6edf
| ← 5edf | 6edf | 7edf → |
6 equal divisions of the perfect fifth (abbreviated 6edf or 6ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 6 equal parts of about 117 ¢ each. Each step represents a frequency ratio of (3/2)1/6, or the 6th root of 3/2. It corresponds to 10.2571 edo.
Theory
6edf is related to the miracle temperament, which tempers out 225/224 and 1029/1024 in the 7-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -30.1 | -30.1 | +56.8 | +21.5 | +56.8 | +24.0 | +26.8 | +56.8 | -8.6 | -56.6 | +26.8 |
| Relative (%) | -25.7 | -25.7 | +48.6 | +18.4 | +48.6 | +20.5 | +22.9 | +48.6 | -7.3 | -48.4 | +22.9 | |
| Steps (reduced) |
10 (4) |
16 (4) |
21 (3) |
24 (0) |
27 (3) |
29 (5) |
31 (1) |
33 (3) |
34 (4) |
35 (5) |
37 (1) | |
Intervals
| degrees | cents ~ cents octave-reduced | approximate ratios | Neptunian notation |
|---|---|---|---|
| 0 | 0 (perfect unison, 1:1) | 1/1 | C |
| 1 | 117 | 16/15, 15/14 | C# |
| 2 | 234 | 8/7 | Db |
| 3 | 351 | 11/9, 27/22 | D |
| 4 | 468 | 21/16 | E |
| 5 | 585 | 7/5, 45/32 | F |
| 6 | 702 (just perfect fifth, 3:2) | 3/2 | C |
| 7 | 819 | 8/5, 21/13 | C# |
| 8 | 936 | 12/7, 55/32 | Db |
| 9 | 1053 | 11/6 | D |
| 10 | 1170 | 49/25, 160/81, 2/1 | E |
| 11 | 1287 ~ 87 | F | |
| 12 | 1404 ~ 204 (just major whole tone/ninth, 9:4) | C | |
| 13 | 1521 ~ 321 | C# | |
| 14 | 1638 ~ 438 | Db | |
| 15 | 1755 ~ 555 | D | |
| 16 | 1872 ~ 672 | E | |
| 17 | 1988 ~ 788 | F | |
| 18 | 2106 ~ 906 (Pythagorean major sixth, 27:8) | C | |
| 19 | 2223 ~ 1023 | C# | |
| 20 | 2340 ~ 1140 | Db | |
| 21 | 2457 ~ 57 | D | |
| 22 | 2574 ~ 174 | E | |
| 23 | 2691 ~ 291 | F | |
| 24 | 2808 ~ 408 (Pythagorean major third, 81:16) | C |
Music
- "The Blame Game" from State of the World (XLP) (2023)