77ed4

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77ed4

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Prime factorization	7 × 11
Step size	31.1688¢
Octave	39\77ed4 (1215.58¢)
Twelfth	61\77ed4 (1901.3¢)
Consistency limit	1
Distinct consistency limit	1

77 equal divisions of the 4th harmonic (abbreviated 77ed4) is a nonoctave tuning system that divides the interval of 4/1 into 77 equal parts of about 31.2 ¢ each. Each step represents a frequency ratio of 4^1/77, or the 77th root of 4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	31.169
2	62.338	27/26
3	93.506	19/18
4	124.675	29/27
5	155.844	23/21
6	187.013	29/26, 39/35
7	218.182	17/15
8	249.351	15/13
9	280.519	27/23
10	311.688
11	342.857
12	374.026
13	405.195
14	436.364	9/7
15	467.532	17/13
16	498.701
17	529.87	19/14
18	561.039	29/21
19	592.208	31/22
20	623.377	33/23
21	654.545
22	685.714
23	716.883
24	748.052
25	779.221	11/7
26	810.39
27	841.558
28	872.727
29	903.896
30	935.065
31	966.234
32	997.403
33	1028.571
34	1059.74
35	1090.909
36	1122.078	21/11
37	1153.247	37/19
38	1184.416
39	1215.584
40	1246.753	37/18
41	1277.922	23/11
42	1309.091
43	1340.26
44	1371.429
45	1402.597
46	1433.766
47	1464.935	7/3
48	1496.104
49	1527.273
50	1558.442
51	1589.61
52	1620.779
53	1651.948	13/5
54	1683.117	37/14
55	1714.286	35/13
56	1745.455
57	1776.623
58	1807.792
59	1838.961	26/9
60	1870.13
61	1901.299	3/1
62	1932.468
63	1963.636
64	1994.805	19/6
65	2025.974	29/9
66	2057.143	23/7
67	2088.312
68	2119.481	17/5
69	2150.649
70	2181.818
71	2212.987
72	2244.156
73	2275.325
74	2306.494
75	2337.662	27/7
76	2368.831
77	2400

Harmonics

Approximation of harmonics in 77ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+15.6	-0.7	+0.0	-12.3	+14.9	-2.6	+15.6	-1.3	+3.3	-5.9	-0.7
	Relative (%)	+50.0	-2.1	+0.0	-39.4	+47.9	-8.3	+50.0	-4.2	+10.6	-18.8	-2.1
Steps (reduced)		39 (39)	61 (61)	77 (0)	89 (12)	100 (23)	108 (31)	116 (39)	122 (45)	128 (51)	133 (56)	138 (61)

Approximation of harmonics in 77ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-14.6	+13.0	-12.9	+0.0	-11.4	+14.3	+14.2	-12.3	-3.2	+9.7	-4.9
	Relative (%)	-46.7	+41.7	-41.5	+0.0	-36.7	+45.8	+45.5	-39.4	-10.4	+31.2	-15.7
Steps (reduced)		142 (65)	147 (70)	150 (73)	154 (0)	157 (3)	161 (7)	164 (10)	166 (12)	169 (15)	172 (18)	174 (20)