72edt

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← 71edt

72edt

73edt →

Prime factorization	23 × 32
Step size	26.416¢
Octave	45\72edt (1188.72¢) (→5\8edt)
Consistency limit	2
Distinct consistency limit	2

72 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 72edt or 72ed3), is a nonoctave tuning system that divides the interval of 3/1 into 72 equal parts of about 26.4 ¢ each. Each step represents a frequency ratio of 3^1/72, or the 72nd root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	26.416
2	52.832	34/33, 35/34
3	79.248	23/22
4	105.664	33/31
5	132.08
6	158.496	34/31
7	184.912
8	211.328	26/23, 35/31
9	237.744	31/27
10	264.16
11	290.576	13/11
12	316.993	6/5
13	343.409	28/23
14	369.825
15	396.241	34/27
16	422.657	23/18, 37/29
17	449.073	35/27
18	475.489
19	501.905
20	528.321	19/14
21	554.737
22	581.153
23	607.569	27/19
24	633.985	13/9, 36/25
25	660.401	19/13, 22/15
26	686.817
27	713.233
28	739.649	23/15
29	766.065	14/9
30	792.481
31	818.897
32	845.313	31/19
33	871.729	38/23
34	898.145
35	924.561	29/17
36	950.978	26/15
37	977.394	37/21
38	1003.81	34/19
39	1030.226
40	1056.642	35/19
41	1083.058	28/15
42	1109.474
43	1135.89	27/14
44	1162.306
45	1188.722
46	1215.138
47	1241.554
48	1267.97	25/12, 27/13
49	1294.386	19/9
50	1320.802
51	1347.218	37/17
52	1373.634	31/14
53	1400.05
54	1426.466
55	1452.882
56	1479.298
57	1505.714	31/13
58	1532.13
59	1558.546
60	1584.963	5/2
61	1611.379	33/13, 38/15
62	1637.795
63	1664.211	34/13
64	1690.627
65	1717.043	35/13
66	1743.459
67	1769.875
68	1796.291	31/11
69	1822.707
70	1849.123
71	1875.539
72	1901.955	3/1

Harmonics

Approximation of harmonics in 72edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-11.3	+0.0	+3.9	-12.6	-11.3	+12.4	-7.4	+0.0	+2.5	-4.0	+3.9
	Relative (%)	-42.7	+0.0	+14.6	-47.8	-42.7	+47.0	-28.1	+0.0	+9.5	-15.1	+14.6
Steps (reduced)		45 (45)	72 (0)	91 (19)	105 (33)	117 (45)	128 (56)	136 (64)	144 (0)	151 (7)	157 (13)	163 (19)

Approximation of harmonics in 72edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.6	+1.1	-12.6	+7.7	+8.4	-11.3	+0.8	-8.8	+12.4	+11.1	-13.0
	Relative (%)	-10.0	+4.4	-47.8	+29.2	+31.9	-42.7	+3.0	-33.2	+47.0	+42.2	-49.2
Steps (reduced)		168 (24)	173 (29)	177 (33)	182 (38)	186 (42)	189 (45)	193 (49)	196 (52)	200 (56)	203 (59)	205 (61)