# 5ed5/4

5ED5/4 is the equal division of the just major third into five parts of 77.2627 cents each, corresponding to every second step of 31edo. It is related to Carlos Alpha and the 7-limit temperaments which temper out 2100875/2097152 (including the tertiaseptal temperament and the valentine temperament).

## Intervals

degree cents value ratio
0 0.0000 1/1
1 77.2627 (5/4)1/5
2 154.5255 (5/4)2/5
3 231.7882 (5/4)3/5
4 309.0510 (5/4)4/5
5 386.3137 5/4
6 463.5765 (5/4)6/5
7 540.8392 (5/4)7/5
8 618.1019 (5/4)8/5
9 695.3647 (5/4)9/5
10 772.6274 (5/4)2 = 25/16
11 849.8902 (5/4)11/5
12 927.1529 (5/4)12/5
13 1004.4157 (5/4)13/5
14 1081.6784 (5/4)14/5
15 1158.9411 (5/4)3 = 125/64
16 1236.2039 (5/4)16/5
17 1313.4666 (5/4)17/5
18 1390.7294 (5/4)18/5
19 1467.9921 (5/4)19/5
20 1545.2549 (5/4)4 = 625/256
21 1622.5176 (5/4)21/5
22 1699.7803 (5/4)22/5
23 1777.0431 (5/4)23/5
24 1854.3058 (5/4)24/5
25 1931.5686 (5/4)5 = 3125/1024
26 2008.8313 (5/4)26/5
27 2086.0941 (5/4)27/5
28 2163.3568 (5/4)28/5
29 2240.6195 (5/4)29/5
30 2317.8823 (5/4)6 = 15625/4096
31 2395.1450 (5/4)31/5
32 2472.4078 (5/4)32/5
33 2549.6705 (5/4)33/5
34 2626.9333 (5/4)34/5
35 2704.1960 (5/4)7 = 78125/16384
36 2781.4587 (5/4)36/5
37 2858.7215 (5/4)37/5
38 2935.9842 (5/4)38/5
39 3013.2470 (5/4)39/5
40 3090.5097 (5/4)8 = 390625/65536
41 3167.7725 (5/4)41/5
42 3245.0352 (5/4)42/5
43 3322.2979 (5/4)43/5
44 3399.5607 (5/4)44/5
45 3476.8234 (5/4)9 = 1953125/262144
46 3554.0862 (5/4)46/5
47 3631.3489 (5/4)47/5
48 3708.6117 (5/4)48/5
49 3785.8744 (5/4)49/5
50 3863.1371 (5/4)10 = 9765625/1048576
51 3940.3999 (5/4)51/5
52 4017.6626 (5/4)52/5
53 4094.9254 (5/4)53/5
54 4172.1881 (5/4)54/5
55 4249.4509 (5/4)11 = 48828125/4194304
56 4326.7136 (5/4)56/5
57 4403.9763 (5/4)57/5
58 4481.2391 (5/4)58/5
59 4558.5018 (5/4)59/5
60 4635.7646 (5/4)12 = 244140625/16777216
61 4713.0273 (5/4)61/5
62 4790.2901 (5/4)62/5
63 4867.5528 (5/4)63/5
64 4944.8155 (5/4)64/5
65 5022.0783 (5/4)13 = 1220703125/67108864

## 5ED5/4 as a generator

### Valentine

Aside from 2100875/2097152, valentine temperament tempers out 126/125, 1029/1024, 6144/6125, and 64827/64000 in the 7-limit. It can be described as the 31&46 temperament, and the step interval of 5ED5/4 (tuned between 256/245 and 22/21) can serve as its generator. In the 11-limit, it tempers out 121/120, 176/175, and 441/440.

### Tertiaseptal

Aside from 2100875/2097152, tertiaseptal temperament tempers out 2401/2400, 65625/65536, and 703125/702464 in the 7-limit. It can be described as the 31&171 temperament, and the step interval of 5ED5/4 (tuned between 256/245 and 68/65) can serve as its generator. In the 17-limit, it tempers out 243/242, 375/374, 441/440, 625/624, and 3584/3575.

### Tertia

Aside from 2100875/2097152, tertia temperament tempers out 385/384, 1331/1323, and 1375/1372 in the 11-limit. It can be described as the 31&140 temperament, and the step interval of 5ED5/4 (tuned between 256/245 and 68/65) can serve as its generator. In the 17-limit, it tempers out 352/351, 385/384, 561/560, 625/624, and 715/714.