72edt

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72edt

73edt →

Prime factorization	23 × 32
Step size	26.416 ¢
Octave	45\72edt (1188.72 ¢) (→ 5\8edt)
Consistency limit	3
Distinct consistency limit	3

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	Hekts	Approximate ratios
0	0	0	1/1
1	26.4	18.1
2	52.8	36.1	34/33, 35/34
3	79.2	54.2	23/22
4	105.7	72.2	33/31
5	132.1	90.3
6	158.5	108.3	34/31
7	184.9	126.4
8	211.3	144.4	26/23, 35/31
9	237.7	162.5	31/27
10	264.2	180.6
11	290.6	198.6	13/11
12	317	216.7	6/5
13	343.4	234.7	28/23
14	369.8	252.8
15	396.2	270.8	34/27
16	422.7	288.9	23/18, 37/29
17	449.1	306.9	35/27
18	475.5	325
19	501.9	343.1
20	528.3	361.1	19/14
21	554.7	379.2
22	581.2	397.2
23	607.6	415.3	27/19
24	634	433.3	13/9, 36/25
25	660.4	451.4	19/13, 22/15
26	686.8	469.4
27	713.2	487.5
28	739.6	505.6	23/15
29	766.1	523.6	14/9
30	792.5	541.7
31	818.9	559.7
32	845.3	577.8	31/19
33	871.7	595.8	38/23
34	898.1	613.9
35	924.6	631.9	29/17
36	951	650	26/15
37	977.4	668.1	37/21
38	1003.8	686.1	34/19
39	1030.2	704.2
40	1056.6	722.2	35/19
41	1083.1	740.3	28/15
42	1109.5	758.3
43	1135.9	776.4	27/14
44	1162.3	794.4
45	1188.7	812.5
46	1215.1	830.6
47	1241.6	848.6
48	1268	866.7	25/12, 27/13
49	1294.4	884.7	19/9
50	1320.8	902.8
51	1347.2	920.8	37/17
52	1373.6	938.9	31/14
53	1400.1	956.9
54	1426.5	975
55	1452.9	993.1
56	1479.3	1011.1
57	1505.7	1029.2	31/13
58	1532.1	1047.2
59	1558.5	1065.3
60	1585	1083.3	5/2
61	1611.4	1101.4	33/13, 38/15
62	1637.8	1119.4
63	1664.2	1137.5	34/13
64	1690.6	1155.6
65	1717	1173.6	35/13
66	1743.5	1191.7
67	1769.9	1209.7
68	1796.3	1227.8	31/11
69	1822.7	1245.8
70	1849.1	1263.9
71	1875.5	1281.9
72	1902	1300	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)