28edt
Jump to navigation
Jump to search
Prime factorization
22 × 7
Step size
67.927¢
Octave
18\28edt (1222.69¢) (→9\14edt)
Consistency limit
2
Distinct consistency limit
2
← 27edt | 28edt | 29edt → |
28edt divides the third harmonic into 28 equal parts of 67.9 cents each. It is the simplest edt which intelligibly doubles the Anti-BP harmonic chain[clarification needed]. One step is very close to every third step of 53edo. It tempers out the schisma in the 8.3.5 subgroup, albeit a really strange tuning due to being a multiple of 4edt and being index-2 in BP. It also supports deneb temperament in the 3.5.11 subgroup, equating 4 11/9s with 11/5.
Integer harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | absolute (¢) | +22.7 | +0.0 | -22.6 | -1.3 | +22.7 | +27.5 | +0.1 | +0.0 | +21.4 | -7.8 | -22.6 |
relative (%) | +33 | +0 | -33 | -2 | +33 | +41 | +0 | +0 | +31 | -11 | -33 | |
Steps (reduced) |
18 (18) |
28 (0) |
35 (7) |
41 (13) |
46 (18) |
50 (22) |
53 (25) |
56 (0) |
59 (3) |
61 (5) |
63 (7) |
Intervals
Steps | cents | hekts | notation |
---|---|---|---|
1 | 67.927 | 46.429 | Cq/D\\y |
2 | 135.854 | 92.857 | Cp/D\\ |
3 | 203.781 | 139.286 | Cpq/Dy |
4 | 271.708 | 185.714 | D |
5 | 339.635 | 232.143 | Dp/Ey |
6 | 407.562 | 278.571 | E |
7 | 475.489 | 325.000 | Epq/F\\y |
8 | 543.416 | 371.429 | Ep/F\\ |
9 | 611.343 | 417.857 | Eq/Fy |
10 | 679.270 | 464.286 | F |
11 | 747.197 | 510.714 | Fq/Gy |
12 | 815.124 | 557.143 | G |
13 | 883.051 | 603.571 | Gq/H\\y |
14 | 950.978 | 650.000 | Gp/H\\ |
15 | 1018.904 | 696.429 | Gpq/Hy |
16 | 1086.831 | 742.857 | H |
17 | 1154.758 | 789.286 | Hq/Jy |
18 | 1222.685 | 835.714 | J |
19 | 1290.612 | 882.143 | Jq/A\\y |
20 | 1358.539 | 928.571 | Jp/A\\ |
21 | 1426.466 | 975.000 | Jpq/Ay |
22 | 1494.393 | 1021.429 | A |
23 | 1562.320 | 1067.857 | Aq/B\\y |
24 | 1630.247 | 1114.286 | Ap/B\\ |
25 | 1698.174 | 1160.714 | Apq/By |
26 | 1766.101 | 1207.143 | B |
27 | 1834.028 | 1253.571 | Bq/Cy |
28 | 1901.955 | 1300.000 | C |