72ed7/3

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72ed7/3

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Prime factorization	23 × 32
Step size	20.3732¢
Octave	59\72ed7/3 (1202.02¢)
Twelfth	93\72ed7/3 (1894.71¢) (→31\24ed7/3)
Consistency limit	3
Distinct consistency limit	3

72 equal divisions of 7/3 (abbreviated 72ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 72 equal parts of about 20.4 ¢ each. Each step represents a frequency ratio of (7/3)^1/72, or the 72nd root of 7/3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	20.373
2	40.746
3	61.12	29/28, 30/29
4	81.493
5	101.866	17/16, 35/33
6	122.239	15/14
7	142.612	38/35
8	162.986	11/10, 34/31
9	183.359
10	203.732
11	224.105	25/22, 33/29
12	244.478	15/13, 38/33
13	264.852	7/6
14	285.225	33/28
15	305.598	31/26, 37/31
16	325.971	29/24, 35/29
17	346.345
18	366.718	37/30
19	387.091	5/4
20	407.464	19/15, 24/19
21	427.837	23/18, 32/25
22	448.211	22/17
23	468.584	38/29
24	488.957
25	509.33
26	529.703	19/14, 34/25
27	550.077	11/8
28	570.45
29	590.823	31/22
30	611.196	37/26
31	631.569
32	651.943	16/11, 35/24
33	672.316	28/19
34	692.689
35	713.062
36	733.435	26/17, 29/19
37	753.809	17/11
38	774.182	25/16, 36/23
39	794.555	19/12
40	814.928	8/5
41	835.301
42	855.675
43	876.048
44	896.421	37/22
45	916.794	17/10
46	937.168
47	957.541	33/19
48	977.914
49	998.287
50	1018.66
51	1039.034	31/17
52	1059.407	24/13, 35/19
53	1079.78	28/15
54	1100.153
55	1120.526
56	1140.9	29/15
57	1161.273
58	1181.646
59	1202.019	2/1
60	1222.392
61	1242.766
62	1263.139	29/14
63	1283.512
64	1303.885	17/8
65	1324.258
66	1344.632	37/17
67	1365.005	11/5
68	1385.378
69	1405.751
70	1426.124
71	1446.498	30/13
72	1466.871	7/3

Harmonics

Approximation of harmonics in 72ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+2.02	-7.25	+4.04	+4.82	-5.23	-7.25	+6.06	+5.88	+6.83	+4.82	-3.21
	Relative (%)	+9.9	-35.6	+19.8	+23.6	-25.7	-35.6	+29.7	+28.9	+33.5	+23.6	-15.7
Steps (reduced)		59 (59)	93 (21)	118 (46)	137 (65)	152 (8)	165 (21)	177 (33)	187 (43)	196 (52)	204 (60)	211 (67)

Approximation of harmonics in 72ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+0.83	-5.23	-2.43	+8.08	+4.99	+7.90	-4.21	+8.85	+5.88	+6.84	-9.00
	Relative (%)	+4.1	-25.7	-11.9	+39.6	+24.5	+38.8	-20.7	+43.5	+28.9	+33.6	-44.2
Steps (reduced)		218 (2)	224 (8)	230 (14)	236 (20)	241 (25)	246 (30)	250 (34)	255 (39)	259 (43)	263 (47)	266 (50)