40/21 - Revision history

Pailiaq at 08:48, 16 November 2025

2025-11-16T08:48:51Z

← Older revision		Revision as of 08:48, 16 November 2025
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	== Terminology ==		== Terminology ==
	Despite being approximated by the diminished octave in systems like [[septimal meantone]], and even being called the '''small septimal diminished octave''' by some musicians due to analogy with [[21/20]] being called the "large septimal chroma", 40/21 is a major seventh in just intonation notation systems such as [[Sagittal notation]], [[Helmholtz-Ellis notation]] and [[Functional Just System]], viewed as the [[243/128\|Pythagorean major seventh (243/128)]] altered by [[5120/5103]].		Despite being approximated by the diminished octave in systems like [[septimal meantone]], and even being called the '''small septimal diminished octave''' by some musicians due to analogy with [[21/20]] being called the "large septimal chroma", 40/21 is a major seventh in just intonation notation systems such as [[Sagittal notation]], [[Helmholtz-Ellis notation]] and [[Functional Just System]], viewed as the [[243/128\|Pythagorean major seventh (243/128)]] altered by [[5120/5103]].
			== Approximation ==
			{{Interval edo approximation\|40/21}}

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

Plumtree: Normalising usage of Infobox Interval

2022-10-25T15:39:19Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 15:39, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 40/21~~		\| Name = septimal acute major seventh, small septimal diminished octave
	~~\| Monzo = 3 -1 1 -1~~
	~~\| Cents = 1115.53281~~
	\| Name = septimal acute major seventh, ~~<br>~~small septimal diminished octave
	\| Color name = ry7, ruyo 7th		\| Color name = ry7, ruyo 7th
	~~\| FJS name = M7<sup>5</sup><sub>7</sub>~~
	\| Sound = jid_40_21_pluck_adu_dr220.mp3		\| Sound = jid_40_21_pluck_adu_dr220.mp3
	}}		}}
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	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

	~~[[Category:7-limit]]~~
	[[Category:Seventh]]		[[Category:Seventh]]
	[[Category:Major seventh]]		[[Category:Major seventh]]

Fredg999 category edits: Removing from Category:Pages with internal sound examples using Cat-a-lot

2022-02-22T23:47:25Z

Removing from Category:Pages with internal sound examples using Cat-a-lot

← Older revision		Revision as of 23:47, 22 February 2022
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	[[Category:Seventh]]		[[Category:Seventh]]
	[[Category:Major seventh]]		[[Category:Major seventh]]
	~~[[Category:Pages with internal sound examples]]~~

Fredg999: Added color name, misc. edits, categories

2021-12-19T19:37:56Z

Added color name, misc. edits, categories

← Older revision		Revision as of 19:37, 19 December 2021
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	{{Infobox Interval		{{Infobox Interval
	~~\| JI glyph =~~
	\| Ratio = 40/21		\| Ratio = 40/21
	\| Monzo = 3 -1 1 -1		\| Monzo = 3 -1 1 -1
	\| Cents = 1115.53281		\| Cents = 1115.53281
	\| Name = septimal acute major seventh, <br>small septimal diminished octave		\| Name = septimal acute major seventh, <br>small septimal diminished octave
	\| Color name =		\| Color name = ry7, ruyo 7th
	\| FJS name = M7<sup>5</sup><sub>7</sub>		\| FJS name = M7<sup>5</sup><sub>7</sub>
	\| Sound = jid_40_21_pluck_adu_dr220.mp3		\| Sound = jid_40_21_pluck_adu_dr220.mp3
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	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

	~~[[Category:Interval]]~~
	[[Category:7-limit]]		[[Category:7-limit]]
	[[Category:Seventh]]		[[Category:Seventh]]
	[[Category:Major seventh]]		[[Category:Major seventh]]
	[[Category:Pages with internal sound examples]]		[[Category:Pages with internal sound examples]]

FloraC: +temperament section; +category

2021-04-10T16:13:47Z

+temperament section; +category

← Older revision		Revision as of 16:13, 10 April 2021
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	\| Monzo = 3 -1 1 -1		\| Monzo = 3 -1 1 -1
	\| Cents = 1115.53281		\| Cents = 1115.53281
	\| Name = acute major seventh, <br>small septimal diminished octave		\| Name = septimal acute major seventh, <br>small septimal diminished octave
	\| Color name =		\| Color name =
	\| FJS name = M7<sup>5</sup><sub>7</sub>		\| FJS name = M7<sup>5</sup><sub>7</sub>
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	}}		}}

	'''40/21''', the '''acute major seventh''', is a [[7-limit]] interval measuring about 1115.5 cents. Despite being approximated by the diminished octave in systems like [[septimal meantone]], and even being called the "'''small septimal diminished octave'''" by some musicians due to analogy with [[21/20]] being called the "large septimal chroma", 40/21 is a major seventh in ~~both~~ [[Helmholtz-Ellis notation]] and [[Functional Just System]] ~~because it is sharp of~~ the [[243/128\|Pythagorean major seventh (243/128)]] by [[5120/5103]].		'''40/21''', the '''septimal acute major seventh''', is a [[7-limit]] interval measuring about 1115.5 cents.

			== Terminology ==
			Despite being approximated by the diminished octave in systems like [[septimal meantone]], and even being called the '''small septimal diminished octave''' by some musicians due to analogy with [[21/20]] being called the "large septimal chroma", 40/21 is a major seventh in just intonation notation systems such as [[Sagittal notation]], [[Helmholtz-Ellis notation]] and [[Functional Just System]], viewed as the [[243/128\|Pythagorean major seventh (243/128)]] altered by [[5120/5103]].

	== See also ==		== See also ==
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	[[Category:Seventh]]		[[Category:Seventh]]
	[[Category:Major seventh]]		[[Category:Major seventh]]
			[[Category:Pages with internal sound examples]]

Aura at 15:14, 25 December 2020

2020-12-25T15:14:02Z

← Older revision		Revision as of 15:14, 25 December 2020
Line 10:		Line 10:
	}}		}}

	'''40/21''', the '''acute major seventh''', is a [[7-limit]] interval measuring about 1115.5 cents. Despite being approximated by the diminished octave in systems like [[septimal meantone]], and even being called the "'''small septimal diminished octave'''" by some musicians ~~through~~ analogy with [[21/20]] being called the "large septimal chroma", 40/21 is a major seventh in both [[Helmholtz-Ellis notation]] and [[Functional Just System]] because it is sharp of the [[243/128\|Pythagorean major seventh (243/128)]] by [[5120/5103]].		'''40/21''', the '''acute major seventh''', is a [[7-limit]] interval measuring about 1115.5 cents. Despite being approximated by the diminished octave in systems like [[septimal meantone]], and even being called the "'''small septimal diminished octave'''" by some musicians due to analogy with [[21/20]] being called the "large septimal chroma", 40/21 is a major seventh in both [[Helmholtz-Ellis notation]] and [[Functional Just System]] because it is sharp of the [[243/128\|Pythagorean major seventh (243/128)]] by [[5120/5103]].

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

Aura at 15:09, 25 December 2020

2020-12-25T15:09:35Z

← Older revision		Revision as of 15:09, 25 December 2020
Line 10:		Line 10:
	}}		}}

	'''40/21''', is a [[7-limit]] interval measuring about 1115.5 cents. Despite being approximated by the diminished octave in systems like [[septimal meantone]], and even being called the "'''small septimal diminished octave'''" by some musicians through analogy with [[21/20]] being called the "large septimal chroma", 40/21 is a major seventh in both [[Helmholtz-Ellis notation]] and [[Functional Just System]] because it is sharp of the [[243/128\|Pythagorean major seventh (243/128)]] by [[5120/5103]].		'''40/21''', the '''acute major seventh''', is a [[7-limit]] interval measuring about 1115.5 cents. Despite being approximated by the diminished octave in systems like [[septimal meantone]], and even being called the "'''small septimal diminished octave'''" by some musicians through analogy with [[21/20]] being called the "large septimal chroma", 40/21 is a major seventh in both [[Helmholtz-Ellis notation]] and [[Functional Just System]] because it is sharp of the [[243/128\|Pythagorean major seventh (243/128)]] by [[5120/5103]].

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

Aura: added "small septimal diminished octave" back as an option- only remove this if you also plan on removing the name "large septimal chroma" from the entry on 21/20

2020-12-25T15:09:17Z

added "small septimal diminished octave" back as an option- only remove this if you also plan on removing the name "large septimal chroma" from the entry on 21/20

← Older revision		Revision as of 15:09, 25 December 2020
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	\| Monzo = 3 -1 1 -1		\| Monzo = 3 -1 1 -1
	\| Cents = 1115.53281		\| Cents = 1115.53281
	\| Name = acute major seventh		\| Name = acute major seventh, <br>small septimal diminished octave
	\| Color name =		\| Color name =
	\| FJS name = M7<sup>5</sup><sub>7</sub>		\| FJS name = M7<sup>5</sup><sub>7</sub>
Line 10:		Line 10:
	}}		}}

	'''40/21''', is a [[7-limit]] interval measuring about 1115.5 cents. Despite being approximated by the diminished octave in systems like [[septimal meantone]], it is a major seventh in both [[Helmholtz-Ellis notation]] and [[Functional Just System]] because it is sharp of the [[243/128\|Pythagorean major seventh (243/128)]] by [[5120/5103]].		'''40/21''', is a [[7-limit]] interval measuring about 1115.5 cents. Despite being approximated by the diminished octave in systems like [[septimal meantone]], and even being called the "'''small septimal diminished octave'''" by some musicians through analogy with [[21/20]] being called the "large septimal chroma", 40/21 is a major seventh in both [[Helmholtz-Ellis notation]] and [[Functional Just System]] because it is sharp of the [[243/128\|Pythagorean major seventh (243/128)]] by [[5120/5103]].

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

FloraC: Fix a link

2020-12-25T10:27:59Z

Fix a link

← Older revision		Revision as of 10:27, 25 December 2020
Line 10:		Line 10:
	}}		}}

	'''40/21''', is a [[7-limit]] interval measuring about 1115.5 cents. Despite being approximated by the diminished octave in systems like [[septimal meantone]], it is a major seventh in both [[Helmholtz-Ellis notation]] and [[Functional Just System]] because it is sharp of the [[Pythagorean major seventh (243/128)]] by [[5120/5103]].		'''40/21''', is a [[7-limit]] interval measuring about 1115.5 cents. Despite being approximated by the diminished octave in systems like [[septimal meantone]], it is a major seventh in both [[Helmholtz-Ellis notation]] and [[Functional Just System]] because it is sharp of the [[243/128\|Pythagorean major seventh (243/128)]] by [[5120/5103]].

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

FloraC: +logical reasons for both d8 and M7 but let's just remove "small septimal diminished octave" since the term is out of nowhere

2020-12-25T10:27:34Z

+logical reasons for both d8 and M7 but let's just remove "small septimal diminished octave" since the term is out of nowhere

← Older revision		Revision as of 10:27, 25 December 2020
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	\| Monzo = 3 -1 1 -1		\| Monzo = 3 -1 1 -1
	\| Cents = 1115.53281		\| Cents = 1115.53281
	\| Name = ~~small septimal suboctave, <br>~~ acute major seventh		\| Name = acute major seventh
	\| Color name =		\| Color name =
	\| FJS name =		\| FJS name = M7<sup>5</sup><sub>7</sub>
	\| Sound = jid_40_21_pluck_adu_dr220.mp3		\| Sound = jid_40_21_pluck_adu_dr220.mp3
	}}		}}

	'''40/21''', is a [[7-limit]] interval ~~which despite~~ being ~~dubbed~~ the ~~'''small septimal~~ diminished octave~~''' by some musicians~~, ~~can also be~~ a ~~type of~~ major seventh ~~for much the same reason that~~ [[~~21/20~~]] ~~can be a diatonic semitone~~ of ~~sorts- specifically is it dubbed~~ the ~~'''acute~~ major seventh~~'''~~ by ~~the Huygens-Fokker Foundation~~.		'''40/21''', is a [[7-limit]] interval measuring about 1115.5 cents. Despite being approximated by the diminished octave in systems like [[septimal meantone]], it is a major seventh in both [[Helmholtz-Ellis notation]] and [[Functional Just System]] because it is sharp of the [[Pythagorean major seventh (243/128)]] by [[5120/5103]].

	== See also ==		== See also ==
	* [[21/20]] – its [[octave complement]]		* [[21/20]] – its [[octave complement]]
			* [[Gallery of just intervals]]

	[[~~category~~:~~interval~~]]		[[Category:Interval]]
	[[~~category~~:7-limit]]		[[Category:7-limit]]
	[[Category:~~todo~~:~~expand~~]]		[[Category:Seventh]]
			[[Category:Major seventh]]