6ed5/4
Jump to navigation
Jump to search
Prime factorization
2 × 3
Step size
64.3856¢
Octave
19\6ed5/4 (1223.33¢)
Twelfth
30\6ed5/4 (1931.57¢) (→5\1ed5/4)
Consistency limit
3
Distinct consistency limit
2
Special properties
| ← 5ed5/4 | 6ed5/4 | 7ed5/4 → |
6ED5/4 is the equal division of the just major third into six parts of 64.3856 cents each, corresponding to 18.6377 edo. It is related to the 17-limit temperament which tempers out 561/560, 715/714, 729/728, 847/845, and 5632/5625, which is supported by 149edo and 205edo.
Intervals
| degree | cents value | ratio |
|---|---|---|
| 0 | 0.0000 | 1/1 |
| 1 | 64.3856 | (5/4)1/6 |
| 2 | 128.7712 | (5/4)1/3 |
| 3 | 193.1569 | (5/4)1/2 |
| 4 | 257.5425 | (5/4)2/3 |
| 5 | 321.9281 | (5/4)5/6 |
| 6 | 386.3137 | 5/4 |
| 7 | 450.6993 | (5/4)7/6 |
| 8 | 515.0850 | (5/4)4/3 |
| 9 | 579.4706 | (5/4)3/2 |
| 10 | 643.8562 | (5/4)5/3 |
| 11 | 708.2418 | (5/4)11/6 |
| 12 | 772.6274 | (5/4)2 = 25/16 |
| 13 | 837.0130 | (5/4)13/6 |
| 14 | 901.3987 | (5/4)7/3 |
| 15 | 965.7843 | (5/4)5/2 |
| 16 | 1030.1699 | (5/4)8/3 |
| 17 | 1094.5555 | (5/4)17/6 |
| 18 | 1158.9411 | (5/4)3 = 125/64 |
| 19 | 1223.3268 | (5/4)19/6 |
| 20 | 1287.7124 | (5/4)10/3 |
| 21 | 1352.0980 | (5/4)7/2 |
| 22 | 1416.4836 | (5/4)11/3 |
| 23 | 1480.8692 | (5/4)23/6 |
| 24 | 1545.2549 | (5/4)4 = 625/256 |
| 25 | 1609.6405 | (5/4)25/6 |
| 26 | 1674.0261 | (5/4)13/3 |
| 27 | 1738.4117 | (5/4)9/2 |
| 28 | 1802.7973 | (5/4)14/3 |
| 29 | 1867.1830 | (5/4)29/6 |
| 30 | 1931.5686 | (5/4)5 = 3125/1024 |
| 31 | 1995.9542 | (5/4)31/6 |
| 32 | 2060.3398 | (5/4)16/3 |
| 33 | 2124.7254 | (5/4)11/2 |
| 34 | 2189.1110 | (5/4)17/3 |
| 35 | 2253.4967 | (5/4)35/6 |
| 36 | 2317.8823 | (5/4)6 = 15625/4096 |
| 37 | 2382.2679 | (5/4)37/6 |
| 38 | 2446.6535 | (5/4)19/3 |
| 39 | 2511.0391 | (5/4)13/2 |
| 40 | 2575.4248 | (5/4)20/3 |
| 41 | 2639.8104 | (5/4)41/6 |
| 42 | 2704.1960 | (5/4)7 = 78125/16384 |
| 43 | 2768.5816 | (5/4)43/6 |
| 44 | 2832.9672 | (5/4)22/3 |
| 45 | 2897.3529 | (5/4)15/2 |
| 46 | 2961.7385 | (5/4)23/3 |
| 47 | 3026.1241 | (5/4)47/6 |
| 48 | 3090.5097 | (5/4)8 = 390625/65536 |
| 49 | 3154.8953 | (5/4)49/6 |
| 50 | 3219.2809 | (5/4)25/3 |
| 51 | 3283.6666 | (5/4)17/2 |
| 52 | 3348.0522 | (5/4)26/3 |
| 53 | 3412.4378 | (5/4)53/6 |
| 54 | 3476.8234 | (5/4)9 = 1953125/262144 |
| 55 | 3541.2090 | (5/4)55/6 |
| 56 | 3605.5947 | (5/4)28/3 |
| 57 | 3669.9803 | (5/4)19/2 |
| 58 | 3734.3659 | (5/4)29/3 |
| 59 | 3798.7515 | (5/4)59/6 |
| 60 | 3863.1371 | (5/4)10 = 9765625/1048576 |
| 61 | 3927.5228 | (5/4)61/6 |
| 62 | 3991.9084 | (5/4)31/3 |
| 63 | 4056.2940 | (5/4)21/2 |
| 64 | 4120.6796 | (5/4)32/3 |
| 65 | 4185.0652 | (5/4)65/6 |
| 66 | 4249.4509 | (5/4)11 = 48828125/4194304 |
| 67 | 4313.8365 | (5/4)67/6 |
| 68 | 4378.2221 | (5/4)34/3 |
| 69 | 4442.6077 | (5/4)23/2 |
| 70 | 4506.9933 | (5/4)35/3 |
| 71 | 4571.3789 | (5/4)71/6 |
| 72 | 4635.7646 | (5/4)12 = 244140625/16777216 |
| 73 | 4700.1502 | (5/4)73/6 |
| 74 | 4764.5358 | (5/4)37/3 |
| 75 | 4828.9214 | (5/4)25/2 |
| 76 | 4893.3070 | (5/4)38/3 |
| 77 | 4957.6927 | (5/4)77/6 |
| 78 | 5022.0783 | (5/4)13 = 1220703125/67108864 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +23.3 | +29.6 | -17.7 | -17.7 | -11.4 | -20.8 | +5.6 | -5.2 | +5.6 | -30.6 | +11.9 |
| Relative (%) | +36.2 | +46.0 | -27.5 | -27.5 | -17.8 | -32.3 | +8.7 | -8.0 | +8.7 | -47.6 | +18.5 | |
| Steps (reduced) |
19 (1) |
30 (0) |
37 (1) |
43 (1) |
48 (0) |
52 (4) |
56 (2) |
59 (5) |
62 (2) |
64 (4) |
67 (1) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.1 | +2.6 | +11.9 | +28.9 | -11.6 | +18.2 | -11.0 | +28.9 | +8.8 | -7.3 | -19.9 |
| Relative (%) | +3.2 | +4.0 | +18.5 | +44.9 | -18.1 | +28.2 | -17.2 | +44.9 | +13.7 | -11.4 | -30.9 | |
| Steps (reduced) |
69 (3) |
71 (5) |
73 (1) |
75 (3) |
76 (4) |
78 (0) |
79 (1) |
81 (3) |
82 (4) |
83 (5) |
84 (0) | |