77ed7/3

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77ed7/3

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Prime factorization	7 × 11
Step size	19.0503¢
Octave	63\77ed7/3 (1200.17¢) (→9\11ed7/3)
Twelfth	100\77ed7/3 (1905.03¢)
Consistency limit	8
Distinct consistency limit	8

77 equal divisions of 7/3 (abbreviated 77ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 77 equal parts of about 19.1 ¢ each. Each step represents a frequency ratio of (7/3)^1/77, or the 77th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	19.1
2	38.1
3	57.2	30/29, 31/30, 32/31
4	76.2	23/22, 24/23
5	95.3	19/18, 37/35
6	114.3	16/15, 31/29
7	133.4
8	152.4	12/11, 35/32
9	171.5	21/19, 32/29
10	190.5	29/26, 39/35
11	209.6	26/23, 35/31
12	228.6	8/7
13	247.7	15/13
14	266.7	7/6
15	285.8	33/28
16	304.8	31/26, 37/31
17	323.9	35/29
18	342.9	28/23, 39/32
19	362	16/13, 37/30
20	381
21	400.1	29/23, 39/31
22	419.1	14/11, 37/29
23	438.2	9/7
24	457.2	13/10, 30/23
25	476.3	29/22
26	495.3	4/3
27	514.4	31/23, 35/26, 39/29
28	533.4	34/25
29	552.5	11/8
30	571.5	32/23, 39/28
31	590.6	31/22, 38/27
32	609.6	27/19, 37/26
33	628.7	23/16
34	647.7	16/11
35	666.8	25/17
36	685.8
37	704.9	3/2
38	723.9	35/23
39	743	20/13, 23/15
40	762	14/9, 31/20
41	781.1	11/7
42	800.1
43	819.2
44	838.2	13/8
45	857.3	23/14
46	876.3
47	895.4
48	914.4	39/23
49	933.5	12/7
50	952.5	26/15, 33/19
51	971.6	7/4
52	990.6	23/13, 39/22
53	1009.7
54	1028.7	29/16, 38/21
55	1047.8	11/6
56	1066.8	37/20
57	1085.9	15/8
58	1104.9	36/19
59	1124	23/12
60	1143	29/15, 31/16
61	1162.1
62	1181.1
63	1200.2	2/1
64	1219.2
65	1238.3
66	1257.3	31/15
67	1276.4	23/11
68	1295.4	19/9
69	1314.5	32/15
70	1333.5
71	1352.6	24/11, 35/16
72	1371.6
73	1390.7	29/13
74	1409.7
75	1428.8	16/7
76	1447.8	30/13
77	1466.9	7/3

Harmonics

Approximation of harmonics in 77ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.17	+3.07	+0.33	-4.97	+3.24	+3.07	+0.50	+6.14	-4.81	+1.64	+3.41
	Relative (%)	+0.9	+16.1	+1.8	-26.1	+17.0	+16.1	+2.6	+32.3	-25.2	+8.6	+17.9
Steps (reduced)		63 (63)	100 (23)	126 (49)	146 (69)	163 (9)	177 (23)	189 (35)	200 (46)	209 (55)	218 (64)	226 (72)

Approximation of harmonics in 77ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-1.81	+3.24	-1.90	+0.67	-9.04	+6.31	+7.96	-4.64	+6.14	+1.81	+1.05
	Relative (%)	-9.5	+17.0	-10.0	+3.5	-47.4	+33.1	+41.8	-24.4	+32.3	+9.5	+5.5
Steps (reduced)		233 (2)	240 (9)	246 (15)	252 (21)	257 (26)	263 (32)	268 (37)	272 (41)	277 (46)	281 (50)	285 (54)