6561/4096 - Revision history

FloraC: Undo revision 211137 by M1k1 H2tsun2 (talk)

2025-09-27T11:52:41Z

Undo revision 211137 by M1k1 H2tsun2 (talk)

← Older revision		Revision as of 11:52, 27 September 2025
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	{{Infobox Interval		{{Infobox Interval
	\| Name = ~~Threerish augmented fifth,~~ Pythagorean augmented fifth, tetratone		\| Name = Pythagorean augmented fifth, tetratone
	\| Color name = Lw5, lawa 5th		\| Color name = Lw5, lawa 5th
	}}		}}

M1k1 H2tsun2: add it them

2025-09-27T10:52:27Z

add it them

← Older revision		Revision as of 10:52, 27 September 2025
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	{{Infobox Interval		{{Infobox Interval
	\| Name = Pythagorean augmented fifth, tetratone		\| Name = Threerish augmented fifth, Pythagorean augmented fifth, tetratone
	\| Color name = Lw5, lawa 5th		\| Color name = Lw5, lawa 5th
	}}		}}

FloraC: Misc. style improvements

2024-06-24T08:06:08Z

Misc. style improvements

← Older revision		Revision as of 08:06, 24 June 2024
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	}}		}}

	The '''Pythagorean augmented fifth''', '''6561/4096''', may be reached by stacking two [[81/64]] ~~intervals~~. The Medieval music theorist Jacques de Liège referred to it as the '''tetratone''' (akin to the [[ditone]] and [[729/512\|tritone]]), as it may be reached by stacking four (Pythagorean whole) ~~[[tone]]s~~ ([[9/8]]), and he considered it highly discordant.<ref>''Pythagorean Tuning and Medieval Polyphony'', Margo Schulter, 10 June 1998</ref> It differs from [[8/5]] by the [[schisma]], and from [[3/2]] by the [[apotome]].		The '''Pythagorean augmented fifth''', '''6561/4096''', may be reached by stacking two [[81/64]] major thirds. The Medieval music theorist {{w\|Jacques de Liège}} referred to it as the '''tetratone''' (akin to the [[ditone]] and [[729/512\|tritone]]), as it may be reached by stacking four [[9/8\|(Pythagorean whole) tones (9/8)]], and he considered it highly discordant.<ref>''Pythagorean Tuning and Medieval Polyphony'', Margo Schulter, 10 June 1998</ref> It differs from [[8/5]] by the [[schisma]], and from [[3/2]] by the [[apotome]].

	== See also ==		== See also ==
	* [[8192/6561]] – its [[octave complement]]		* [[8192/6561]] – its [[octave complement]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[Pythagorean tuning]]		* [[Pythagorean tuning]]

			== Notes ==

	[[Category:Fifth]]		[[Category:Fifth]]
	[[Category:Augmented fifth]]		[[Category:Augmented fifth]]

Cmloegcmluin at 06:18, 24 June 2024

2024-06-24T06:18:12Z

← Older revision		Revision as of 06:18, 24 June 2024
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	}}		}}

	The '''Pythagorean augmented fifth''', '''6561/4096''', may be reached by stacking two [[81/64]] intervals. The Medieval music theorist Jacques de Liège referred to it as the '''tetratone''' (akin to the [[ditone]] and [[729/512\|tritone]]), as it may be reached by stacking four (Pythagorean whole) [[tone]]s ([[9/8]]). It differs from [[8/5]] by the [[schisma]], and from [[3/2]] by the [[apotome]].		The '''Pythagorean augmented fifth''', '''6561/4096''', may be reached by stacking two [[81/64]] intervals. The Medieval music theorist Jacques de Liège referred to it as the '''tetratone''' (akin to the [[ditone]] and [[729/512\|tritone]]), as it may be reached by stacking four (Pythagorean whole) [[tone]]s ([[9/8]]), and he considered it highly discordant.<ref>''Pythagorean Tuning and Medieval Polyphony'', Margo Schulter, 10 June 1998</ref> It differs from [[8/5]] by the [[schisma]], and from [[3/2]] by the [[apotome]].
	== See also ==		== See also ==
	* [[8192/6561]] – its [[octave complement]]		* [[8192/6561]] – its [[octave complement]]

Cmloegcmluin at 06:15, 24 June 2024

2024-06-24T06:15:21Z

← Older revision		Revision as of 06:15, 24 June 2024
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	}}		}}

	The '''Pythagorean augmented fifth''', '''6561/4096''', may be reached by stacking two [[81/64]] intervals. The Medieval music theorist Jacques de Liège referred to it as the '''tetratone''' (akin to the [[ditone]] and [[729/512\|tritone]]), as it may be reached by stacking four (Pythagorean whole) [[tone]]s ([[9/8]]). It differs from [[8/5]] by the [[schisma]].		The '''Pythagorean augmented fifth''', '''6561/4096''', may be reached by stacking two [[81/64]] intervals. The Medieval music theorist Jacques de Liège referred to it as the '''tetratone''' (akin to the [[ditone]] and [[729/512\|tritone]]), as it may be reached by stacking four (Pythagorean whole) [[tone]]s ([[9/8]]). It differs from [[8/5]] by the [[schisma]], and from [[3/2]] by the [[apotome]].
	== See also ==		== See also ==
	* [[8192/6561]] – its [[octave complement]]		* [[8192/6561]] – its [[octave complement]]

CompactStar: "81/64 is a dissonance" is not a universal view

2024-06-23T23:58:59Z

"81/64 is a dissonance" is not a universal view

← Older revision		Revision as of 23:58, 23 June 2024
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	}}		}}

	The '''Pythagorean augmented fifth''', '''6561/4096''', may be reached by stacking two [[81/64]] intervals. The Medieval music theorist Jacques de Liège referred to it as the '''tetratone''' (akin to the [[ditone]] and [[729/512\|tritone]]), as it may be reached by stacking four (Pythagorean whole) [[tone]]s ([[9/8]]). It differs from [[8/5]] by the [[schisma]]~~, and, as a result, despite 81/64 being a dissonance, the Pythagorean augmented fifth is in fact rather consonant~~.		The '''Pythagorean augmented fifth''', '''6561/4096''', may be reached by stacking two [[81/64]] intervals. The Medieval music theorist Jacques de Liège referred to it as the '''tetratone''' (akin to the [[ditone]] and [[729/512\|tritone]]), as it may be reached by stacking four (Pythagorean whole) [[tone]]s ([[9/8]]). It differs from [[8/5]] by the [[schisma]].

	== See also ==		== See also ==
	* [[8192/6561]] – its [[octave complement]]		* [[8192/6561]] – its [[octave complement]]

Cmloegcmluin at 21:30, 23 June 2024

2024-06-23T21:30:09Z

← Older revision		Revision as of 21:30, 23 June 2024
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	{{Infobox Interval		{{Infobox Interval
	\| Name = Pythagorean augmented fifth		\| Name = Pythagorean augmented fifth, tetratone
	\| Color name = Lw5, lawa 5th		\| Color name = Lw5, lawa 5th
	}}		}}

	The '''Pythagorean augmented fifth''', '''6561/4096''', may be reached by stacking two [[81/64]] intervals. It differs from [[8/5]] by the [[schisma]], and, as a result, despite 81/64 being a dissonance, the Pythagorean augmented fifth is in fact rather consonant.		The '''Pythagorean augmented fifth''', '''6561/4096''', may be reached by stacking two [[81/64]] intervals. The Medieval music theorist Jacques de Liège referred to it as the '''tetratone''' (akin to the [[ditone]] and [[729/512\|tritone]]), as it may be reached by stacking four (Pythagorean whole) [[tone]]s ([[9/8]]). It differs from [[8/5]] by the [[schisma]], and, as a result, despite 81/64 being a dissonance, the Pythagorean augmented fifth is in fact rather consonant.

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

Plumtree: Normalising usage of Infobox Interval

2022-10-25T16:42:30Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 16:42, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 6561/4096~~
	~~\| Monzo = -12 8~~
	~~\| Cents = 815.64000~~
	\| Name = Pythagorean augmented fifth		\| Name = Pythagorean augmented fifth
	\| Color name = Lw5, lawa 5th		\| Color name = Lw5, lawa 5th
	~~\| FJS name = A5~~
	~~\| Sound =~~
	}}		}}

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	* [[Pythagorean tuning]]		* [[Pythagorean tuning]]

	~~[[Category:3-limit]]~~
	[[Category:Fifth]]		[[Category:Fifth]]
	[[Category:Augmented fifth]]		[[Category:Augmented fifth]]

Fredg999: Added color and FJS names, misc. edits, categories

2022-01-01T20:00:17Z

Added color and FJS names, misc. edits, categories

← Older revision		Revision as of 20:00, 1 January 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~
	\| Ratio = 6561/4096		\| Ratio = 6561/4096
	\| Monzo = -12 8		\| Monzo = -12 8
	\| Cents = 815.64000		\| Cents = 815.64000
	\| Name = Pythagorean augmented fifth		\| Name = Pythagorean augmented fifth
	\| Color name =		\| Color name = Lw5, lawa 5th
	\| FJS name =		\| FJS name = A5
	\| Sound =		\| Sound =
	}}		}}
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	[[Category:3-limit]]		[[Category:3-limit]]
	[[Category:~~Interval~~]]		[[Category:Fifth]]
	[[Category:~~Ratio]]~~		[[Category:Augmented fifth]]
	~~[[Category:Pythagorean~~]]

Aura at 14:52, 15 November 2021

2021-11-15T14:52:42Z

← Older revision		Revision as of 14:52, 15 November 2021
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	}}		}}

	The '''Pythagorean augmented fifth''', '''~~6564~~/4096''', may be reached by stacking two [[81/64]] intervals. It differs from [[8/5]] by the [[schisma]], and, as a result, despite 81/64 being a dissonance, the Pythagorean augmented fifth is in fact rather consonant.		The '''Pythagorean augmented fifth''', '''6561/4096''', may be reached by stacking two [[81/64]] intervals. It differs from [[8/5]] by the [[schisma]], and, as a result, despite 81/64 being a dissonance, the Pythagorean augmented fifth is in fact rather consonant.

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