8/7 - Revision history

Squib at 16:02, 11 April 2026

2026-04-11T16:02:26Z

← Older revision		Revision as of 16:02, 11 April 2026
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	{{Wikipedia\|Septimal whole tone}}		{{Wikipedia\|Septimal whole tone}}

	In [[just intonation]], 8/7 is the '''septimal major second''', or '''septimal supermajor second''', of approximately 231.2{{cent}}. Although it falls between the familiar major second and minor third of [[12edo]], it ~~generally sounds~~ more like a wide second than a narrow third. It can be found between the 7th and 8th [[harmonic]]s and is thus a [[superparticular]] ratio. In [[7-limit]] JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh ([[7/4]]) and octave. It differs from the Pythagorean major second of [[9/8]] by [[64/63]], a microtone of about 27.3{{cent}}. It is close in size to 5edo's 240{{c}} step.		In [[just intonation]], 8/7 is the '''septimal major second''', or '''septimal supermajor second''', of approximately 231.2{{cent}}. Although it falls between the familiar major second and minor third of [[12edo]], most people think of it more like a wide second than a narrow third. It can be found between the 7th and 8th [[harmonic]]s and is thus a [[superparticular]] ratio. In [[7-limit]] JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh ([[7/4]]) and octave. It differs from the Pythagorean major second of [[9/8]] by [[64/63]], a microtone of about 27.3{{cent}}. It is close in size to 5edo's 240{{c}} step.

	A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is [[1029/1024]] (about 8.4{{c}}), which is tempered out in [[slendric]] systems like [[31edo]].		A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is [[1029/1024]] (about 8.4{{c}}), which is tempered out in [[slendric]] systems like [[31edo]].

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

2025-11-03T13:01:47Z

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

← Older revision		Revision as of 13:01, 3 November 2025
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	A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is [[1029/1024]] (about 8.4{{c}}), which is tempered out in [[slendric]] systems like [[31edo]].		A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is [[1029/1024]] (about 8.4{{c}}), which is tempered out in [[slendric]] systems like [[31edo]].
	== Approximation ==		== Approximation ==
	{{~~Interval_Edo_Approximation~~ \| 8/7}}		{{Interval edo approximation\|8/7}}
	== See also ==		== See also ==
	* [[7/4]] – its [[octave complement]]		* [[7/4]] – its [[octave complement]]

Pailiaq at 06:57, 3 November 2025

2025-11-03T06:57:45Z

← Older revision		Revision as of 06:57, 3 November 2025
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	A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is [[1029/1024]] (about 8.4{{c}}), which is tempered out in [[slendric]] systems like [[31edo]].		A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is [[1029/1024]] (about 8.4{{c}}), which is tempered out in [[slendric]] systems like [[31edo]].
			== Approximation ==
			{{Interval_Edo_Approximation \| 8/7}}
	== See also ==		== See also ==
	* [[7/4]] – its [[octave complement]]		* [[7/4]] – its [[octave complement]]

Fredg999: Remove link to deleted page

2025-08-15T03:49:05Z

Remove link to deleted page

← Older revision		Revision as of 03:49, 15 August 2025
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	* [[7/6]] – its [[fourth complement]]		* [[7/6]] – its [[fourth complement]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[8/7 equal-step tuning]]

	[[Category:Second]]		[[Category:Second]]
	[[Category:Supermajor second]]		[[Category:Supermajor second]]
	[[Category:Over-7 intervals]]		[[Category:Over-7 intervals]]

VectorGraphics at 16:56, 14 April 2025

2025-04-14T16:56:59Z

← Older revision		Revision as of 16:56, 14 April 2025
Line 6:		Line 6:
	{{Wikipedia\|Septimal whole tone}}		{{Wikipedia\|Septimal whole tone}}

	In [[just intonation]], 8/7 is the ~~'''supermajor second''',~~ '''septimal major second''', or '''septimal supermajor second''', of approximately 231.2{{cent}}. Although it falls between the familiar major second and minor third of [[12edo]], it generally sounds more like a wide second than a narrow third. It can be found between the 7th and 8th [[harmonic]]s and is thus a [[superparticular]] ratio. In [[7-limit]] JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh ([[7/4]]) and octave. It differs from the Pythagorean major second of [[9/8]] by [[64/63]], a microtone of about 27.3{{cent}}. It is close in size to 5edo's 240{{c}} step.		In [[just intonation]], 8/7 is the '''septimal major second''', or '''septimal supermajor second''', of approximately 231.2{{cent}}. Although it falls between the familiar major second and minor third of [[12edo]], it generally sounds more like a wide second than a narrow third. It can be found between the 7th and 8th [[harmonic]]s and is thus a [[superparticular]] ratio. In [[7-limit]] JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh ([[7/4]]) and octave. It differs from the Pythagorean major second of [[9/8]] by [[64/63]], a microtone of about 27.3{{cent}}. It is close in size to 5edo's 240{{c}} step.

	A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is [[1029/1024]] (about 8.4{{c}}), which is tempered out in [[slendric]] systems like [[31edo]].		A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is [[1029/1024]] (about 8.4{{c}}), which is tempered out in [[slendric]] systems like [[31edo]].

ArrowHead294 at 13:20, 26 February 2025

2025-02-26T13:20:08Z

← Older revision		Revision as of 13:20, 26 February 2025
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	{{Infobox Interval		{{Infobox Interval
	\| Name = septimal whole tone, supermajor second, septimal major second		\| Name = septimal whole tone, supermajor second, septimal major second, septimal supermajor second
	\| Color name = r2, ru 2nd		\| Color name = r2, ru 2nd
	\| Sound = jid_8_7_pluck_adu_dr220.mp3		\| Sound = jid_8_7_pluck_adu_dr220.mp3
Line 6:		Line 6:
	{{Wikipedia\|Septimal whole tone}}		{{Wikipedia\|Septimal whole tone}}

	In [[just intonation]], 8/7 is the '''supermajor second''' or '''septimal ~~major~~ second''' of approximately 231.2{{cent}}. Although it falls between the familiar major second and minor third of [[12edo]], it generally sounds more like a wide second than a narrow third. It can be found between the 7th and 8th [[harmonic]]s and is thus a [[superparticular]] ratio. In [[7-limit]] JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh ([[7/4]]) and octave. It differs from the Pythagorean major second of [[9/8]] by [[64/63]], a microtone of about 27.3{{cent}}. It is close in size to ~~one step of~~ 5edo = 240{{~~cent~~}}.		In [[just intonation]], 8/7 is the '''supermajor second''', '''septimal major second''', or '''septimal supermajor second''', of approximately 231.2{{cent}}. Although it falls between the familiar major second and minor third of [[12edo]], it generally sounds more like a wide second than a narrow third. It can be found between the 7th and 8th [[harmonic]]s and is thus a [[superparticular]] ratio. In [[7-limit]] JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh ([[7/4]]) and octave. It differs from the Pythagorean major second of [[9/8]] by [[64/63]], a microtone of about 27.3{{cent}}. It is close in size to 5edo's 240{{c}} step.

	A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is [[1029/1024]] (about 8.4{{~~cent~~}}), which is tempered out in [[slendric]] systems like [[31edo]].		A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is [[1029/1024]] (about 8.4{{c}}), which is tempered out in [[slendric]] systems like [[31edo]].

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

Lériendil at 08:55, 26 February 2025

2025-02-26T08:55:59Z

← Older revision		Revision as of 08:55, 26 February 2025
Line 8:		Line 8:
	In [[just intonation]], 8/7 is the '''supermajor second''' or '''septimal major second''' of approximately 231.2{{cent}}. Although it falls between the familiar major second and minor third of [[12edo]], it generally sounds more like a wide second than a narrow third. It can be found between the 7th and 8th [[harmonic]]s and is thus a [[superparticular]] ratio. In [[7-limit]] JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh ([[7/4]]) and octave. It differs from the Pythagorean major second of [[9/8]] by [[64/63]], a microtone of about 27.3{{cent}}. It is close in size to one step of 5edo = 240{{cent}}.		In [[just intonation]], 8/7 is the '''supermajor second''' or '''septimal major second''' of approximately 231.2{{cent}}. Although it falls between the familiar major second and minor third of [[12edo]], it generally sounds more like a wide second than a narrow third. It can be found between the 7th and 8th [[harmonic]]s and is thus a [[superparticular]] ratio. In [[7-limit]] JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh ([[7/4]]) and octave. It differs from the Pythagorean major second of [[9/8]] by [[64/63]], a microtone of about 27.3{{cent}}. It is close in size to one step of 5edo = 240{{cent}}.

	A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is [[1029/1024]] (about 8.4{{cent}}), which is tempered out in [[slendric]] ~~and~~ [[31edo]].		A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is [[1029/1024]] (about 8.4{{cent}}), which is tempered out in [[slendric]] systems like [[31edo]].

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

FloraC: Recategorize

2024-09-30T08:41:52Z

Recategorize

← Older revision		Revision as of 08:41, 30 September 2024
Line 19:		Line 19:
	[[Category:Second]]		[[Category:Second]]
	[[Category:Supermajor second]]		[[Category:Supermajor second]]
	[[Category:Over-7]]		[[Category:Over-7 intervals]]

Plumtree: Normalising usage of Infobox Interval

2022-10-25T16:59:41Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 16:59, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 8/7~~		\| Name = septimal whole tone, supermajor second, septimal major second
	~~\| Monzo = 3 0 0 -1~~
	~~\| Cents = 231.17409~~
	\| Name = septimal whole tone, ~~<br>~~supermajor second, ~~<br>~~septimal major second
	\| Color name = r2, ru 2nd		\| Color name = r2, ru 2nd
	~~\| FJS name = M2<sub>7</sub>~~
	\| Sound = jid_8_7_pluck_adu_dr220.mp3		\| Sound = jid_8_7_pluck_adu_dr220.mp3
	}}		}}
Line 21:		Line 17:
	* [[8/7 equal-step tuning]]		* [[8/7 equal-step tuning]]

	~~[[Category:7-limit]]~~
	[[Category:Second]]		[[Category:Second]]
	[[Category:Supermajor second]]		[[Category:Supermajor second]]
	~~[[Category:Superparticular]]~~
	~~[[Category:Octave-reduced subharmonics]]~~
	[[Category:Over-7]]		[[Category:Over-7]]

Fredg999: Added internal link

2022-03-23T17:44:21Z

Added internal link

← Older revision		Revision as of 17:44, 23 March 2022
Line 12:		Line 12:
	In [[just intonation]], 8/7 is the '''supermajor second''' or '''septimal major second''' of approximately 231.2{{cent}}. Although it falls between the familiar major second and minor third of [[12edo]], it generally sounds more like a wide second than a narrow third. It can be found between the 7th and 8th [[harmonic]]s and is thus a [[superparticular]] ratio. In [[7-limit]] JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh ([[7/4]]) and octave. It differs from the Pythagorean major second of [[9/8]] by [[64/63]], a microtone of about 27.3{{cent}}. It is close in size to one step of 5edo = 240{{cent}}.		In [[just intonation]], 8/7 is the '''supermajor second''' or '''septimal major second''' of approximately 231.2{{cent}}. Although it falls between the familiar major second and minor third of [[12edo]], it generally sounds more like a wide second than a narrow third. It can be found between the 7th and 8th [[harmonic]]s and is thus a [[superparticular]] ratio. In [[7-limit]] JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh ([[7/4]]) and octave. It differs from the Pythagorean major second of [[9/8]] by [[64/63]], a microtone of about 27.3{{cent}}. It is close in size to one step of 5edo = 240{{cent}}.

	A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is 1029/1024 (about 8.4{{cent}}), which is tempered out in [[slendric]] and [[31edo]].		A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is [[1029/1024]] (about 8.4{{cent}}), which is tempered out in [[slendric]] and [[31edo]].

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