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	32.877
2	65.753	26/25, 27/26, 28/27
3	98.63	35/33, 37/35
4	131.507	14/13, 27/25
5	164.384
6	197.26	28/25, 37/33
7	230.137
8	263.014
9	295.89
10	328.767	23/19, 35/29
11	361.644
12	394.521
13	427.397
14	460.274
15	493.151
16	526.027	19/14, 23/17
17	558.904	29/21
18	591.781	31/22, 38/27
19	624.658	33/23
20	657.534	19/13
21	690.411
22	723.288	35/23, 38/25
23	756.164	17/11
24	789.041
25	821.918	37/23
26	854.795
27	887.671	5/3
28	920.548
29	953.425	26/15, 33/19
30	986.301	23/13
31	1019.178	9/5
32	1052.055
33	1084.932
34	1117.808	21/11
35	1150.685	33/17, 37/19
36	1183.562
37	1216.438
38	1249.315	35/17
39	1282.192
40	1315.068
41	1347.945	37/17
42	1380.822
43	1413.699	34/15
44	1446.575
45	1479.452
46	1512.329
47	1545.205	22/9
48	1578.082
49	1610.959	33/13, 38/15
50	1643.836
51	1676.712	29/11
52	1709.589
53	1742.466
54	1775.342
55	1808.219	37/13
56	1841.096
57	1873.973
58	1906.849
59	1939.726
60	1972.603
61	2005.479	35/11
62	2038.356
63	2071.233
64	2104.11
65	2136.986
66	2169.863
67	2202.74
68	2235.616
69	2268.493
70	2301.37	34/9
71	2334.247
72	2367.123
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)