Dominant (temperament): Difference between revisions

Revision as of 10:04, 2 September 2024

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.

In the following table, odd harmonics 1–9 are in bold.

* in 7-limit CWE tuning

Much of 12edo harmony can be used. Dominant enables chords of didymic and archytas.

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
	21/20	703.107
17\29		703.448	29cd val
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

@@ Line 2: / Line 2: @@
 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 ==