| Prime factorization
|
3 (prime)
|
| Step size
|
128.771¢
|
| Octave
|
9\3ed5/4 (1158.94¢) (→3\1ed5/4)
|
| Twelfth
|
15\3ed5/4 (1931.57¢) (→5\1ed5/4)
|
| Consistency limit
|
2
|
| Distinct consistency limit
|
1
|
3ED5/4 is the equal division of the just major third into three parts of 128.7712 cents each, approximately corresponding to every third step of 28edo. It is related to the 13-limit temperaments which temper out 10985/10976 and 537109375/536870912.
Intervals
| degree
|
cents value
|
ratio
|
| 0
|
0.0000
|
1/1
|
| 1
|
128.7712
|
(5/4)1/3
|
| 2
|
257.5425
|
(5/4)2/3
|
| 3
|
386.3137
|
5/4
|
| 4
|
515.0850
|
(5/4)4/3
|
| 5
|
643.8562
|
(5/4)5/3
|
| 6
|
772.6274
|
(5/4)2 = 25/16
|
| 7
|
901.3987
|
(5/4)7/3
|
| 8
|
1030.1699
|
(5/4)8/3
|
| 9
|
1158.9411
|
(5/4)3 = 125/64
|
| 10
|
1287.7124
|
(5/4)10/3
|
| 11
|
1416.4836
|
(5/4)11/3
|
| 12
|
1545.2549
|
(5/4)4 = 625/256
|
| 13
|
1674.0261
|
(5/4)13/3
|
| 14
|
1802.7973
|
(5/4)14/3
|
| 15
|
1931.5686
|
(5/4)5 = 3125/1024
|
| 16
|
2060.3398
|
(5/4)16/3
|
| 17
|
2189.1110
|
(5/4)17/3
|
| 18
|
2317.8823
|
(5/4)6 = 15625/4096
|
| 19
|
2446.6535
|
(5/4)19/3
|
| 20
|
2575.4248
|
(5/4)20/3
|
| 21
|
2704.1960
|
(5/4)7 = 78125/16384
|
| 22
|
2832.9672
|
(5/4)22/3
|
| 23
|
2961.7385
|
(5/4)23/3
|
| 24
|
3090.5097
|
(5/4)8 = 390625/65536
|
| 25
|
3219.2809
|
(5/4)25/3
|
| 26
|
3348.0522
|
(5/4)26/3
|
| 27
|
3476.8234
|
(5/4)9 = 1953125/262144
|
| 28
|
3605.5947
|
(5/4)28/3
|
| 29
|
3734.3659
|
(5/4)29/3
|
| 30
|
3863.1371
|
(5/4)10 = 9765625/1048576
|
| 31
|
3991.9084
|
(5/4)31/3
|
| 32
|
4120.6796
|
(5/4)32/3
|
| 33
|
4249.4509
|
(5/4)11 = 48828125/4194304
|
| 34
|
4378.2221
|
(5/4)34/3
|
| 35
|
4506.9933
|
(5/4)35/3
|
| 36
|
4635.7646
|
(5/4)12 = 244140625/16777216
|
| 37
|
4764.5358
|
(5/4)37/3
|
| 38
|
4893.3070
|
(5/4)38/3
|
| 39
|
5022.0783
|
(5/4)13 = 1220703125/67108864
|