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	Hekts	Approximate ratios
0	0	0	1/1
1	24.7	16.9
2	49.4	33.8	38/37
3	74.1	50.6	23/22
4	98.8	67.5	18/17, 35/33, 37/35
5	123.5	84.4	29/27
6	148.2	101.3
7	172.9	118.2	21/19, 31/28
8	197.6	135.1	28/25, 37/33
9	222.3	151.9	25/22, 33/29
10	247	168.8	15/13, 38/33
11	271.7	185.7
12	296.4	202.6
13	321.1	219.5
14	345.8	236.4	11/9
15	370.5	253.2	31/25
16	395.2	270.1	39/31
17	419.9	287	14/11, 37/29
18	444.6	303.9	22/17
19	469.3	320.8	38/29
20	494	337.7
21	518.7	354.5	31/23
22	543.4	371.4	37/27
23	568.1	388.3	25/18
24	592.8	405.2	31/22, 38/27
25	617.5	422.1
26	642.2	439
27	666.9	455.8	25/17
28	691.6	472.7
29	716.3	489.6
30	741	506.5	23/15
31	765.7	523.4	14/9
32	790.4	540.3
33	815.1	557.1
34	839.8	574
35	864.5	590.9	28/17
36	889.2	607.8
37	913.9	624.7	22/13, 39/23
38	938.6	641.6	31/18
39	963.3	658.4
40	988	675.3	23/13, 39/22
41	1012.7	692.2
42	1037.4	709.1	31/17
43	1062.1	726
44	1086.8	742.9
45	1111.5	759.7
46	1136.2	776.6	27/14
47	1160.9	793.5
48	1185.6	810.4
49	1210.3	827.3
50	1235	844.2
51	1259.7	861	29/14, 31/15
52	1284.4	877.9
53	1309.1	894.8
54	1333.8	911.7
55	1358.5	928.6
56	1383.2	945.5
57	1407.9	962.3
58	1432.6	979.2
59	1457.3	996.1
60	1482	1013	33/14
61	1506.7	1029.9	31/13
62	1531.4	1046.8
63	1556.1	1063.6	27/11
64	1580.8	1080.5
65	1605.5	1097.4
66	1630.2	1114.3
67	1654.9	1131.2	13/5
68	1679.6	1148.1	29/11, 37/14
69	1704.3	1164.9
70	1729.1	1181.8	19/7
71	1753.8	1198.7
72	1778.5	1215.6
73	1803.2	1232.5	17/6
74	1827.9	1249.4
75	1852.6	1266.2
76	1877.3	1283.1
77	1902	1300	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)