77ed12

← 76ed12

77ed12

78ed12 →

Prime factorization	7 × 11
Step size	55.8695 ¢
Octave	21\77ed12 (1173.26 ¢) (→ 3\11ed12)
Twelfth	34\77ed12 (1899.56 ¢)
Consistency limit	3
Distinct consistency limit	3

77 equal divisions of the 12th harmonic (abbreviated 77ed12) is a nonoctave tuning system that divides the interval of 12/1 into 77 equal parts of about 55.9 ¢ each. Each step represents a frequency ratio of 12^1/77, or the 77th root of 12.

Interval table

Steps	Cents	Approximate ratios
0	0	1/1
1	55.9	30/29, 31/30
2	111.7
3	167.6	11/10
4	223.5	33/29
5	279.3	27/23
6	335.2
7	391.1
8	447	35/27
9	502.8
10	558.7	29/21
11	614.6	10/7
12	670.4	25/17
13	726.3	35/23
14	782.2	11/7
15	838
16	893.9
17	949.8
18	1005.7	34/19
19	1061.5
20	1117.4	21/11
21	1173.3
22	1229.1
23	1285	21/10
24	1340.9	13/6
25	1396.7
26	1452.6
27	1508.5
28	1564.3	37/15
29	1620.2
30	1676.1	29/11
31	1732	19/7
32	1787.8
33	1843.7	29/10
34	1899.6	3/1
35	1955.4	31/10, 34/11
36	2011.3
37	2067.2	33/10
38	2123
39	2178.9
40	2234.8
41	2290.7
42	2346.5
43	2402.4
44	2458.3	29/7
45	2514.1
46	2570
47	2625.9
48	2681.7	33/7
49	2737.6	34/7
50	2793.5
51	2849.3
52	2905.2
53	2961.1
54	3017
55	3072.8
56	3128.7
57	3184.6
58	3240.4	13/2
59	3296.3
60	3352.2
61	3408
62	3463.9	37/5
63	3519.8
64	3575.7
65	3631.5
66	3687.4
67	3743.3
68	3799.1
69	3855
70	3910.9
71	3966.7
72	4022.6
73	4078.5
74	4134.3
75	4190.2
76	4246.1
77	4302

Harmonics

Approximation of harmonics in 77ed12

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-26.7	-2.4	+2.4	+7.2	+26.7	-16.7	-24.3	-4.8	-19.6	-17.0	+0.0
	Relative (%)	-47.9	-4.3	+4.3	+12.8	+47.9	-29.8	-43.6	-8.6	-35.0	-30.4	+0.0
Steps (reduced)		21 (21)	34 (34)	43 (43)	50 (50)	56 (56)	60 (60)	64 (64)	68 (68)	71 (71)	74 (74)	77 (0)