77edo

77 tone Equal Temperament

77-tET or 77-EDO divides the octave into 77 steps of size 15.5844 cents each. With fifths less than a cent flat, major thirds a bit over three cents sharp and 7/4s less flat than that, it represents an excellent tuning choice for both valentine, the 31&46 temperament, and starling, the 126/125 planar temperament, giving the optimal patent val for 11-limit valentine and its 13-limit extensions dwynwen and valentino, as well as 11-limit starling and oxpecker temperaments. It also gives the optimal patent val for various members of the unicorn family, with a generator of 4\77 instead of the 5\77 which gives valentine. These are 7-limit alicorn and 11- and 13-limit camahueto.

77et tempers out 32805/32768 in the 5-limit, 126/125, 1029/1024 and 6144/6125 in the 7-limit, 121/120, 176/175, 385/384 and 441/440 in the 11-limit, and 196/195, 351/350, 352/351, 676/675 and 729/728 in the 13-limit.

Intervals

Degree	Cents Value	Approximate Ratios in the 13-limit
0	0.000	1/1
1	15.584	81/80, 99/98
2	31.169	64/63, 49/48
3	46.753	33/32, 36/35
4	62.338	28/27, 26/25
5	77.922	21/20, 25/24
6	93.506	135/128
7	109.091	16/15
8	124.675	15/14, 14/13
9	140.260	13/12
10	155.844	12/11, 11/10
11	171.429	72/65
12	187.013	10/9
13	202.597	9/8
14	218.182	256/225
15	233.766	8/7
16	249.351	15/13
17	264.935	7/6
18	280.519	33/28
19	296.104	32/27, 13/11
20	311.688	6/5
21	327.273	98/81
22	342.857	11/9, 39/32
23	358.442	16/13
24	374.026	56/45, 26/21
25	389.610	5/4
26	405.195	33/26, 81/64
27	420.779	14/11, 32/25
28	436.364	9/7
29	451.948	13/10
30	467.532	21/16
31	483.117	120/91
32	498.701	4/3
33	514.286	27/20
34	529.870	49/36
35	545.455	11/8, 15/11
36	561.039	18/13
37	576.623	7/5
38	592.208	45/32
39	607.792	64/45
40	623.377	10/7
41	638.961	13/9
42	654.545	16/11, 22/15
43	670.130	72/49
44	685.714	40/27
45	701.299	3/2
46	716.883	91/60
47	732.468	32/21
48	748.052	20/13
49	763.636	14/9
50	779.221	11/7, 25/16
51	794.805	52/33, 128/81
52	810.390	8/5
53	825.974	45/28, 21/13
54	841.558	13/8
55	857.143	18/11, 64/39
56	872.727	81/49
57	888.312	5/3
58	903.896	27/16, 22/13
59	919.481	56/33
60	935.065	12/7
61	950.649	26/15
62	966.234	7/4
63	981.818	225/128
64	997.403	16/9
65	1012.987	9/5
66	1028.571	65/36
67	1044.156	11/6, 20/11
68	1059.740	24/13
69	1075.325	28/15, 13/7
70	1090.909	15/8
71	1106.494	256/135
72	1122.078	40/21, 48/25
73	1137.662	27/14, 25/13
74	1153.247	64/33, 35/18
75	1168.831	63/32, 96/49
76	1184.416	160/81, 196/99
77	1200.000	2/1

Linear temperaments

Periods per Octave	Generator	Temperaments
1	1\77
1	2\77
1	3\77
1	4\77	Unicorn/alicorn/camahueto/qilin
1	5\77	Valentine
1	6\77
1	8\77
1	9\77	Tsaharuk
1	10\77
1	12\77
1	13\77
1	15\77	Guiron
1	16\77	Hemischis
1	17\77
1	18\77
1	19\77
1	20\77
1	23\77	Restles (77&87)
1	24\77
1	25\77
1	26\77
1	27\77
1	29\77
1	30\77
1	31\77	Hemiseven
1	32\77	Hendecatonic, grackle
1	34\77	Mabila (34&43)
1	36\77
1	37\77
1	38\77
7	1\77	"Absurdity" (7&84)
7	2\77
7	3\77
7	4\77
7	5\77
11	1\77
11	2\77
11	3\77

Music

Star 1-GrimaldiA+Bmod by Joel Grant Taylor

77et Star by Chris Vaisvil

A Seed Planted A Seed Planted by Jake Freivald, in an organ version of Claudi Meneghin.