3ed5/4
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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
| ← 2ed5/4 | 3ed5/4 | 4ed5/4 → |
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 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -41.1 | +29.6 | +46.7 | +46.7 | -11.4 | -20.8 | +5.6 | +59.2 | +5.6 | -30.6 | -52.5 |
| Relative (%) | -31.9 | +23.0 | +36.2 | +36.2 | -8.9 | -16.1 | +4.3 | +46.0 | +4.3 | -23.8 | -40.8 | |
| Steps (reduced) |
9 (0) |
15 (0) |
19 (1) |
22 (1) |
24 (0) |
26 (2) |
28 (1) |
30 (0) |
31 (1) |
32 (2) |
33 (0) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -62.3 | -61.8 | -52.5 | -35.5 | -11.6 | +18.2 | +53.3 | -35.5 | +8.8 | +57.1 | -19.9 |
| Relative (%) | -48.4 | -48.0 | -40.8 | -27.5 | -9.0 | +14.1 | +41.4 | -27.5 | +6.9 | +44.3 | -15.4 | |
| Steps (reduced) |
34 (1) |
35 (2) |
36 (0) |
37 (1) |
38 (2) |
39 (0) |
40 (1) |
40 (1) |
41 (2) |
42 (0) |
42 (0) | |