10edt
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Prime factorization
2 × 5
Step size
190.196¢
Octave
6\10edt (1141.17¢) (→3\5edt)
Consistency limit
2
Distinct consistency limit
2
| ← 9edt | 10edt | 11edt → |
10EDT is the equal division of the third harmonic (tritave) into ten parts of 190.1955 cents each, corresponding to 6.3093 edo. It is related to the pocus temperament, which tempers out 169/168, 225/224, and 245/243 in the 2.3.5.7.13 subgroup.
| Degrees | Cents | Hekts | Approximate Ratios |
|---|---|---|---|
| 0 | 1/1 | ||
| 1 | 190.196 | 130 | 10/9, 28/25 |
| 2 | 380.391 | 260 | 5/4 |
| 3 | 570.587 | 390 | 7/5 |
| 4 | 760.782 | 520 | 14/9 |
| 5 | 950.978 | 650 | 45/26, 26/15 |
| 6 | 1141.173 | 780 | 27/14 |
| 7 | 1331.369 | 910 | 15/7 (15/14 plus an octave) |
| 8 | 1521.564 | 1040 | 12/5 (6/5 plus an octave) |
| 9 | 1711.760 | 1170 | 27/10 |
| 10 | 1901.955 | 1300 | 3/1 |
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | -58.8 | +0.0 | +66.6 | +54.7 | +33.0 | -66.0 | +40.1 | +37.8 | +87.4 | +66.5 | -49.0 |
| relative (%) | -31 | +0 | +35 | +29 | +17 | -35 | +21 | +20 | +46 | +35 | -26 | |
| Steps (reduced) |
6 (6) |
10 (0) |
15 (5) |
18 (8) |
22 (2) |
23 (3) |
26 (6) |
27 (7) |
29 (9) |
31 (1) |
31 (1) | |
10edt, like 5edt, has very accurate 5-limit harmony for such a small number of steps per tritave. 10edt introduces some new harmonic properties though; notably the 571 cent tritone which can function as 7/5. It also splits the major third in half, categorizing this tuning as a fringe variety of "meantone" temperament.