7
60	1972.6
61	2005.5	35/11
62	2038.4
63	2071.2
64	2104.1
65	2137
66	2169.9
67	2202.7
68	2235.6
69	2268.5
70	2301.4	34/9
71	2334.2
72	2367.1
73	2400

Harmonics

Approximation of harmonics in 73ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+16.4	+4.9	+0.0	+8.2	-11.5	-15.4	+16.4	+9.8	-8.2	-8.9	+4.9
	Relative (%)	+50.0	+14.9	+0.0	+25.0	-35.1	-46.8	+50.0	+29.8	-25.0	-26.9	+14.9
Steps (reduced)		37 (37)	58 (58)	73 (0)	85 (12)	94 (21)	102 (29)	110 (37)	116 (43)	121 (48)	126 (53)	131 (58)

Approximation of harmonics in 73ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.2	+1.0	+13.1	+0.0	-6.3	-6.6	-1.6	+8.2	-10.5	+7.6	-3.6
	Relative (%)	-6.6	+3.2	+39.8	+0.0	-19.2	-20.2	-4.9	+25.0	-32.0	+23.1	-11.0
Steps (reduced)		135 (62)	139 (66)	143 (70)	146 (0)	149 (3)	152 (6)	155 (9)	158 (12)	160 (14)	163 (17)	165 (19)