Dominant (temperament)

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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.

See Meantone family #Dominant for technical data.

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.

Tunings

Tuning spectrum

Edo
Generator
Eigenmonzo
(Unchanged-interval)
*
Generator (¢) Comments
9/5 691.202 1/2 syntonic comma
5/3 694.786 1/3 syntonic comma
5/4 696.578 1/4 syntonic comma, 5-odd-limit minimax
15/8 697.654 1/5 syntonic comma
7\12 700.000 Lower bound of 7- and 9-odd-limit diamond monotone
3/2 701.955 Pythagorean tuning
15/14 702.778
7/5 702.915 7 & 9-odd limit minimax tuning
21/20 703.107
17\29 703.448 29cd val
11/10 703.499 11-odd-limit minimax tuning
13/10 703.522 13-odd-limit minimax tuning
10\17 705.882 17c val
9/7 708.771 1/4 septimal comma
7/6 711.043 1/3 septimal comma
7/4 715.587 1/2 septimal comma
3\5 720.000 Upper bound of 7- and 9-odd-limit diamond monotone
21/16 729.219 Full septimal comma

* Besides the octave