Dominant (temperament)
Dominant is a temperament tempering out the syntonic comma (81/80) and septimal comma (64/63) in the 7-limit. It also tempers out the septimal quartertone (36/35), as 36/35 = (64/63)(81/80). It is the unique temperament that identifies the harmonic seventh chord with the dominant seventh chord, which is a familiar feature from 12edo.
Other possible tunings include 17edo (17c val), 29edo (29cd val), 41edo (41cd val), 53edo (53cdd val), as well as Pythagorean tuning.
Interval chain
In the following table, odd harmonics 1–9 are in bold.
| # | Cents* | Approximate Ratios |
|---|---|---|
| 0 | 0.0 | 1/1 |
| 1 | 701.1 | 3/2 |
| 2 | 202.2 | 8/7, 9/8, 10/9 |
| 3 | 903.3 | 5/3, 12/7 |
| 4 | 404.5 | 5/4, 9/7 |
| 5 | 1105.6 | 15/8, 27/14, 40/21 |
| 6 | 606.7 | 10/7 |
| 7 | 107.8 | 15/14 |
* in 7-limit CWE tuning
Chords and harmony
Much of 12edo harmony can be used. Dominant enables chords of didymic and archytas.