78ed7/3

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78ed7/3

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Prime factorization	2 × 3 × 13
Step size	18.806¢
Octave	64\78ed7/3 (1203.59¢) (→32\39ed7/3)
Twelfth	101\78ed7/3 (1899.41¢)
Consistency limit	3
Distinct consistency limit	3

78 equal divisions of 7/3 (abbreviated 78ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 78 equal parts of about 18.8⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/78, or the 78th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	18.8
2	37.6
3	56.4	30/29, 31/30
4	75.2	23/22, 24/23
5	94	19/18, 37/35, 39/37
6	112.8	31/29
7	131.6	27/25
8	150.4	12/11
9	169.3
10	188.1	29/26, 39/35
11	206.9	35/31
12	225.7	33/29
13	244.5	15/13, 23/20, 38/33
14	263.3
15	282.1	20/17, 33/28
16	300.9	25/21
17	319.7
18	338.5	17/14, 28/23
19	357.3
20	376.1	36/29
21	394.9	39/31
22	413.7	33/26
23	432.5	9/7
24	451.3	13/10, 35/27
25	470.2	38/29
26	489
27	507.8
28	526.6	19/14, 23/17
29	545.4	26/19, 37/27
30	564.2	18/13
31	583	7/5
32	601.8	17/12
33	620.6	10/7
34	639.4	13/9
35	658.2	19/13
36	677	31/21, 34/23, 37/25
37	695.8
38	714.6
39	733.4	26/17, 29/19
40	752.2	17/11
41	771	39/25
42	789.9	30/19
43	808.7
44	827.5	21/13, 29/18
45	846.3	31/19
46	865.1	28/17, 33/20
47	883.9	5/3
48	902.7
49	921.5	17/10, 29/17
50	940.3	31/18
51	959.1
52	977.9	37/21
53	996.7
54	1015.5	9/5
55	1034.3	20/11
56	1053.1
57	1071.9	13/7
58	1090.8
59	1109.6	19/10, 36/19
60	1128.4	23/12
61	1147.2	33/17
62	1166
63	1184.8
64	1203.6
65	1222.4
66	1241.2
67	1260	29/14, 31/15
68	1278.8	23/11
69	1297.6	36/17
70	1316.4	15/7
71	1335.2
72	1354
73	1372.8
74	1391.6	29/13, 38/17
75	1410.5
76	1429.3
77	1448.1	30/13
78	1466.9	7/3

Harmonics

Approximation of harmonics in 78ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3.59	-2.55	+7.17	-3.02	+1.04	-2.55	-8.05	-5.09	+0.57	+4.82	+4.63
	Relative (%)	+19.1	-13.5	+38.1	-16.1	+5.5	-13.5	-42.8	-27.1	+3.0	+25.6	+24.6
Steps (reduced)		64 (64)	101 (23)	128 (50)	148 (70)	165 (9)	179 (23)	191 (35)	202 (46)	212 (56)	221 (65)	229 (73)

Approximation of harmonics in 78ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.30	+1.04	-5.57	-4.46	+3.42	-1.50	-1.08	+4.15	-5.09	+8.40	+6.67
	Relative (%)	-12.2	+5.5	-29.6	-23.7	+18.2	-8.0	-5.7	+22.1	-27.1	+44.7	+35.5
Steps (reduced)		236 (2)	243 (9)	249 (15)	255 (21)	261 (27)	266 (32)	271 (37)	276 (42)	280 (46)	285 (51)	289 (55)