Twelfth complement - Revision history

FloraC: Cleanup

2026-04-11T08:10:00Z

Cleanup

← Older revision		Revision as of 08:10, 11 April 2026
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	== Examples ==		== Examples ==
	The following interval pairs are ''twelfth complementary'' to each other		The following interval pairs are ''twelfth complementary'' to each other:
	* [[7/4]] and [[12/7]]		* [[7/4]] and [[12/7]]
	* [[5/3]] and [[9/5]]		* [[5/3]] and [[9/5]]
Line 14:		Line 14:
	* [[Fifth complement]]		* [[Fifth complement]]
	* [[Fourth complement]]		* [[Fourth complement]]

	~~== Footnotes ==~~
	~~<references/>~~

	[[Category:Terms]]		[[Category:Terms]]

Jerdle: /* Examples */The previous "twelfth complements" were often actually eleventh complements. Replaced them with actual twelfth complements.

2023-05-14T10:23:26Z

Examples: The previous "twelfth complements" were often actually eleventh complements. Replaced them with actual twelfth complements.

← Older revision		Revision as of 10:23, 14 May 2023
Line 7:		Line 7:
	The following interval pairs are ''twelfth complementary'' to each other		The following interval pairs are ''twelfth complementary'' to each other
	* [[7/4]] and [[12/7]]		* [[7/4]] and [[12/7]]
	* [[5/3]] and [[8/5]]		* [[5/3]] and [[9/5]]
	* [[19/12]] and [[32/19]]		* [[11/6]] and [[18/11]]

	== See also ==		== See also ==

FloraC: Created page with "Analogous to the octave complement, the '''twelfth''' or '''tritave complement''' of a given twelfth-reduced interval is its interval distance from the 3/1|perfect twelf..."

2023-05-12T14:07:09Z

Created page with "Analogous to the octave complement, the '''twelfth''' or '''tritave complement''' of a given twelfth-reduced interval is its interval distance from the 3/1|perfect twelf..."

New page

Analogous to the [[octave complement]], the '''twelfth''' or '''tritave complement''' of a given twelfth-reduced interval is its interval distance from the [[3/1|perfect twelfth (3/1)]]. It seems to be very useful as a way of conceptualizing and constructing semiquartal triads in extended voices, and even as a way of describing the relationships between different hemitwelfths.

== History ==
The thought that the minor seventh and the major sixth complement or contrast each other is discussed in [[Flora Canou]]'s 2022 essay [[User:FloraC/Analysis on the 13-limit just intonation space: episode i|''Analysis on the 13-limit Just Intonation Space: Episode I'']]. In "Chapter VII. Septimal Chord Construction", it is suggested that the triads 1–7/4–3 and 1–12/7–3 are the septimal counterparts of the classical triads and that they come out superior to 1–7/6–4/3 and 1–8/7–4/3, which are formed on [[fourth complement]]s.

== Examples ==
The following interval pairs are ''twelfth complementary'' to each other
* [[7/4]] and [[12/7]]
* [[5/3]] and [[8/5]]
* [[19/12]] and [[32/19]]

== See also ==
* [[Octave complement]]
* [[Fifth complement]]
* [[Fourth complement]]

== Footnotes ==
<references/>

[[Category:Terms]]
[[Category:Interval]]
[[Category:Tritave]]
[[Category:Method]]