74edt

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74edt

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Prime factorization	2 × 37
Step size	25.7021¢
Octave	47\74edt (1208¢)
Consistency limit	2
Distinct consistency limit	2

74 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 74edt or 74ed3), is a nonoctave tuning system that divides the interval of 3/1 into 74 equal parts of about 25.7⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/74, or the 74th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	25.7	17.6
2	51.4	35.1	34/33
3	77.1	52.7
4	102.8	70.3
5	128.5	87.8	14/13
6	154.2	105.4	23/21
7	179.9	123	10/9
8	205.6	140.5
9	231.3	158.1
10	257	175.7
11	282.7	193.2	20/17, 33/28
12	308.4	210.8	37/31
13	334.1	228.4	17/14, 23/19
14	359.8	245.9	37/30
15	385.5	263.5
16	411.2	281.1	19/15, 33/26
17	436.9	298.6	9/7
18	462.6	316.2	17/13, 30/23
19	488.3	333.8
20	514	351.4	31/23
21	539.7	368.9
22	565.4	386.5	18/13
23	591.1	404.1	38/27
24	616.9	421.6	10/7
25	642.6	439.2	29/20
26	668.3	456.8
27	694	474.3
28	719.7	491.9
29	745.4	509.5	20/13
30	771.1	527
31	796.8	544.6
32	822.5	562.2	29/18, 37/23
33	848.2	579.7	31/19
34	873.9	597.3
35	899.6	614.9
36	925.3	632.4	29/17
37	951	650
38	976.7	667.6
39	1002.4	685.1
40	1028.1	702.7	38/21
41	1053.8	720.3
42	1079.5	737.8
43	1105.2	755.4
44	1130.9	773
45	1156.6	790.5	37/19
46	1182.3	808.1
47	1208	825.7
48	1233.7	843.2
49	1259.4	860.8	29/14, 31/15
50	1285.1	878.4	21/10
51	1310.8	895.9
52	1336.5	913.5	13/6
53	1362.2	931.1
54	1387.9	948.6	29/13
55	1413.6	966.2
56	1439.3	983.8	23/10
57	1465	1001.4	7/3
58	1490.7	1018.9	26/11
59	1516.4	1036.5
60	1542.1	1054.1
61	1567.8	1071.6
62	1593.5	1089.2
63	1619.2	1106.8	28/11
64	1644.9	1124.3
65	1670.6	1141.9
66	1696.3	1159.5
67	1722	1177	27/10
68	1747.7	1194.6
69	1773.4	1212.2
70	1799.1	1229.7
71	1824.8	1247.3
72	1850.6	1264.9
73	1876.3	1282.4
74	1902	1300	3/1

Harmonics

Approximation of harmonics in 74edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+8.0	+0.0	-9.7	-10.5	+8.0	-1.9	-1.7	+0.0	-2.5	+12.4	-9.7
	Relative (%)	+31.1	+0.0	-37.8	-40.8	+31.1	-7.2	-6.6	+0.0	-9.7	+48.3	-37.8
Steps (reduced)		47 (47)	74 (0)	93 (19)	108 (34)	121 (47)	131 (57)	140 (66)	148 (0)	155 (7)	162 (14)	167 (19)

Approximation of harmonics in 74edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.9	+6.1	-10.5	+6.3	+4.1	+8.0	-8.5	+5.5	-1.9	-5.3	-5.1
	Relative (%)	+23.1	+23.9	-40.8	+24.5	+16.1	+31.1	-33.1	+21.4	-7.2	-20.6	-20.0
Steps (reduced)		173 (25)	178 (30)	182 (34)	187 (39)	191 (43)	195 (47)	198 (50)	202 (54)	205 (57)	208 (60)	211 (63)