27ed5
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Prime factorization
33
Step size
103.197¢
Octave
12\27ed5 (1238.36¢) (→4\9ed5)
Twelfth
18\27ed5 (1857.54¢) (→2\3ed5)
Consistency limit
2
Distinct consistency limit
2
| ← 26ed5 | 27ed5 | 28ed5 → |
Division of the 5th harmonic into 27 equal parts (27ED5) is a good hyperpyth tuning. The step size is about 103.1968 cents, corresponding to 11.6283 EDO.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +38.4 | -44.4 | -26.5 | +0.0 | -6.1 | +36.7 | +11.9 | +14.4 | +38.4 | -23.4 | +32.3 |
| Relative (%) | +37.2 | -43.0 | -25.7 | +0.0 | -5.9 | +35.5 | +11.5 | +13.9 | +37.2 | -22.7 | +31.3 | |
| Steps (reduced) |
12 (12) |
18 (18) |
23 (23) |
27 (0) |
30 (3) |
33 (6) |
35 (8) |
37 (10) |
39 (12) |
40 (13) |
42 (15) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.1 | -28.2 | -44.4 | +50.2 | +48.5 | -50.5 | -40.9 | -26.5 | -7.7 | +14.9 | +41.2 |
| Relative (%) | -3.0 | -27.3 | -43.0 | +48.7 | +47.0 | -48.9 | -39.6 | -25.7 | -7.5 | +14.5 | +39.9 | |
| Steps (reduced) |
43 (16) |
44 (17) |
45 (18) |
47 (20) |
48 (21) |
48 (21) |
49 (22) |
50 (23) |
51 (24) |
52 (25) |
53 (26) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 103.1968 | 17/16, 35/33 | |
| 2 | 206.3936 | 9/8, 44/39 | |
| 3 | 309.5904 | 25/21, 6/5 | |
| 4 | 412.7872 | 14/11, 19/15 | |
| 5 | 515.9840 | 35/26 | |
| 6 | 619.1808 | 10/7 | |
| 7 | 722.3776 | 38/25 | |
| 8 | 825.5744 | 8/5 | |
| 9 | 928.7712 | 12/7 | |
| 10 | 1031.9680 | 9/5 | |
| 11 | 1135.1648 | 27/14 | |
| 12 | 1238.3617 | 45/22 | |
| 13 | 1341.5585 | 13/6 | |
| 14 | 1444.7553 | 23/10, 30/13 | |
| 15 | 1547.9521 | 22/9 | |
| 16 | 1651.1489 | 13/5 | |
| 17 | 1754.3457 | 11/4 | |
| 18 | 1857.5425 | 38/13, 44/15 | |
| 19 | 1960.7393 | 31/10 | |
| 20 | 2063.9361 | 33/10, 56/17 | |
| 21 | 2167.1329 | 7/2 | 17/5 plus 48.5 cents |
| 22 | 2270.3297 | 26/7 | 19/5 minus 40.9 cents |
| 23 | 2373.5265 | 63/16 | |
| 24 | 2476.7233 | 21/5, 88/21 | |
| 25 | 2579.9201 | 22/5, 40/9 | |
| 26 | 2683.1169 | 33/7, 52/11, 80/17 | |
| 27 | 2786.3137 | exact 5/1 | just major third plus two octaves |