9/7 - Revision history

Overthink: space out links

2026-03-12T04:08:55Z

space out links

← Older revision		Revision as of 04:08, 12 March 2026
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	{{Wikipedia\|Septimal major third}}		{{Wikipedia\|Septimal major third}}
	In [[just intonation]], '''9/7''' is the '''supermajor third'''<ref>[[Hermann von Helmholtz\|Hermann L. F. von Helmholtz]] (1875). ''On the sensations of tone as a physiological basis for the theory of music'', p. 284.</ref> or '''septimal major third''' of approximately 435.1{{cent}}, characteristic of [[7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The [[9-odd-limit]] [[pentad]] [[4:5:6:7:9]] includes a septimal supermajor third between the seventh and the ninth. The interval has an interesting "neutral" quality to it similar to the way [[9/8]] behaves as ratios of [[9/1\|9]] all share this quality.		In [[just intonation]], '''9/7''' is the '''supermajor third'''<ref>[[Hermann von Helmholtz\|Hermann L. F. von Helmholtz]] (1875). ''On the sensations of tone as a physiological basis for the theory of music'', p. 284.</ref> or '''septimal major third''' of approximately 435.1{{cent}}, characteristic of [[7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The [[9-odd-limit]] harmonic ninth chord, a [[pentad]] with ratios [[4:5:6:7:9]], includes a septimal supermajor third between the seventh and the ninth. The interval has an interesting "neutral" quality to it similar to the way [[9/8]] behaves as ratios of [[9/1\|9]] all share this quality.

	A just chord can be built with this wide third in place of the more traditional [[5/4]]. This supermajor triad would be [[14:18:21]]. This triad can be very effective in music, but in this context, the modern ear accustomed to [[12edo]] thirds of 400{{cent}} is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with 9/8 much more than 5/4. Chords such as the 9-odd-limit pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant.		A just chord can be built with this wide third in place of the more traditional [[5/4]]. This supermajor triad would be [[14:18:21]]. This triad can be very effective in music, but in this context, the modern ear accustomed to [[12edo]] thirds of 400{{cent}} is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with 9/8 much more than 5/4. Chords such as the 9-odd-limit pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant.

FloraC: Formatting and linking

2026-01-21T20:18:04Z

Formatting and linking

← Older revision		Revision as of 20:18, 21 January 2026
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	}}		}}
	{{Wikipedia\|Septimal major third}}		{{Wikipedia\|Septimal major third}}
	In [[just intonation]], '''9/7''' is the '''supermajor third'''<ref>[[Hermann von Helmholtz\|Hermann L. F. von Helmholtz]] (1875). ''On the sensations of tone as a physiological basis for the theory of music'', p. 284.</ref> or '''septimal major third''' of approximately 435.1{{cent}}, characteristic of [[7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The 9-limit pentad 4:5:6:7:9 includes a septimal supermajor third between the ~~7th~~ and the ~~9th~~. The interval has an interesting neutral quality to it similar to the way 9/8 behaves as ratios of ~~nine~~ all share this quality.		In [[just intonation]], '''9/7''' is the '''supermajor third'''<ref>[[Hermann von Helmholtz\|Hermann L. F. von Helmholtz]] (1875). ''On the sensations of tone as a physiological basis for the theory of music'', p. 284.</ref> or '''septimal major third''' of approximately 435.1{{cent}}, characteristic of [[7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The [[9-odd-limit]] [[pentad]] [[4:5:6:7:9]] includes a septimal supermajor third between the seventh and the ninth. The interval has an interesting "neutral" quality to it similar to the way [[9/8]] behaves as ratios of [[9/1\|9]] all share this quality.

	A just chord can be built with this wide third in place of the more traditional [[5/4]]. This supermajor triad would be 14:18:21. This triad can be very effective in music, but in this context, the modern ear accustomed to 12edo thirds of 400{{cent}} is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with [[9/8]] much more than 5/4. Chords such as the [[9-odd-limit]] pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant.		A just chord can be built with this wide third in place of the more traditional [[5/4]]. This supermajor triad would be [[14:18:21]]. This triad can be very effective in music, but in this context, the modern ear accustomed to [[12edo]] thirds of 400{{cent}} is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with 9/8 much more than 5/4. Chords such as the 9-odd-limit pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant.

	In Ancient Greek music, Archytas used the 9/7 interval in his [[tetrachord]] tunings (in all three genera), for the interval between the ''parhypate'' (second degree) and ''mese'' (fourth degree).		In [[Ancient Greek music]], {{w\|Archytas}} used the 9/7 interval in his [[tetrachord]] tunings (in all three genera), for the interval between the ''parhypate'' (second degree) and ''mese'' (fourth degree).

	== Approximation ==		== Approximation ==
	In [[11edo]], 4\11 is about 1.3{{cent}} sharp of 9/7.		In [[11edo]], 4\11 is about 1.3{{cent}} sharp of 9/7.

	{{Interval edo approximation\|9/7}}		{{Interval edo approximation\|9/7}}

	== See also ==		== See also ==
	* [[14/9]] – its [[octave complement]]		* [[14/9]] – its [[octave complement]]

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

2025-11-03T13:05:53Z

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

← Older revision		Revision as of 13:05, 3 November 2025
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	== Approximation ==		== Approximation ==
	In [[11edo]], 4\11 is about 1.3{{cent}} sharp of 9/7.		In [[11edo]], 4\11 is about 1.3{{cent}} sharp of 9/7.
	{{~~Interval_Edo_Approximation~~ \| 9/7}}		{{Interval edo approximation\|9/7}}
	== See also ==		== See also ==
	* [[14/9]] – its [[octave complement]]		* [[14/9]] – its [[octave complement]]

Pailiaq at 07:17, 3 November 2025

2025-11-03T07:17:21Z

← Older revision		Revision as of 07:17, 3 November 2025
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	== Approximation ==		== Approximation ==
	In [[11edo]], 4\11 is about 1.3{{cent}} sharp of 9/7.		In [[11edo]], 4\11 is about 1.3{{cent}} sharp of 9/7.
			{{Interval_Edo_Approximation \| 9/7}}
	== See also ==		== See also ==
	* [[14/9]] – its [[octave complement]]		* [[14/9]] – its [[octave complement]]

Sintel at 15:07, 16 April 2025

2025-04-16T15:07:47Z

← Older revision		Revision as of 15:07, 16 April 2025
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	}}		}}
	{{Wikipedia\|Septimal major third}}		{{Wikipedia\|Septimal major third}}
	In [[just intonation]], '''9/7''' is the '''supermajor third'''<ref>Hermann L. F. von Helmholtz (1875). ''On the sensations of tone as a physiological basis for the theory of music'', p. 284.</ref> or '''septimal major third''' of approximately 435.1{{cent}}, characteristic of [[7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The 9-limit pentad 4:5:6:7:9 includes a septimal supermajor third between the 7th and the 9th. The interval has an interesting neutral quality to it similar to the way 9/8 behaves as ratios of nine all share this quality.		In [[just intonation]], '''9/7''' is the '''supermajor third'''<ref>[[Hermann von Helmholtz\|Hermann L. F. von Helmholtz]] (1875). ''On the sensations of tone as a physiological basis for the theory of music'', p. 284.</ref> or '''septimal major third''' of approximately 435.1{{cent}}, characteristic of [[7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The 9-limit pentad 4:5:6:7:9 includes a septimal supermajor third between the 7th and the 9th. The interval has an interesting neutral quality to it similar to the way 9/8 behaves as ratios of nine all share this quality.

	A just chord can be built with this wide third in place of the more traditional [[5/4]]. This supermajor triad would be 14:18:21. This triad can be very effective in music, but in this context, the modern ear accustomed to 12edo thirds of 400{{cent}} is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with [[9/8]] much more than 5/4. Chords such as the [[9-odd-limit]] pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant.		A just chord can be built with this wide third in place of the more traditional [[5/4]]. This supermajor triad would be 14:18:21. This triad can be very effective in music, but in this context, the modern ear accustomed to 12edo thirds of 400{{cent}} is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with [[9/8]] much more than 5/4. Chords such as the [[9-odd-limit]] pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant.

Sintel: Add a citation for this apparently controversial name

2025-04-16T14:41:55Z

Add a citation for this apparently controversial name

← Older revision		Revision as of 14:41, 16 April 2025
Line 5:		Line 5:
	}}		}}
	{{Wikipedia\|Septimal major third}}		{{Wikipedia\|Septimal major third}}
	In [[just intonation]], '''9/7''' is the '''supermajor third''' or '''septimal major third''' of approximately 435.1{{cent}}, characteristic of [[7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The 9-limit pentad 4:5:6:7:9 includes a septimal supermajor third between the 7th and the 9th. The interval has an interesting neutral quality to it similar to the way 9/8 behaves as ratios of nine all share this quality.		In [[just intonation]], '''9/7''' is the '''supermajor third'''<ref>Hermann L. F. von Helmholtz (1875). ''On the sensations of tone as a physiological basis for the theory of music'', p. 284.</ref> or '''septimal major third''' of approximately 435.1{{cent}}, characteristic of [[7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The 9-limit pentad 4:5:6:7:9 includes a septimal supermajor third between the 7th and the 9th. The interval has an interesting neutral quality to it similar to the way 9/8 behaves as ratios of nine all share this quality.

	A just chord can be built with this wide third in place of the more traditional [[5/4]]. This supermajor triad would be 14:18:21. This triad can be very effective in music, but in this context, the modern ear accustomed to 12edo thirds of 400{{cent}} is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with [[9/8]] much more than 5/4. Chords such as the [[9-odd-limit]] pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant.		A just chord can be built with this wide third in place of the more traditional [[5/4]]. This supermajor triad would be 14:18:21. This triad can be very effective in music, but in this context, the modern ear accustomed to 12edo thirds of 400{{cent}} is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with [[9/8]] much more than 5/4. Chords such as the [[9-odd-limit]] pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant.
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	* [[28/27]] – its [[fourth complement]]		* [[28/27]] – its [[fourth complement]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

			== References ==
			<references />

	[[Category:Third]]		[[Category:Third]]

Sintel: Undo revision 192129 by VectorGraphics (talk)

2025-04-16T14:38:24Z

Undo revision 192129 by VectorGraphics (talk)

← Older revision		Revision as of 14:38, 16 April 2025
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	}}		}}
	{{Wikipedia\|Septimal major third}}		{{Wikipedia\|Septimal major third}}
	In [[just intonation]], '''9/7''' is the '''septimal ~~(super)~~major third''' of approximately 435.1{{cent}}, characteristic of [[7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The 9-limit pentad 4:5:6:7:9 includes a septimal supermajor third between the 7th and the 9th. The interval has an interesting neutral quality to it similar to the way 9/8 behaves as ratios of nine all share this quality.		In [[just intonation]], '''9/7''' is the '''supermajor third''' or '''septimal major third''' of approximately 435.1{{cent}}, characteristic of [[7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The 9-limit pentad 4:5:6:7:9 includes a septimal supermajor third between the 7th and the 9th. The interval has an interesting neutral quality to it similar to the way 9/8 behaves as ratios of nine all share this quality.

	A just chord can be built with this wide third in place of the more traditional [[5/4]]. This supermajor triad would be 14:18:21. This triad can be very effective in music, but in this context, the modern ear accustomed to 12edo thirds of 400{{cent}} is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with [[9/8]] much more than 5/4. Chords such as the [[9-odd-limit]] pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant.		A just chord can be built with this wide third in place of the more traditional [[5/4]]. This supermajor triad would be 14:18:21. This triad can be very effective in music, but in this context, the modern ear accustomed to 12edo thirds of 400{{cent}} is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with [[9/8]] much more than 5/4. Chords such as the [[9-odd-limit]] pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant.

VectorGraphics at 16:56, 14 April 2025

2025-04-14T16:56:15Z

← Older revision		Revision as of 16:56, 14 April 2025
Line 5:		Line 5:
	}}		}}
	{{Wikipedia\|Septimal major third}}		{{Wikipedia\|Septimal major third}}
	In [[just intonation]], '''9/7''' is the ~~'''supermajor third''' or~~ '''septimal major third''' of approximately 435.1{{cent}}, characteristic of [[7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The 9-limit pentad 4:5:6:7:9 includes a septimal supermajor third between the 7th and the 9th. The interval has an interesting neutral quality to it similar to the way 9/8 behaves as ratios of nine all share this quality.		In [[just intonation]], '''9/7''' is the '''septimal (super)major third''' of approximately 435.1{{cent}}, characteristic of [[7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The 9-limit pentad 4:5:6:7:9 includes a septimal supermajor third between the 7th and the 9th. The interval has an interesting neutral quality to it similar to the way 9/8 behaves as ratios of nine all share this quality.

	A just chord can be built with this wide third in place of the more traditional [[5/4]]. This supermajor triad would be 14:18:21. This triad can be very effective in music, but in this context, the modern ear accustomed to 12edo thirds of 400{{cent}} is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with [[9/8]] much more than 5/4. Chords such as the [[9-odd-limit]] pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant.		A just chord can be built with this wide third in place of the more traditional [[5/4]]. This supermajor triad would be 14:18:21. This triad can be very effective in music, but in this context, the modern ear accustomed to 12edo thirds of 400{{cent}} is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with [[9/8]] much more than 5/4. Chords such as the [[9-odd-limit]] pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant.

FloraC: Undo revision 192027 by VectorGraphics (talk). I don't necessarily disagree, but don't just edit one article out of many (systematicity)

2025-04-14T16:40:33Z

Undo revision 192027 by VectorGraphics (talk). I don't necessarily disagree, but don't just edit one article out of many (systematicity)

← Older revision		Revision as of 16:40, 14 April 2025
Line 5:		Line 5:
	}}		}}
	{{Wikipedia\|Septimal major third}}		{{Wikipedia\|Septimal major third}}
	In [[just intonation]], '''9/7''' is the '''septimal ~~(super)~~major third''' of approximately 435.1{{cent}}, characteristic of [[7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The 9-limit pentad 4:5:6:7:9 includes a septimal supermajor third between the 7th and the 9th. The interval has an interesting neutral quality to it similar to the way 9/8 behaves as ratios of nine all share this quality.		In [[just intonation]], '''9/7''' is the '''supermajor third''' or '''septimal major third''' of approximately 435.1{{cent}}, characteristic of [[7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The 9-limit pentad 4:5:6:7:9 includes a septimal supermajor third between the 7th and the 9th. The interval has an interesting neutral quality to it similar to the way 9/8 behaves as ratios of nine all share this quality.

	A just chord can be built with this wide third in place of the more traditional [[5/4]]. This supermajor triad would be 14:18:21. This triad can be very effective in music, but in this context, the modern ear accustomed to 12edo thirds of 400{{cent}} is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with [[9/8]] much more than 5/4. Chords such as the [[9-odd-limit]] pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant.		A just chord can be built with this wide third in place of the more traditional [[5/4]]. This supermajor triad would be 14:18:21. This triad can be very effective in music, but in this context, the modern ear accustomed to 12edo thirds of 400{{cent}} is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with [[9/8]] much more than 5/4. Chords such as the [[9-odd-limit]] pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant.

VectorGraphics: if sqrt(3/2) doesn't get to be called "the" neutral third, 9/7 doesn't get to be called "the" supermajor third

2025-04-14T02:26:39Z

if sqrt(3/2) doesn't get to be called "the" neutral third, 9/7 doesn't get to be called "the" supermajor third

← Older revision		Revision as of 02:26, 14 April 2025
Line 5:		Line 5:
	}}		}}
	{{Wikipedia\|Septimal major third}}		{{Wikipedia\|Septimal major third}}
	In [[just intonation]], '''9/7''' is the ~~'''supermajor third''' or~~ '''septimal major third''' of approximately 435.1{{cent}}, characteristic of [[7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The 9-limit pentad 4:5:6:7:9 includes a septimal supermajor third between the 7th and the 9th. The interval has an interesting neutral quality to it similar to the way 9/8 behaves as ratios of nine all share this quality.		In [[just intonation]], '''9/7''' is the '''septimal (super)major third''' of approximately 435.1{{cent}}, characteristic of [[7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The 9-limit pentad 4:5:6:7:9 includes a septimal supermajor third between the 7th and the 9th. The interval has an interesting neutral quality to it similar to the way 9/8 behaves as ratios of nine all share this quality.

	A just chord can be built with this wide third in place of the more traditional [[5/4]]. This supermajor triad would be 14:18:21. This triad can be very effective in music, but in this context, the modern ear accustomed to 12edo thirds of 400{{cent}} is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with [[9/8]] much more than 5/4. Chords such as the [[9-odd-limit]] pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant.		A just chord can be built with this wide third in place of the more traditional [[5/4]]. This supermajor triad would be 14:18:21. This triad can be very effective in music, but in this context, the modern ear accustomed to 12edo thirds of 400{{cent}} is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with [[9/8]] much more than 5/4. Chords such as the [[9-odd-limit]] pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant.