Superfourth - Revision history

FloraC: Style

2025-03-06T08:57:45Z

Style

← Older revision		Revision as of 08:57, 6 March 2025
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	A '''superfourth, ultrafourth''' or '''semi-augmented fourth''' is an [[interval]] that spans three steps of the [[5L 2s\|diatonic]] scale with a quality between augmented and perfect. It exists in [[neutralization\|neutralized]] diatonic scales as exactly one half of a [[major seventh]].		A '''superfourth''', '''ultrafourth''' or '''semi-augmented fourth''' is an [[interval]] that spans three steps of the [[5L 2s\|diatonic]] scale with a quality between augmented and perfect. It exists in [[neutralization\|neutralized]] diatonic scales as exactly one half of a [[major seventh]].

	In [[just intonation]], an interval may be classified as a superfourth if it is reasonably mapped to [[7edo\|3\7]] and [[24edo\|11\24]] (precisely three steps of the diatonic scale and five and a half steps of the chromatic scale).		In [[just intonation]], an interval may be classified as a superfourth if it is reasonably mapped to [[7edo\|3\7]] and [[24edo\|11\24]] (precisely three steps of the diatonic scale and five and a half steps of the chromatic scale).

VectorGraphics at 20:29, 5 March 2025

2025-03-05T20:29:44Z

← Older revision		Revision as of 20:29, 5 March 2025
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	The inversion of a superfourth is a [[subfifth]].		The inversion of a superfourth is a [[subfifth]].

			Information about superfourths in the conventional interval-region format may be found at [[Tritone]].

	== Examples ==		== Examples ==

VectorGraphics at 20:29, 5 March 2025

2025-03-05T20:29:19Z

← Older revision		Revision as of 20:29, 5 March 2025
Line 1:		Line 1:
	A '''superfourth''' or '''semi-augmented fourth''' is an [[interval]] that spans three steps of the [[5L 2s\|diatonic]] scale with a quality between augmented and perfect. It exists in [[neutralization\|neutralized]] diatonic scales as exactly one half of a [[major seventh]].		A '''superfourth, ultrafourth''' or '''semi-augmented fourth''' is an [[interval]] that spans three steps of the [[5L 2s\|diatonic]] scale with a quality between augmented and perfect. It exists in [[neutralization\|neutralized]] diatonic scales as exactly one half of a [[major seventh]].

	In [[just intonation]], an interval may be classified as a superfourth if it is reasonably mapped to [[7edo\|3\7]] and [[24edo\|11\24]] (precisely three steps of the diatonic scale and five and a half steps of the chromatic scale).		In [[just intonation]], an interval may be classified as a superfourth if it is reasonably mapped to [[7edo\|3\7]] and [[24edo\|11\24]] (precisely three steps of the diatonic scale and five and a half steps of the chromatic scale).

FloraC: Unify precision. -redundant links

2025-03-05T14:35:22Z

Unify precision. -redundant links

← Older revision		Revision as of 14:35, 5 March 2025
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	As a concrete [[interval region]], it is typically near 550{{cent}} in size. It is too wide to sound like a [[perfect fourth]] and too narrow to sound like a [[tritone]]. [[Margo Schulter]], in her article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum], proposes an approximate range for a superfourth to be from 528{{cent}} to 560{{cent}}. Of course, this categorization should not be taken for granted. Since music is subjective and culturally influenced, the borders of what is a superfourth are "fuzzy". Other descriptions are possible and legitimate.		As a concrete [[interval region]], it is typically near 550{{cent}} in size. It is too wide to sound like a [[perfect fourth]] and too narrow to sound like a [[tritone]]. [[Margo Schulter]], in her article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum], proposes an approximate range for a superfourth to be from 528{{cent}} to 560{{cent}}. Of course, this categorization should not be taken for granted. Since music is subjective and culturally influenced, the borders of what is a superfourth are "fuzzy". Other descriptions are possible and legitimate.

	Some of the simplest superfourths in [[just intonation]] are [[11/8]] (about 551.3{{c}}) and [[15/11]] (about 537{{c}}), both undecimal (11-based) superfourths; and [[48/35]] (about ~~546.8~~{{c}}) and [[49/36]] (about ~~533.7~~{{c}}), both septimal (7-based) superfourths.		Some of the simplest superfourths in [[just intonation]] are [[11/8]] (about 551{{c}}) and [[15/11]] (about 537{{c}}), both undecimal (11-based) superfourths; and [[48/35]] (about 547{{c}}) and [[49/36]] (about 534{{c}}), both septimal (7-based) superfourths.

	The inversion of a superfourth is a [[subfifth]].		The inversion of a superfourth is a [[subfifth]].
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	== See also ==		== See also ==
	* [[43/31]] – a tritone with a "superfourth-ish" taste		* [[43/31]] – a tritone with a "superfourth-ish" taste
	* [[Interval category]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[Subfifth]] – the [[octave complement]] region		* [[Subfifth]] – the [[octave complement]] region

FloraC: Rework the intro to address the abstract approach

2025-03-05T14:23:40Z

Rework the intro to address the abstract approach

← Older revision		Revision as of 14:23, 5 March 2025
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	A '''superfourth''' is an [[interval]] too wide to sound like a [[perfect fourth]] and too narrow to sound like a [[tritone]]. [[Margo Schulter]], in her article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum], proposes an approximate range for a superfourth to be from 528{{cent}} to 560{{cent}}. Some of the simplest superfourths in [[just intonation]] are [[11/8]] (about 551.3{{c}}) and [[15/11]] (about 537{{c}}), both undecimal (11-based) superfourths; and [[48/35]] (about 546.8{{c}}) and [[49/36]] (about 533.7{{c}}), both septimal (7-based) superfourths.		A '''superfourth''' or '''semi-augmented fourth''' is an [[interval]] that spans three steps of the [[5L 2s\|diatonic]] scale with a quality between augmented and perfect. It exists in [[neutralization\|neutralized]] diatonic scales as exactly one half of a [[major seventh]].

			In [[just intonation]], an interval may be classified as a superfourth if it is reasonably mapped to [[7edo\|3\7]] and [[24edo\|11\24]] (precisely three steps of the diatonic scale and five and a half steps of the chromatic scale).

			As a concrete [[interval region]], it is typically near 550{{cent}} in size. It is too wide to sound like a [[perfect fourth]] and too narrow to sound like a [[tritone]]. [[Margo Schulter]], in her article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum], proposes an approximate range for a superfourth to be from 528{{cent}} to 560{{cent}}. Of course, this categorization should not be taken for granted. Since music is subjective and culturally influenced, the borders of what is a superfourth are "fuzzy". Other descriptions are possible and legitimate.

			Some of the simplest superfourths in [[just intonation]] are [[11/8]] (about 551.3{{c}}) and [[15/11]] (about 537{{c}}), both undecimal (11-based) superfourths; and [[48/35]] (about 546.8{{c}}) and [[49/36]] (about 533.7{{c}}), both septimal (7-based) superfourths.

	The inversion of a superfourth is a [[subfifth]].		The inversion of a superfourth is a [[subfifth]].

	Of course, this categorization should not be taken for granted. Since music is subjective and culturally influenced, the borders of what is a superfourth are "fuzzy". Other descriptions are possible and legitimate.

	== Examples ==		== Examples ==
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	! Interval		! Interval
	! Cents		! Cents
	! Prime limit<br />(if applicable)		! Prime limit<br>(if applicable)
	\|-		\|-
	\| 6\[[88cET]]<br />or ~~11\~~[[25edo\|25]]		\| [[88cET\|6\88cET]]<br>or [[25edo\|11\25]]
	\| 528.000		\| 528.000
	\| —		\| —
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	\| 17		\| 17
	\|-		\|-
	\| 4\[[9edo\|9]]		\| [[9edo\|4\9]]
	\| 533.333		\| 533.333
	\| —		\| —
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	\| 11		\| 11
	\|-		\|-
	\| ~~13\~~[[29edo\|29]]		\| [[29edo\|13\29]]
	\| 537.931		\| 537.931
	\| —		\| —
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	\| 41		\| 41
	\|-		\|-
	\| 9\[[20edo\|20]]		\| [[20edo\|9\20]]
	\| 540.000		\| 540.000
	\| —		\| —
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	\| 7		\| 7
	\|-		\|-
	\| ~~14\~~[[31edo\|31]]		\| [[31edo\|14\31]]
	\| 541.935		\| 541.935
	\| —		\| —
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	\| 19		\| 19
	\|-		\|-
	\| 5\[[11edo\|11]]		\| [[11edo\|5\11]]
	\| 545.455		\| 545.455
	\| —		\| —
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	\| 7		\| 7
	\|-		\|-
	\| ~~11\~~[[24edo\|24]]		\| [[24edo\|11\24]]
	\| 550.000		\| 550.000
	\| —		\| —
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	\| 11		\| 11
	\|-		\|-
	\| 6\[[13edo\|13]]		\| [[13edo\|6\13]]
	\| 553.846		\| 553.846
	\| —		\| —
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	\| 29		\| 29
	\|-		\|-
	\| ~~13\~~[[28edo\|28]]		\| [[28edo\|13\28]]
	\| 557.143		\| 557.143
	\| —		\| —
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	\| 47		\| 47
	\|-		\|-
	\| 7\[[15edo\|15]]		\| [[15edo\|7\15]]
	\| 560.000		\| 560.000
	\| —		\| —

ArrowHead294 at 13:12, 5 March 2025

2025-03-05T13:12:18Z

← Older revision		Revision as of 13:12, 5 March 2025
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	\| 6\[[88cET]]<br />or 11\[[25edo\|25]]		\| 6\[[88cET]]<br />or 11\[[25edo\|25]]
	\| 528.000		\| 528.000
	\| -		\| —
	\|-		\|-
	\| [[19/14]]		\| [[19/14]]
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	\| 4\[[9edo\|9]]		\| 4\[[9edo\|9]]
	\| 533.333		\| 533.333
	\| -		\| —
	\|-		\|-
	\| [[49/36]]		\| [[49/36]]
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	\| 13\[[29edo\|29]]		\| 13\[[29edo\|29]]
	\| 537.931		\| 537.931
	\| -		\| —
	\|-		\|-
	\| 56/41		\| 56/41
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	\| 9\[[20edo\|20]]		\| 9\[[20edo\|20]]
	\| 540.000		\| 540.000
	\| -		\| —
	\|-		\|-
	\| 41/30		\| 41/30
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	\| 14\[[31edo\|31]]		\| 14\[[31edo\|31]]
	\| 541.935		\| 541.935
	\| -		\| —
	\|-		\|-
	\| [[26/19]]		\| [[26/19]]
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	\| 5\[[11edo\|11]]		\| 5\[[11edo\|11]]
	\| 545.455		\| 545.455
	\| -		\| —
	\|-		\|-
	\| 37/27		\| 37/27
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	\| 11\[[24edo\|24]]		\| 11\[[24edo\|24]]
	\| 550.000		\| 550.000
	\| -		\| —
	\|-		\|-
	\| [[11/8]]		\| [[11/8]]
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	\| 6\[[13edo\|13]]		\| 6\[[13edo\|13]]
	\| 553.846		\| 553.846
	\| -		\| —
	\|-		\|-
	\| 62/45		\| 62/45
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	\| 13\[[28edo\|28]]		\| 13\[[28edo\|28]]
	\| 557.143		\| 557.143
	\| -		\| —
	\|-		\|-
	\| 243/176		\| 243/176
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	\| 7\[[15edo\|15]]		\| 7\[[15edo\|15]]
	\| 560.000		\| 560.000
	\| -		\| —
	\|}		\|}

ArrowHead294 at 13:10, 5 March 2025

2025-03-05T13:10:13Z

← Older revision		Revision as of 13:10, 5 March 2025
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	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[Subfifth]] – the [[octave complement]] region		* [[Subfifth]] – the [[octave complement]] region

			{{Navbox intervals}}

	[[Category:Superfourth\| ]] <!-- main article -->		[[Category:Superfourth\| ]] <!-- main article -->

ArrowHead294 at 13:10, 5 March 2025

2025-03-05T13:10:00Z

← Older revision		Revision as of 13:10, 5 March 2025
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	A '''superfourth''' is an [[interval]] too wide to sound like a [[perfect fourth]] and too narrow to sound like a [[tritone]]. [[Margo Schulter]], in her article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum], proposes an approximate range for a superfourth to be from 528{{cent}} to 560{{cent}}. Some of the simplest superfourths in [[just intonation]] are [[11/8]] (about 551.3{{c}}) and [[15/11]] (about 537{{c}}), both undecimal (11-based) superfourths; and [[48/35]] (about 546.8¢) and [[49/36]] (about 533.7{{c}}), both septimal (7-based) superfourths.		A '''superfourth''' is an [[interval]] too wide to sound like a [[perfect fourth]] and too narrow to sound like a [[tritone]]. [[Margo Schulter]], in her article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum], proposes an approximate range for a superfourth to be from 528{{cent}} to 560{{cent}}. Some of the simplest superfourths in [[just intonation]] are [[11/8]] (about 551.3{{c}}) and [[15/11]] (about 537{{c}}), both undecimal (11-based) superfourths; and [[48/35]] (about 546.8{{c}}) and [[49/36]] (about 533.7{{c}}), both septimal (7-based) superfourths.

	The inversion of a superfourth is a [[subfifth]].		The inversion of a superfourth is a [[subfifth]].

ArrowHead294 at 13:09, 5 March 2025

2025-03-05T13:09:52Z

← Older revision		Revision as of 13:09, 5 March 2025
Line 1:		Line 1:
	A '''superfourth''' is an [[interval]] too wide to sound like a [[perfect fourth]] and too narrow to sound like a [[tritone]]. [[Margo Schulter]], in her article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum], proposes an approximate range for a superfourth to be from ~~528¢~~ to ~~560¢~~. Some of the simplest superfourths in [[just intonation]] are [[11/8]] (about 551.3¢) and [[15/11]] (about ~~537¢~~), both undecimal (11-based) superfourths; and [[48/35]] (about 546.8¢) and [[49/36]] (about 533.7¢), both septimal (7-based) superfourths.		A '''superfourth''' is an [[interval]] too wide to sound like a [[perfect fourth]] and too narrow to sound like a [[tritone]]. [[Margo Schulter]], in her article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum], proposes an approximate range for a superfourth to be from 528{{cent}} to 560{{cent}}. Some of the simplest superfourths in [[just intonation]] are [[11/8]] (about 551.3{{c}}) and [[15/11]] (about 537{{c}}), both undecimal (11-based) superfourths; and [[48/35]] (about 546.8¢) and [[49/36]] (about 533.7{{c}}), both septimal (7-based) superfourths.

	The inversion of a superfourth is a [[subfifth]].		The inversion of a superfourth is a [[subfifth]].
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	\|-		\|-
	! Interval		! Interval
	! Cents ~~Value~~		! Cents
	! Prime ~~Limit~~ <br> (if applicable)		! Prime limit<br />(if applicable)
	\|-		\|-
	\| 6\[[88cET]] <br> or 11\[[25edo\|25]]		\| 6\[[88cET]]<br />or 11\[[25edo\|25]]
	\| 528.000		\| 528.000
	\| -		\| -
Line 128:		Line 128:

	== See also ==		== See also ==
	* [[43/31]] -- a tritone with a "~~superfourthish~~" taste		* [[43/31]] – a tritone with a "superfourth-ish" taste
	* [[Interval category]]		* [[Interval category]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[Subfifth]] — the [[octave ~~complement\|octave-~~complement]] region		* [[Subfifth]] – the [[octave complement]] region

	[[Category:Superfourth\| ]] <!-- main article -->		[[Category:Superfourth\| ]] <!-- main article -->

Fredg999: Misc. edits, categories

2022-01-22T05:35:00Z

Misc. edits, categories

← Older revision		Revision as of 05:35, 22 January 2022
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	A '''superfourth''' is an [[interval]] too wide to sound like a [[perfect fourth]] and too narrow to sound like a [[tritone]]. [[Margo Schulter]], in her article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum], proposes an approximate range for a superfourth to be from 528¢ to 560¢. Some of the simplest superfourths in [[~~Just~~ intonation]] are [[11/8]] (about 551.3¢) and [[15/11]] (about 537¢), both undecimal (11-based) superfourths; and [[48/35]] (about 546.8¢) and [[49/36]] (about 533.7¢), both septimal (7-based) superfourths.		A '''superfourth''' is an [[interval]] too wide to sound like a [[perfect fourth]] and too narrow to sound like a [[tritone]]. [[Margo Schulter]], in her article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum], proposes an approximate range for a superfourth to be from 528¢ to 560¢. Some of the simplest superfourths in [[just intonation]] are [[11/8]] (about 551.3¢) and [[15/11]] (about 537¢), both undecimal (11-based) superfourths; and [[48/35]] (about 546.8¢) and [[49/36]] (about 533.7¢), both septimal (7-based) superfourths.

	The inversion of a superfourth is a [[subfifth]].		The inversion of a superfourth is a [[subfifth]].
Line 5:		Line 5:
	Of course, this categorization should not be taken for granted. Since music is subjective and culturally influenced, the borders of what is a superfourth are "fuzzy". Other descriptions are possible and legitimate.		Of course, this categorization should not be taken for granted. Since music is subjective and culturally influenced, the borders of what is a superfourth are "fuzzy". Other descriptions are possible and legitimate.

	==Examples==		== Examples ==
	Below is a list of some intervals in the superfourth range, both just and tempered.		Below is a list of some intervals in the superfourth range, both just and tempered.

Line 128:		Line 128:

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

	* [[43/31]] -- a tritone with a "superfourthish" taste		* [[43/31]] -- a tritone with a "superfourthish" taste
	* [[Interval category]]		* [[Interval category]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[Subfifth]]		* [[Subfifth]] — the [[octave complement\|octave-complement]] region

	[[Category:Superfourth]]		[[Category:Superfourth\| ]] <!-- main article -->
	~~[[Category:Interval]]~~