77edt

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77edt

78edt →

Prime factorization	7 × 11
Step size	24.7007¢
Octave	49\77edt (1210.34¢) (→7\11edt)
Consistency limit	2
Distinct consistency limit	2

77 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 77edt or 77ed3), is a nonoctave tuning system that divides the interval of 3/1 into 77 equal parts of about 24.7 ¢ each. Each step represents a frequency ratio of 3^1/77, or the 77th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	24.701
2	49.401	38/37
3	74.102	23/22
4	98.803	18/17, 35/33, 37/35
5	123.504	29/27
6	148.204
7	172.905	21/19, 31/28
8	197.606	28/25, 37/33
9	222.306	25/22, 33/29
10	247.007	15/13, 38/33
11	271.708
12	296.409
13	321.109
14	345.81	11/9
15	370.511	31/25
16	395.211	39/31
17	419.912	14/11, 37/29
18	444.613	22/17
19	469.314	38/29
20	494.014
21	518.715	31/23
22	543.416	37/27
23	568.116	25/18
24	592.817	31/22, 38/27
25	617.518
26	642.219
27	666.919	25/17
28	691.62
29	716.321
30	741.021	23/15
31	765.722	14/9
32	790.423
33	815.124
34	839.824
35	864.525	28/17
36	889.226
37	913.926	22/13, 39/23
38	938.627	31/18
39	963.328
40	988.029	23/13, 39/22
41	1012.729
42	1037.43	31/17
43	1062.131
44	1086.831
45	1111.532
46	1136.233	27/14
47	1160.934
48	1185.634
49	1210.335
50	1235.036
51	1259.736	29/14, 31/15
52	1284.437
53	1309.138
54	1333.839
55	1358.539
56	1383.24
57	1407.941
58	1432.641
59	1457.342
60	1482.043	33/14
61	1506.744	31/13
62	1531.444
63	1556.145	27/11
64	1580.846
65	1605.546
66	1630.247
67	1654.948	13/5
68	1679.649	29/11, 37/14
69	1704.349
70	1729.05	19/7
71	1753.751
72	1778.451
73	1803.152	17/6
74	1827.853
75	1852.554
76	1877.254
77	1901.955	3/1

Harmonics

Approximation of harmonics in 77edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+10.3	+0.0	-4.0	+4.9	+10.3	-9.5	+6.3	+0.0	-9.5	-1.6	-4.0
	Relative (%)	+41.8	+0.0	-16.3	+19.7	+41.8	-38.6	+25.5	+0.0	-38.5	-6.5	-16.3
Steps (reduced)		49 (49)	77 (0)	97 (20)	113 (36)	126 (49)	136 (59)	146 (69)	154 (0)	161 (7)	168 (14)	174 (20)

Approximation of harmonics in 77edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.6	+0.8	+4.9	-8.1	+10.5	+10.3	-9.2	+0.8	-9.5	+8.7	+5.9
	Relative (%)	+22.7	+3.3	+19.7	-32.6	+42.5	+41.8	-37.1	+3.4	-38.6	+35.4	+23.8
Steps (reduced)		180 (26)	185 (31)	190 (36)	194 (40)	199 (45)	203 (49)	206 (52)	210 (56)	213 (59)	217 (63)	220 (66)