6edϕ
| ← 5edϕ | 6edϕ | 7edϕ → |
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 best known as the equal-tempered version of the Bohlen-Pierce scale.
It serves as a tempered approximation for 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.
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 |