3-odd-limit - Revision history

Overthink: perfect consonances

2026-06-14T01:27:20Z

perfect consonances

← Older revision		Revision as of 01:27, 14 June 2026
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	* [[1/1]]		* [[1/1]]
	* '''[[4/3]], [[3/2]]'''		* '''[[4/3]], [[3/2]]'''

			The 3-odd-limit can be considered the set of {{W\|perfect consonance}}s, containing the unison, octave, perfect fifth, and perfect fourth, which have the simplest [[frequency ratio]]s.

	{\| class="wikitable center-all right-2 left-5"		{\| class="wikitable center-all right-2 left-5"

2026-03-15T05:18:01Z

use proper reason

← Older revision		Revision as of 05:18, 15 March 2026
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	\|}		\|}

	All ~~edos~~ are [[consistent]] in the 3-odd-limit, since ~~there are only two~~ [[~~pitch class~~]]~~es besides the octave~~.		All [[edo]]s are [[consistent]] in the 3-odd-limit, since every edo maps 3/2 and 4/3 to the nearest step by [[patent val]].

	The {{w\|natural density\|density}} of edos consistent in the 3-odd-limit to distance ''d'' is expected to be 1/''d'' for {{nowrap\| ''d'' ≥ 1 }}.		The {{w\|natural density\|density}} of edos consistent in the 3-odd-limit to distance ''d'' is expected to be 1/''d'' for {{nowrap\| ''d'' ≥ 1 }}.

2025-10-08T13:31:11Z

Proposing separating the lines before the table to be separated in paragraphs

← Older revision		Revision as of 13:31, 8 October 2025
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	\|}		\|}

	All edos are [[consistent]] in the 3-odd-limit, since there are only two [[pitch class]]es besides the octave. The {{w\|natural density\|density}} of edos consistent in the 3-odd-limit to distance ''d'' is expected to be 1/''d'' for {{nowrap\| ''d'' ≥ 1 }}.		All edos are [[consistent]] in the 3-odd-limit, since there are only two [[pitch class]]es besides the octave.

			The {{w\|natural density\|density}} of edos consistent in the 3-odd-limit to distance ''d'' is expected to be 1/''d'' for {{nowrap\| ''d'' ≥ 1 }}.

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

2025-09-23T15:16:58Z

2025-08-15T09:47:43Z

Density of edos consistent to distance d

← Older revision		Revision as of 09:47, 15 August 2025
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	\|}		\|}

	All edos are [[consistent]] in the 3-odd-limit, since there are only two [[pitch class]]es besides the octave.		All edos are [[consistent]] in the 3-odd-limit, since there are only two [[pitch class]]es besides the octave. The {{w\|natural density\|density}} of edos consistent in the 3-odd-limit to distance ''d'' is expected to be 1/''d'' for {{nowrap\| ''d'' ≥ 1 }}.

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

2025-02-14T10:11:52Z

Edo approximation, may be obvious but still important to note

← Older revision		Revision as of 10:11, 14 February 2025
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	{{~~odd~~-limit navigation}}		{{Odd-limit navigation}}
	{{~~odd~~-limit intro\|3}}		{{Odd-limit intro\|3}}

	* [[1/1]]		* [[1/1]]
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	\| just perfect fifth		\| just perfect fifth
	\|}		\|}

			All edos are [[consistent]] in the 3-odd-limit, since there are only two [[pitch class]]es besides the octave.

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

2023-09-13T15:54:15Z

Sort key

← Older revision		Revision as of 15:54, 13 September 2023
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	* [[3-limit]] ([[prime limit]])		* [[3-limit]] ([[prime limit]])

	[[Category:3-odd-limit]]		[[Category:3-odd-limit\| ]] <!-- main article -->

2023-09-13T15:53:53Z

Remove category from article body

← Older revision		Revision as of 15:53, 13 September 2023
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	* [[1/1]]		* [[1/1]]
	* '''[[4/3]], [[3/2]]'''		* '''[[4/3]], [[3/2]]'''

	~~[[Category:Odd limit]]~~

	{\| class="wikitable center-all right-2 left-5"		{\| class="wikitable center-all right-2 left-5"

2023-09-13T15:53:36Z

2023-09-13T15:27:40Z

Add intro, move see also, fix typo

← Older revision		Revision as of 15:27, 13 September 2023
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	{{odd-limit navigation}}		{{odd-limit navigation}}
	~~This is a list of '''3-[[~~odd-limit~~]]''' intervals. To [[1-odd-limit]], it adds 1 interval pair involving 3. See also [[~~3~~-limit]]~~		{{odd-limit intro\|3}}

	* [[1/1]]		* [[1/1]]
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	\| w4		\| w4
	\| wa 4th		\| wa 4th
	\| just perfect ~~forth~~		\| just perfect fourth
	\|-		\|-
	\| [[3/2]]		\| [[3/2]]
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	\| just perfect fifth		\| just perfect fifth
	\|}		\|}

			== See also ==
			* [[3-limit]] ([[prime limit]])

	[[Category:Odd limit]]		[[Category:Odd limit]]