70edt

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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	Approximate Ratios
0	0	1/1
1	27.171
2	54.342	31/30, 34/33
3	81.512	21/20, 22/21
4	108.683	33/31
5	135.854	13/12
6	163.025	11/10, 34/31
7	190.196	19/17
8	217.366	17/15
9	244.537	23/20
10	271.708	34/29
11	298.879
12	326.049	35/29
13	353.22	27/22
14	380.391
15	407.562	19/15
16	434.733	9/7
17	461.903	30/23
18	489.074
19	516.245	27/20, 31/23
20	543.416	37/27
21	570.587
22	597.757
23	624.928	33/23
24	652.099
25	679.27	34/23
26	706.44
27	733.611	29/19
28	760.782	31/20
29	787.953	30/19
30	815.124
31	842.294	13/8
32	869.465	33/20
33	896.636	37/22
34	923.807	29/17
35	950.978
36	978.148	37/21
37	1005.319	34/19
38	1032.49	20/11
39	1059.661	24/13, 35/19
40	1086.831
41	1114.002	19/10
42	1141.173	29/15
43	1168.344
44	1195.515
45	1222.685
46	1249.856	35/17, 37/18
47	1277.027	23/11
48	1304.198
49	1331.369	28/13
50	1358.539
51	1385.71	20/9
52	1412.881
53	1440.052	23/10
54	1467.222	7/3
55	1494.393
56	1521.564
57	1548.735	22/9
58	1575.906
59	1603.076
60	1630.247
61	1657.418
62	1684.589	37/14
63	1711.76
64	1738.93	30/11
65	1766.101	36/13
66	1793.272	31/11
67	1820.443	20/7
68	1847.613
69	1874.784
70	1901.955	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)