70edt

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← 69edt

70edt

71edt →

Prime factorization	2 × 5 × 7
Step size	27.1708¢
Octave	44\70edt (1195.51¢) (→22\35edt)
Consistency limit	4
Distinct consistency limit	4

70 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 70edt or 70ed3), is a nonoctave tuning system that divides the interval of 3/1 into 70 equal parts of about 27.2⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/70, or the 70th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	27.2	18.6
2	54.3	37.1	31/30, 34/33
3	81.5	55.7	21/20, 22/21
4	108.7	74.3	33/31
5	135.9	92.9	13/12
6	163	111.4	11/10, 34/31
7	190.2	130	19/17
8	217.4	148.6	17/15
9	244.5	167.1	23/20
10	271.7	185.7	34/29
11	298.9	204.3
12	326	222.9	35/29
13	353.2	241.4	27/22
14	380.4	260
15	407.6	278.6	19/15
16	434.7	297.1	9/7
17	461.9	315.7	30/23
18	489.1	334.3
19	516.2	352.9	27/20, 31/23
20	543.4	371.4	37/27
21	570.6	390
22	597.8	408.6
23	624.9	427.1	33/23
24	652.1	445.7
25	679.3	464.3	34/23
26	706.4	482.9
27	733.6	501.4	29/19
28	760.8	520	31/20
29	788	538.6	30/19
30	815.1	557.1
31	842.3	575.7	13/8
32	869.5	594.3	33/20
33	896.6	612.9	37/22
34	923.8	631.4	29/17
35	951	650
36	978.1	668.6	37/21
37	1005.3	687.1	34/19
38	1032.5	705.7	20/11
39	1059.7	724.3	24/13, 35/19
40	1086.8	742.9
41	1114	761.4	19/10
42	1141.2	780	29/15
43	1168.3	798.6
44	1195.5	817.1
45	1222.7	835.7
46	1249.9	854.3	35/17, 37/18
47	1277	872.9	23/11
48	1304.2	891.4
49	1331.4	910	28/13
50	1358.5	928.6
51	1385.7	947.1	20/9
52	1412.9	965.7
53	1440.1	984.3	23/10
54	1467.2	1002.9	7/3
55	1494.4	1021.4
56	1521.6	1040
57	1548.7	1058.6	22/9
58	1575.9	1077.1
59	1603.1	1095.7
60	1630.2	1114.3
61	1657.4	1132.9
62	1684.6	1151.4	37/14
63	1711.8	1170
64	1738.9	1188.6	30/11
65	1766.1	1207.1	36/13
66	1793.3	1225.7	31/11
67	1820.4	1244.3	20/7
68	1847.6	1262.9
69	1874.8	1281.4
70	1902	1300	3/1

Harmonics

Approximation of harmonics in 70edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-4.5	+0.0	-9.0	+12.3	-4.5	+0.4	-13.5	+0.0	+7.8	+5.8	-9.0
	Relative (%)	-16.5	+0.0	-33.0	+45.2	-16.5	+1.3	-49.5	+0.0	+28.7	+21.4	-33.0
Steps (reduced)		44 (44)	70 (0)	88 (18)	103 (33)	114 (44)	124 (54)	132 (62)	140 (0)	147 (7)	153 (13)	158 (18)

Approximation of harmonics in 70edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-11.7	-4.1	+12.3	+9.2	+13.0	-4.5	+10.6	+3.3	+0.4	+1.3	+5.9
	Relative (%)	-43.0	-15.2	+45.2	+34.0	+47.7	-16.5	+39.0	+12.2	+1.3	+4.9	+21.7
Steps (reduced)		163 (23)	168 (28)	173 (33)	177 (37)	181 (41)	184 (44)	188 (48)	191 (51)	194 (54)	197 (57)	200 (60)