6edϕ
6 equal divisions of acoustic phi (6edϕ) is the nonoctave tuning system derived by dividing acoustic phi into 6 equal steps of 138.8 cents each, or the sixth root of the golden ratio. It is well-approximated by every third step of 26edo.
| ← 5edϕ | 6edϕ | 7edϕ → |
It serves as a basic tempered approximation for the metallic harmonic series, and the associated metallic intonation. The first metallic harmonic (the golden ratio) is represented exactly by the sixth step, while the second and third metallic harmonics are represented by the 11th and 15th steps respectively, or the 5th and 2nd steps if acoustic phi is taken as an equivalence.
Interval table
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 138.8 | 10/9, 11/10, 14/13, 15/14, 20/19, 21/19 |
| 2 | 277.7 | 13/11, 15/13, 17/14 |
| 3 | 416.5 | 13/10, 14/11, 17/13, 19/15, 21/17 |
| 4 | 555.4 | 4/3, 7/5, 15/11, 19/14 |
| 5 | 694.2 | 3/2, 17/11, 19/13 |
| 6 | 833.1 | 5/3, 11/7, 21/13 |