20ed7
Division of the 7th harmonic into 20 equal parts (20ed7) is related to the meantone temperament. The step size is about 168.4413 cents, corresponding to 7.1241 edo.
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 168.4413 | 11/10 | |
| 2 | 336.8826 | 17/14 | |
| 3 | 505.3239 | 91/68 | |
| 4 | 673.7652 | 28/19, 96/65, 65/44, 34/23 | |
| 5 | 842.2065 | 13/8 | |
| 6 | 1010.6478 | 70/39 | |
| 7 | 1179.0891 | 77/39 | |
| 8 | 1347.5304 | 24/11 | |
| 9 | 1515.9717 | 12/5 | |
| 10 | 1684.4130 | 119/45, 45/17 | |
| 11 | 1852.8542 | 35/12 | |
| 12 | 2021.2955 | 77/24 | |
| 13 | 2189.7368 | 39/11 | |
| 14 | 2358.1781 | 39/10 | |
| 15 | 2526.6194 | 56/13 | |
| 16 | 2695.0607 | 19/4 | |
| 17 | 2863.5020 | 68/13 | |
| 18 | 3031.9433 | 98/17 | |
| 19 | 3200.3846 | 70/11 | |
| 20 | 3368.8259 | exact 7/1 | harmonic seventh plus two octaves |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -20.9 | -49.1 | -41.8 | +77.2 | -70.0 | +0.0 | -62.7 | +70.2 | +56.3 | +59.7 | +77.5 |
| Relative (%) | -12.4 | -29.2 | -24.8 | +45.8 | -41.6 | +0.0 | -37.2 | +41.7 | +33.4 | +35.5 | +46.0 | |
| Steps (reduced) |
7 (7) |
11 (11) |
14 (14) |
17 (17) |
18 (18) |
20 (0) |
21 (1) |
23 (3) |
24 (4) |
25 (5) |
26 (6) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -61.1 | -20.9 | +28.1 | -83.6 | -20.2 | +49.3 | -44.3 | +35.4 | -49.1 | +38.8 | -38.2 |
| Relative (%) | -36.2 | -12.4 | +16.7 | -49.7 | -12.0 | +29.3 | -26.3 | +21.0 | -29.2 | +23.0 | -22.7 | |
| Steps (reduced) |
26 (6) |
27 (7) |
28 (8) |
28 (8) |
29 (9) |
30 (10) |
30 (10) |
31 (11) |
31 (11) |
32 (12) |
32 (12) | |