7/5 - Revision history

Hotcrystal0: adding link

2026-01-08T13:53:53Z

adding link

← Older revision		Revision as of 13:53, 8 January 2026
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	7/5 is notable for its low [[harmonic entropy]], and is often reported to sound more consonant than the half-octave tritone; indeed it appears in the harmonic seventh chord that forms the basis of consonance in 7-limit JI. Its inversion is [[10/7]], which measures about 617.5¢, and these two septimal tritones differ by the [[superparticular]] interval [[50/49]], about 35.0¢. Systems which temper out 50/49 will equate 7/5 and [[10/7]], usually to the 600¢ half-octave.		7/5 is notable for its low [[harmonic entropy]], and is often reported to sound more consonant than the half-octave tritone; indeed it appears in the harmonic seventh chord that forms the basis of consonance in 7-limit JI. Its inversion is [[10/7]], which measures about 617.5¢, and these two septimal tritones differ by the [[superparticular]] interval [[50/49]], about 35.0¢. Systems which temper out 50/49 will equate 7/5 and [[10/7]], usually to the 600¢ half-octave.

	Another just tritone is ~~the~~ [[~~3-limit]]~~ 729/512, 611.7¢, and this is literally a tri-tone, since it is (9/8)<sup>3</sup>, or three "whole tones". Yet another is [[45/32]], about 590.2¢, which appears in the [[5-limit]] (inversion is [[64/45]]). See also [[13/9]], [[18/13]], [[17/12]], [[24/17]], [[25/18]] and [[36/25]].		Another just tritone is [[729/512]] (611.7¢), and this is literally a tri-tone, since it is (9/8)<sup>3</sup>, or three "whole tones". Yet another is [[45/32]], about 590.2¢, which appears in the [[5-limit]] (inversion is [[64/45]]). See also [[13/9]], [[18/13]], [[17/12]], [[24/17]], [[25/18]] and [[36/25]].
	== Approximation ==		== Approximation ==
	{{Interval edo approximation\|7/5}}		{{Interval edo approximation\|7/5}}

FloraC: Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

2025-11-03T13:06:09Z

Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

← Older revision		Revision as of 13:06, 3 November 2025
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	Another just tritone is the [[3-limit]] 729/512, 611.7¢, and this is literally a tri-tone, since it is (9/8)<sup>3</sup>, or three "whole tones". Yet another is [[45/32]], about 590.2¢, which appears in the [[5-limit]] (inversion is [[64/45]]). See also [[13/9]], [[18/13]], [[17/12]], [[24/17]], [[25/18]] and [[36/25]].		Another just tritone is the [[3-limit]] 729/512, 611.7¢, and this is literally a tri-tone, since it is (9/8)<sup>3</sup>, or three "whole tones". Yet another is [[45/32]], about 590.2¢, which appears in the [[5-limit]] (inversion is [[64/45]]). See also [[13/9]], [[18/13]], [[17/12]], [[24/17]], [[25/18]] and [[36/25]].
	== Approximation ==		== Approximation ==
	{{~~Interval_Edo_Approximation~~ \| 7/5}}		{{Interval edo approximation\|7/5}}
	== See also ==		== See also ==

Pailiaq at 07:24, 3 November 2025

2025-11-03T07:24:49Z

← Older revision		Revision as of 07:24, 3 November 2025
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	Another just tritone is the [[3-limit]] 729/512, 611.7¢, and this is literally a tri-tone, since it is (9/8)<sup>3</sup>, or three "whole tones". Yet another is [[45/32]], about 590.2¢, which appears in the [[5-limit]] (inversion is [[64/45]]). See also [[13/9]], [[18/13]], [[17/12]], [[24/17]], [[25/18]] and [[36/25]].		Another just tritone is the [[3-limit]] 729/512, 611.7¢, and this is literally a tri-tone, since it is (9/8)<sup>3</sup>, or three "whole tones". Yet another is [[45/32]], about 590.2¢, which appears in the [[5-limit]] (inversion is [[64/45]]). See also [[13/9]], [[18/13]], [[17/12]], [[24/17]], [[25/18]] and [[36/25]].
			== Approximation ==
			{{Interval_Edo_Approximation \| 7/5}}
	== See also ==		== See also ==

BudjarnLambeth: Category:Taxicab-2 intervals

2024-12-01T23:01:39Z

Category:Taxicab-2 intervals

← Older revision		Revision as of 23:01, 1 December 2024
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	[[Category:Tritone]]		[[Category:Tritone]]
	[[Category:Over-5 intervals]]		[[Category:Over-5 intervals]]
			[[Category:Taxicab-2 intervals]]

FloraC: Paragraphing (following 10/7). Heptatonic -> diatonic. Consistent use of "harmonic seventh chord"

2024-10-09T09:32:14Z

Paragraphing (following 10/7). Heptatonic -> diatonic. Consistent use of "harmonic seventh chord"

← Older revision		Revision as of 09:32, 9 October 2024
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	{{Wikipedia\|Septimal tritone}}		{{Wikipedia\|Septimal tritone}}

	In [[7-limit]] [[just intonation]], '''7/5''' is a '''narrow [[tritone]]''' (or '''Huygens' tritone''') measuring about 582.5¢. It is a noticeable 17.5¢ away from the 600¢ half-octave (square root of 2) tritone of [[12edo]] and every even-numbered [[~~EDO~~]]. It represents the difference between [[7/4]] and [[5/4]]. While in the context of the harmonic seventh chord, it is rightly recognized as a type of diminished fifth, it can also be argued on the basis of the fact that 7/5 interval is smaller than 600 cents that it acts more as a type of augmented fourth than a diminished fifth- an analysis that is required in cases where this interval occurs in a heptatonic scale that demonstrates [[Rothenberg propriety]]. This is one of the reasons why 7/4 can be argued to be a type of "sinth"- a cross between a sixth and a seventh- as opposed to merely a subminor seventh.		In [[7-limit]] [[just intonation]], '''7/5''' is a '''narrow [[tritone]]''' (or '''Huygens' tritone''') measuring about 582.5¢. It is a noticeable 17.5¢ away from the 600¢ half-octave (square root of 2) tritone of [[12edo]] and every even-numbered [[edo]]. It represents the difference between [[7/4]] and [[5/4]].

	7/5 is notable for its low [[harmonic entropy]], and is often reported to sound more consonant than the half-octave tritone; indeed it appears in the ~~4:5:6:7 tetrad~~ that forms the basis of consonance in 7-limit JI. Its inversion is [[10/7]], which measures about 617.5¢, and these two septimal tritones differ by the [[superparticular]] interval [[50/49]], about 35.0¢. Systems which temper out 50/49 will equate 7/5 and [[10/7]], usually to the 600¢ half-octave.		While in the context of the [[harmonic seventh chord]], it is rightly recognized as a type of diminished fifth, it can also be argued on the basis of the fact that 7/5 interval is smaller than 600 cents that it acts more as a type of augmented fourth than a diminished fifth – an analysis that is required in cases where this interval occurs in a [[5L 2s\|diatonic scale]] that demonstrates [[Rothenberg propriety]]. This is one of the reasons why 7/4 can be argued to be a type of "sinth" – a cross between a sixth and a seventh – as opposed to merely a subminor seventh.

			7/5 is notable for its low [[harmonic entropy]], and is often reported to sound more consonant than the half-octave tritone; indeed it appears in the harmonic seventh chord that forms the basis of consonance in 7-limit JI. Its inversion is [[10/7]], which measures about 617.5¢, and these two septimal tritones differ by the [[superparticular]] interval [[50/49]], about 35.0¢. Systems which temper out 50/49 will equate 7/5 and [[10/7]], usually to the 600¢ half-octave.

	Another just tritone is the [[3-limit]] 729/512, 611.7¢, and this is literally a tri-tone, since it is (9/8)<sup>3</sup>, or three "whole tones". Yet another is [[45/32]], about 590.2¢, which appears in the [[5-limit]] (inversion is [[64/45]]). See also [[13/9]], [[18/13]], [[17/12]], [[24/17]], [[25/18]] and [[36/25]].		Another just tritone is the [[3-limit]] 729/512, 611.7¢, and this is literally a tri-tone, since it is (9/8)<sup>3</sup>, or three "whole tones". Yet another is [[45/32]], about 590.2¢, which appears in the [[5-limit]] (inversion is [[64/45]]). See also [[13/9]], [[18/13]], [[17/12]], [[24/17]], [[25/18]] and [[36/25]].

FloraC: Recategorize

2024-09-30T08:39:06Z

Recategorize

← Older revision		Revision as of 08:39, 30 September 2024
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	[[Category:Tritone]]		[[Category:Tritone]]
	[[Category:Over-5]]		[[Category:Over-5 intervals]]

Plumtree: Normalising usage of Infobox Interval

2022-10-25T16:48:36Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 16:48, 25 October 2022
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	}}		}}
	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 7/5~~		\| Name = narrow tritone, lesser septimal tritone, Huygens' tritone
	~~\| Monzo = 0 0 -1 1~~
	~~\| Cents = 582.51219~~
	\| Name = narrow tritone, ~~<br>~~lesser septimal tritone, ~~<br>~~Huygens' tritone
	\| Color name = zg5, zogu 5th		\| Color name = zg5, zogu 5th
	~~\| FJS name = d5<sup>7</sup><sub>5</sub>~~
	\| Sound = jid_7_5_pluck_adu_dr220.mp3		\| Sound = jid_7_5_pluck_adu_dr220.mp3
	}}		}}
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	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

	~~[[Category:7-limit]]~~
	[[Category:Tritone]]		[[Category:Tritone]]
	[[Category:Over-5]]		[[Category:Over-5]]

Fredg999 category edits: Removing from Category:Pages with internal sound examples using Cat-a-lot

2022-02-22T23:47:27Z

Removing from Category:Pages with internal sound examples using Cat-a-lot

← Older revision		Revision as of 23:47, 22 February 2022
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	[[Category:Tritone]]		[[Category:Tritone]]
	[[Category:Over-5]]		[[Category:Over-5]]
	~~[[Category:Pages with internal sound examples]]~~

Fredg999: Categories

2022-01-01T21:30:41Z

Fredg999: Added Wikipedia box, misc. edits, categories

2022-01-01T21:29:19Z

Added Wikipedia box, misc. edits, categories

← Older revision		Revision as of 21:29, 1 January 2022
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	\| Ratio = 7/5		\| Ratio = 7/5
	\| Monzo = 0 0 -1 1		\| Monzo = 0 0 -1 1
	\| Cents = 582.51219		\| Cents = 582.51219
	\| Name = narrow tritone, <br>Huygens' tritone		\| Name = narrow tritone, <br>lesser septimal tritone, <br>Huygens' tritone
	\| Color name = zg5, zogu 5th		\| Color name = zg5, zogu 5th
	\| FJS name = d5<sup>7</sup><sub>5</sub>		\| FJS name = d5<sup>7</sup><sub>5</sub>
	\| Sound = jid_7_5_pluck_adu_dr220.mp3		\| Sound = jid_7_5_pluck_adu_dr220.mp3
	}}		}}
			{{Wikipedia\|Septimal tritone}}

	In [[7-limit]] [[~~Just Intonation~~]], '''7/5''' is a '''narrow [[tritone]]''' (or '''Huygens' tritone''') measuring about 582.5¢. It is a noticeable 17.5¢ away from the 600¢ half-octave (square root of 2) tritone of [[12edo]] and every even-numbered [[EDO]]. It represents the difference between [[7/4]] and [[5/4]]. While in the context of the harmonic seventh chord, it is rightly recognized as a type of diminished fifth, it can also be argued on the basis of the fact that 7/5 interval is smaller than 600 cents that it acts more as a type of augmented fourth than a diminished fifth- an analysis that is required in cases where this interval occurs in a heptatonic scale that demonstrates [[~~Wikipedia:Rothenberg propriety\|~~Rothenberg propriety]]. This is one of the reasons why 7/4 can be argued to be a type of "sinth"- a cross between a sixth and a seventh- as opposed to merely a subminor seventh.		In [[7-limit]] [[just intonation]], '''7/5''' is a '''narrow [[tritone]]''' (or '''Huygens' tritone''') measuring about 582.5¢. It is a noticeable 17.5¢ away from the 600¢ half-octave (square root of 2) tritone of [[12edo]] and every even-numbered [[EDO]]. It represents the difference between [[7/4]] and [[5/4]]. While in the context of the harmonic seventh chord, it is rightly recognized as a type of diminished fifth, it can also be argued on the basis of the fact that 7/5 interval is smaller than 600 cents that it acts more as a type of augmented fourth than a diminished fifth- an analysis that is required in cases where this interval occurs in a heptatonic scale that demonstrates [[Rothenberg propriety]]. This is one of the reasons why 7/4 can be argued to be a type of "sinth"- a cross between a sixth and a seventh- as opposed to merely a subminor seventh.

	7/5 is notable for its low [[~~Harmonic Entropy\|~~harmonic entropy]], and is often reported to sound more consonant than the half-octave tritone; indeed it appears in the 4:5:6:7 tetrad that forms the basis of consonance in 7-limit JI. Its inversion is [[10/7]], which measures about 617.5¢, and these two septimal tritones differ by the [[superparticular]] interval [[50/49]], about 35.0¢. Systems which temper out 50/49 will equate 7/5 and [[10/7]], usually to the 600¢ half-octave.		7/5 is notable for its low [[harmonic entropy]], and is often reported to sound more consonant than the half-octave tritone; indeed it appears in the 4:5:6:7 tetrad that forms the basis of consonance in 7-limit JI. Its inversion is [[10/7]], which measures about 617.5¢, and these two septimal tritones differ by the [[superparticular]] interval [[50/49]], about 35.0¢. Systems which temper out 50/49 will equate 7/5 and [[10/7]], usually to the 600¢ half-octave.

	Another just tritone is the [[3-limit]] 729/512, 611.7¢, and this is literally a tri-tone, since it is (9/8)<sup>3</sup>, or three "whole tones". Yet another is [[45/32]], about 590.2¢, which appears in the [[5-limit]] (inversion is [[64/45]]). See also [[13/9]], [[18/13]], [[17/12]], [[24/17]], [[25/18]] and [[36/25]].		Another just tritone is the [[3-limit]] 729/512, 611.7¢, and this is literally a tri-tone, since it is (9/8)<sup>3</sup>, or three "whole tones". Yet another is [[45/32]], about 590.2¢, which appears in the [[5-limit]] (inversion is [[64/45]]). See also [[13/9]], [[18/13]], [[17/12]], [[24/17]], [[25/18]] and [[36/25]].
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	* [[10/7]] – its [[octave complement]]		* [[10/7]] – its [[octave complement]]
	* [[15/14]] – its [[fifth complement]]		* [[15/14]] – its [[fifth complement]]
	* [[Gallery of ~~Just Intervals]]~~		* [[Gallery of just intervals]]
	* [[Wikipedia:Septimal_tritone\|Septimal tritone - Wikipedia]]

	[[Category:7-limit]]		[[Category:7-limit]]
	~~[[Category:interval]]~~
	~~[[Category:just_interval]]~~
	~~[[Category:ratio]]~~
	[[Category:Tritone]]		[[Category:Tritone]]
	[[Category:Over-5]]		[[Category:Over-5]]

← Older revision		Revision as of 21:30, 1 January 2022
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	[[Category:Tritone]]		[[Category:Tritone]]
	[[Category:Over-5]]		[[Category:Over-5]]
			[[Category:Pages with internal sound examples]]