6edf
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Prime factorization
2 × 3
Step size
116.993¢
Octave
10\6edf (1169.93¢) (→5\3edf)
Twelfth
16\6edf (1871.88¢) (→8\3edf)
Consistency limit
2
Distinct consistency limit
2
Special properties
| ← 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
| # | Cents | Approximate Ratios | Neptunian Notation |
|---|---|---|---|
| 0 | 0 | 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 | 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 | F | |
| 12 | 1404 | 9/4 | C |
| 13 | 1521 | C# | |
| 14 | 1638 | Db | |
| 15 | 1755 | D | |
| 16 | 1872 | E | |
| 17 | 1988 | F | |
| 18 | 2106 | 27/8 | C |
| 19 | 2223 | C# | |
| 20 | 2340 | Db | |
| 21 | 2457 | D | |
| 22 | 2574 | E | |
| 23 | 2691 | F | |
| 24 | 2808 | 81/16 | C |
Music
- "The Blame Game" from State of the World (XLP) (2023)