4:5:6:7:9 - Revision history

Overthink: /* See also */ note octave reduction

2026-02-04T22:46:10Z

FloraC: Correction

2026-02-04T11:49:58Z

Correction

← Older revision		Revision as of 11:49, 4 February 2026
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	Its utonal inverse, [[140:180:210:252:315\|1/(9:7:6:5:4)]], can also be seen as a fundamental chord, and subsets can be taken out of it as well. The 4:5:6:7:9 chord can be modified to get its utonal inverse by inflecting both the third and seventh up by [[36/35]], so the third becomes [[9/7]] and the seventh [[9/5]].		Its utonal inverse, [[140:180:210:252:315\|1/(9:7:6:5:4)]], can also be seen as a fundamental chord, and subsets can be taken out of it as well. The 4:5:6:7:9 chord can be modified to get its utonal inverse by inflecting both the third and seventh up by [[36/35]], so the third becomes [[9/7]] and the seventh [[9/5]].

	4:5:6:7:9 (1–5/4–3/2–7/4–9/4) can be modified by inflecting the [[5/4]] down by [[25/24]], the [[7/4]] down by [[49/48]], and the [[9/4]] down by [[33/32]] to get an [[11-limit]] utonal minor counterpart [[770:924:1155:1320:1680\|1–6/5–3/2–12/7–24/11]]. Meanwhile, the utonal inverse above can be voiced as [[210:252:315:360:560\|1–6/5–3/2–12/7–8/3~~]], which has the inverse [[4:5:6:7:11\|1–5/4–3/2–7/4–11/4~~]]. These four chords form a quadruplet in the [[11-odd-limit]], all being subsets of [[4:5:6:7:9:11\|1–5/4–3/2–7/4–9/4–11/4]] and [[2310:2772:3465:3960:5040:6160\|1–6/5–3/2–12/7–24/11–8/3]].		4:5:6:7:9 (1–5/4–3/2–7/4–9/4) can be modified by inflecting the [[5/4]] down by [[25/24]], the [[7/4]] down by [[49/48]], and the [[9/4]] down by [[33/32]] to get an [[11-limit]] utonal minor counterpart [[770:924:1155:1320:1680\|1–6/5–3/2–12/7–24/11]], which has the inverse [[4:5:6:7:11\|1–5/4–3/2–7/4–11/4]]. Meanwhile, the utonal inverse above can be voiced as [[210:252:315:360:560\|1–6/5–3/2–12/7–8/3]]. These four chords form a quadruplet in the [[11-odd-limit]], all being subsets of [[4:5:6:7:9:11\|1–5/4–3/2–7/4–9/4–11/4]] and [[2310:2772:3465:3960:5040:6160\|1–6/5–3/2–12/7–24/11–8/3]].

	== See also ==		== See also ==
	* [[Otonalpentad]] – this chord as a scale		* [[Otonalpentad]] – this chord as a scale

FloraC: Expand

2026-02-04T11:46:29Z

Expand

← Older revision		Revision as of 11:46, 4 February 2026
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	{{Infobox Chord\|ColorName=yo zo-7 add-9 or y,z7,9, har-9 or h9}}		{{Infobox Chord\|ColorName=yo zo-7 add-9 or y,z7,9, har-9 or h9}}

	'''4:5:6:7:9''', the ''harmonic ninth chord'', is a [[pentad]] in [[7-limit]] harmony. It serves as the fundamental otonal consonance of the 9-odd-limit, with many chords being a subset of it or one of its inversions. Its utonal inverse, [[140:180:210:252:315\|1/(9:7:6:5:4)]], can also be seen as a fundamental chord, and subsets can be taken out of it as well. The 4:5:6:7:9 chord can be modified to get its utonal inverse by inflecting both the third and seventh up by [[36/35]], so the third becomes [[9/7]] and the seventh [[9/5]]. It is an extension of [[4:5:6]] and [[4:5:6:7]].		'''4:5:6:7:9''', the ''harmonic ninth chord'', is a [[pentad]] in [[7-limit]] harmony. It serves as the fundamental otonal consonance of the 9-odd-limit, with many chords being a subset of it or one of its inversions. It is an extension of [[4:5:6]] and [[4:5:6:7]].

	~~== See~~ also ==		Its utonal inverse, [[140:180:210:252:315\|1/(9:7:6:5:4)]], can also be seen as a fundamental chord, and subsets can be taken out of it as well. The 4:5:6:7:9 chord can be modified to get its utonal inverse by inflecting both the third and seventh up by [[36/35]], so the third becomes [[9/7]] and the seventh [[9/5]].

	* [[4:5:6:7:9:11]] - ~~(11~~-limit)		4:5:6:7:9 (1–5/4–3/2–7/4–9/4) can be modified by inflecting the [[5/4]] down by [[25/24]], the [[7/4]] down by [[49/48]], and the [[9/4]] down by [[33/32]] to get an [[11-limit]] utonal minor counterpart [[770:924:1155:1320:1680\|1–6/5–3/2–12/7–24/11]]. Meanwhile, the utonal inverse above can be voiced as [[210:252:315:360:560\|1–6/5–3/2–12/7–8/3]], which has the inverse [[4:5:6:7:11\|1–5/4–3/2–7/4–11/4]]. These four chords form a quadruplet in the [[11-odd-limit]], all being subsets of [[4:5:6:7:9:11\|1–5/4–3/2–7/4–9/4–11/4]] and [[2310:2772:3465:3960:5040:6160\|1–6/5–3/2–12/7–24/11–8/3]].
	* [[~~Otonalpentad~~]] ~~- This chord as a scale~~

	[[~~Category:Todo:expand~~]]		== See also ==
			* [[Otonalpentad]] – this chord as a scale

Overthink: notation

2025-12-22T08:00:33Z

notation

← Older revision		Revision as of 08:00, 22 December 2025
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	{{Infobox Chord\|ColorName=yo zo-7 add-9 or y,z7,9, har-9 or h9}}		{{Infobox Chord\|ColorName=yo zo-7 add-9 or y,z7,9, har-9 or h9}}

	'''4:5:6:7:9''', the ''harmonic ninth chord'', is a [[pentad]] in [[7-limit]] harmony. It serves as the fundamental otonal consonance of the 9-odd-limit, with many chords being a subset of it or one of its inversions. Its utonal inverse, [[140:180:210:252:315\|1/(4:5:6:7:9)]], can also be seen as a fundamental chord, and subsets can be taken out of it as well. The 4:5:6:7:9 chord can be modified to get its utonal inverse by inflecting both the third and seventh up by [[36/35]], so the third becomes [[9/7]] and the seventh [[9/5]]. It is an extension of [[4:5:6]] and [[4:5:6:7]].		'''4:5:6:7:9''', the ''harmonic ninth chord'', is a [[pentad]] in [[7-limit]] harmony. It serves as the fundamental otonal consonance of the 9-odd-limit, with many chords being a subset of it or one of its inversions. Its utonal inverse, [[140:180:210:252:315\|1/(9:7:6:5:4)]], can also be seen as a fundamental chord, and subsets can be taken out of it as well. The 4:5:6:7:9 chord can be modified to get its utonal inverse by inflecting both the third and seventh up by [[36/35]], so the third becomes [[9/7]] and the seventh [[9/5]]. It is an extension of [[4:5:6]] and [[4:5:6:7]].

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

Overthink: + notes on extensions and see also section

2025-11-26T05:10:14Z

+ notes on extensions and see also section

← Older revision		Revision as of 05:10, 26 November 2025
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	{{Infobox Chord\|ColorName=yo zo-7 add-9 or y,z7,9, har-9 or h9}}		{{Infobox Chord\|ColorName=yo zo-7 add-9 or y,z7,9, har-9 or h9}}

	'''4:5:6:7:9''', the ''harmonic ninth chord'', is a [[pentad]] in [[7-limit]] harmony. It serves as the fundamental otonal consonance of the 9-odd-limit, with many chords being a subset of it or one of its inversions. Its utonal inverse, [[140:180:210:252:315\|1/(4:5:6:7:9)]], can also be seen as a fundamental chord, and subsets can be taken out of it as well. The 4:5:6:7:9 chord can be modified to get its utonal inverse by inflecting both the third and seventh up by [[36/35]], so the third becomes [[9/7]] and the seventh [[9/5]].		'''4:5:6:7:9''', the ''harmonic ninth chord'', is a [[pentad]] in [[7-limit]] harmony. It serves as the fundamental otonal consonance of the 9-odd-limit, with many chords being a subset of it or one of its inversions. Its utonal inverse, [[140:180:210:252:315\|1/(4:5:6:7:9)]], can also be seen as a fundamental chord, and subsets can be taken out of it as well. The 4:5:6:7:9 chord can be modified to get its utonal inverse by inflecting both the third and seventh up by [[36/35]], so the third becomes [[9/7]] and the seventh [[9/5]]. It is an extension of [[4:5:6]] and [[4:5:6:7]].

			== See also ==

			* [[4:5:6:7:9:11]] - (11-limit)
			* [[Otonalpentad]] - This chord as a scale

	[[Category:Todo:expand]]		[[Category:Todo:expand]]

Overthink: Expanded description

2025-11-07T17:02:58Z

Expanded description

← Older revision		Revision as of 17:02, 7 November 2025
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	{{Infobox Chord\|ColorName=yo zo-7 add-9 or y,z7,9, har-9 or h9}}		{{Infobox Chord\|ColorName=yo zo-7 add-9 or y,z7,9, har-9 or h9}}

	'''4:5:6:7:9''', the ''harmonic ninth chord'', is a [[pentad]] in [[7-limit]] harmony.		'''4:5:6:7:9''', the ''harmonic ninth chord'', is a [[pentad]] in [[7-limit]] harmony. It serves as the fundamental otonal consonance of the 9-odd-limit, with many chords being a subset of it or one of its inversions. Its utonal inverse, [[140:180:210:252:315\|1/(4:5:6:7:9)]], can also be seen as a fundamental chord, and subsets can be taken out of it as well. The 4:5:6:7:9 chord can be modified to get its utonal inverse by inflecting both the third and seventh up by [[36/35]], so the third becomes [[9/7]] and the seventh [[9/5]].

	~~{{stub}}~~		[[Category:Todo:expand]]

BudjarnLambeth: {{stub}}

2024-10-06T23:31:34Z

← Older revision		Revision as of 23:31, 6 October 2024
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	'''4:5:6:7:9''', the ''harmonic ninth chord'', is a [[pentad]] in [[7-limit]] harmony.		'''4:5:6:7:9''', the ''harmonic ninth chord'', is a [[pentad]] in [[7-limit]] harmony.

			{{stub}}

Bcmills: The Wikipedia page about the harmonic seventh chord is not a page or section specifically about the harmonic ninth chord.

2024-10-02T01:40:17Z

The Wikipedia page about the harmonic seventh chord is not a page or section specifically about the harmonic ninth chord.

← Older revision		Revision as of 01:40, 2 October 2024
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	{{Infobox Chord\|ColorName=yo zo-7 add-9 or y,z7,9, har-9 or h9}}		{{Infobox Chord\|ColorName=yo zo-7 add-9 or y,z7,9, har-9 or h9}}
	~~{{Wikipedia\|Harmonic seventh chord}}~~
	'''4:5:6:7:9''', the ''harmonic ninth chord'', is a [[pentad]] in [[7-limit]] harmony.		'''4:5:6:7:9''', the ''harmonic ninth chord'', is a [[pentad]] in [[7-limit]] harmony.

TallKite: Created page with "{{Infobox Chord|ColorName=yo zo-7 add-9 or y,z7,9, har-9 or h9}} {{Wikipedia|Harmonic seventh chord}} '''4:5:6:7:9''', the ''harmonic ninth chord'', is a pentad in 7-lim..."

2024-09-24T02:00:44Z

Created page with "{{Infobox Chord|ColorName=yo zo-7 add-9 or y,z7,9, har-9 or h9}} {{Wikipedia|Harmonic seventh chord}} '''4:5:6:7:9''', the ''harmonic ninth chord'', is a pentad in 7-lim..."

New page

{{Infobox Chord|ColorName=yo zo-7 add-9 or y,z7,9, har-9 or h9}}
{{Wikipedia|Harmonic seventh chord}}
'''4:5:6:7:9''', the ''harmonic ninth chord'', is a [[pentad]] in [[7-limit]] harmony.

← Older revision		Revision as of 22:46, 4 February 2026
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	== See also ==		== See also ==
	* [[Otonalpentad]] – this chord as a scale		* [[Otonalpentad]] – this chord as a scale, [[octave reduced]]