1/5-comma meantone - Revision history

Hstraub at 08:30, 3 May 2026

2026-05-03T08:30:22Z

← Older revision		Revision as of 08:30, 3 May 2026
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	{{Interwiki		{{Interwiki
	\| en = 1/5-comma ~~mesntone~~		\| en = 1/5-comma meantone
	\| de = Fünftelkomma-mitteltönig		\| de = Fünftelkomma-mitteltönig
	}}		}}

Hstraub: Link to German

2026-05-03T08:29:21Z

Link to German

← Older revision		Revision as of 08:29, 3 May 2026
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			{{Interwiki
			\| en = 1/5-comma mesntone
			\| de = Fünftelkomma-mitteltönig
			}}
	'''1/5-comma meantone''' is the tuning of [[meantone]] temperament in which each perfect fifth is tempered by a fifth of a [[syntonic comma]] from its just value of [[3/2]]. This results in major sevenths being exactly [[15/8]] (and minor seconds being exactly [[16/15]]), and in fact this defines 1/5-comma; it is the regular tuning which tempers out [[81/80]] and tunes [[2/1\|2]] and [[16/15]] purely.		'''1/5-comma meantone''' is the tuning of [[meantone]] temperament in which each perfect fifth is tempered by a fifth of a [[syntonic comma]] from its just value of [[3/2]]. This results in major sevenths being exactly [[15/8]] (and minor seconds being exactly [[16/15]]), and in fact this defines 1/5-comma; it is the regular tuning which tempers out [[81/80]] and tunes [[2/1\|2]] and [[16/15]] purely.

BudjarnLambeth: Music

2025-09-21T13:47:19Z

Music

← Older revision		Revision as of 13:47, 21 September 2025
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	[[Error map]]: {{val\| 0 -4.3013 +4.3013 +7.7115 }}		[[Error map]]: {{val\| 0 -4.3013 +4.3013 +7.7115 }}

			== Music ==
			; [[septimal lemon]]
			* [https://youtu.be/jlbpQqahZh0 ''Bubbles''] (2025)

	[[Category:Meantone]]		[[Category:Meantone]]
	[[Category:Historical]]		[[Category:Historical]]

FloraC: Mistuning -> error

2024-11-07T14:30:01Z

Mistuning -> error

← Older revision		Revision as of 14:30, 7 November 2024
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	[[Tuning map]]: {{val\| 1200 1897.6537 2790.6150 3376.5374 }}		[[Tuning map]]: {{val\| 1200 1897.6537 2790.6150 3376.5374 }}

	[[~~Mistuning~~ map]]: {{val\| 0 -4.3013 +4.3013 +7.7115 }}		[[Error map]]: {{val\| 0 -4.3013 +4.3013 +7.7115 }}

	[[Category:Meantone]]		[[Category:Meantone]]
	[[Category:Historical]]		[[Category:Historical]]

FloraC: Something to note with septimal meantone

2024-09-16T15:48:54Z

Something to note with septimal meantone

← Older revision		Revision as of 15:48, 16 September 2024
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	'''1/5-comma meantone''' is the tuning of [[meantone]] temperament in which each perfect fifth is tempered by a fifth of a [[syntonic comma]] from its just value of [[3/2]]. This results in major sevenths being exactly [[15/8]] (and minor seconds being exactly [[16/15]]), and in fact this defines 1/5-comma; it is the regular tuning which tempers out [[81/80]] and tunes [[2/1\|2]] and [[16/15]] purely.		'''1/5-comma meantone''' is the tuning of [[meantone]] temperament in which each perfect fifth is tempered by a fifth of a [[syntonic comma]] from its just value of [[3/2]]. This results in major sevenths being exactly [[15/8]] (and minor seconds being exactly [[16/15]]), and in fact this defines 1/5-comma; it is the regular tuning which tempers out [[81/80]] and tunes [[2/1\|2]] and [[16/15]] purely.

	The major third ([[5/4]]) and the fifth are equally off from JI by 1/5 syntonic comma (''c''. 4.3 [[cent]]s), with the major third sharp and the fifth flat.		The major third ([[5/4]]) and the fifth are equally off from JI by 1/5 syntonic comma (''c''. 4.3 [[cent]]s), with the major third sharp and the fifth flat. The augmented sixth is exactly [[225/128]], and for septimal meantone, this means the [[7/4]] is sharp by a [[225/224\|septimal kleisma (225/224)]].

	1/5-comma meantone is practically identical to the closed system of [[43edo]] (although technically there is a slight difference, as the fifth of 43 is 0.0207 cents sharper.)		1/5-comma meantone is practically identical to the closed system of [[43edo]] (although technically there is a slight difference, as the fifth of 43 is 0.0207 cents sharper.)

FloraC: +tuning profile

2023-10-01T08:18:17Z

+tuning profile

@@ Line 1: / Line 1: @@
-In '''1/5-comma [[meantone]]''' temperament, each perfect fifth is tempered by a fifth of a [[syntonic comma]] from its just value of [[3/2]]. This results in major sevenths being exactly [[15/8]] (and minor seconds being exactly [[16/15]]), and in fact this defines 1/5-comma; it is the regular tuning which tempers out [[81/80]] and tunes 2 and 16/15 purely.
+'''1/5-comma meantone''' is the tuning of [[meantone]] temperament in which each perfect fifth is tempered by a fifth of a [[syntonic comma]] from its just value of [[3/2]]. This results in major sevenths being exactly [[15/8]] (and minor seconds being exactly [[16/15]]), and in fact this defines 1/5-comma; it is the regular tuning which tempers out [[81/80]] and tunes [[2/1|2]] and [[16/15]] purely.
-The major third ([[5/4]]) and the fifth are equally off from JI by 1/5 syntonic comma (''c''. 4.3 [[Cent|cents]]), with the major third sharp and the fifth flat.
+The major third ([[5/4]]) and the fifth are equally off from JI by 1/5 syntonic comma (''c''. 4.3 [[cent]]s), with the major third sharp and the fifth flat.
 /5-comma meantone is practically identical to the closed system of [[43edo]] (although technically there is a slight difference, as the fifth of 43 is 0.0207 cents sharper.)
 [[Category:Meantone]]
 [[Category:Historical]]

BudjarnLambeth: Added to category "historical"

2023-04-27T01:14:41Z

Added to category "historical"

← Older revision		Revision as of 01:14, 27 April 2023
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	[[Category:Meantone]]		[[Category:Meantone]]
			[[Category:Historical]]

Xenwolf: Xenwolf moved page 1/5 syntonic comma meantone to 1/5-comma meantone: meantone implies "syntonic", so no need for ist in the lemma

2020-11-10T15:24:06Z

Xenwolf moved page 1/5 syntonic comma meantone to 1/5-comma meantone: meantone implies "syntonic", so no need for ist in the lemma

← Older revision	Revision as of 15:24, 10 November 2020
(No difference)

FloraC: Add the amount by which thirds and fifths are off

2020-04-10T14:03:09Z

Add the amount by which thirds and fifths are off

← Older revision		Revision as of 14:03, 10 April 2020
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	In '''1/5-comma [[meantone]]''' temperament, each perfect fifth is tempered by a fifth of a [[syntonic comma]] from its just value of [[3/2]]. This results in major sevenths being exactly [[15/8]] (and minor seconds being exactly [[16/15]]), and in fact this defines 1/5-comma; it is the regular tuning which tempers out [[81/80]] and tunes 2 and 16/15 purely.		In '''1/5-comma [[meantone]]''' temperament, each perfect fifth is tempered by a fifth of a [[syntonic comma]] from its just value of [[3/2]]. This results in major sevenths being exactly [[15/8]] (and minor seconds being exactly [[16/15]]), and in fact this defines 1/5-comma; it is the regular tuning which tempers out [[81/80]] and tunes 2 and 16/15 purely.

	1/5-comma meantone is practically identical to the closed system of [[43edo]] (although technically there is a slight difference, as the fifth of 43 is 0.0207 ~~[[cent]]s~~ sharper.)		The major third ([[5/4]]) and the fifth are equally off from JI by 1/5 syntonic comma (''c''. 4.3 [[Cent\|cents]]), with the major third sharp and the fifth flat.

			1/5-comma meantone is practically identical to the closed system of [[43edo]] (although technically there is a slight difference, as the fifth of 43 is 0.0207 cents sharper.)

	[[Category:Meantone]]		[[Category:Meantone]]

Xenwolf: lemma bold, added links, added cat

2018-10-24T21:40:08Z

lemma bold, added links, added cat

← Older revision		Revision as of 21:40, 24 October 2018
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	In 1/5-comma [[~~Meantone\|~~meantone]] temperament, each perfect fifth is tempered by a fifth of a [[~~Syntonic_Comma\|~~syntonic comma]] from its just value of [[~~3/2\|~~3/2]]. This results in major sevenths being exactly 15/8 (and minor seconds being exactly 16/15), and in fact this defines 1/5-comma; it is the regular tuning which tempers out 81/80 and tunes 2 and 16/15 purely.		In '''1/5-comma [[meantone]]''' temperament, each perfect fifth is tempered by a fifth of a [[syntonic comma]] from its just value of [[3/2]]. This results in major sevenths being exactly [[15/8]] (and minor seconds being exactly [[16/15]]), and in fact this defines 1/5-comma; it is the regular tuning which tempers out [[81/80]] and tunes 2 and 16/15 purely.

	1/5-comma meantone is practically identical to the closed system of [[~~43edo\|~~43edo]] (although technically there is a slight difference, as the fifth of 43 is 0.0207 ~~cents~~ sharper.)		1/5-comma meantone is practically identical to the closed system of [[43edo]] (although technically there is a slight difference, as the fifth of 43 is 0.0207 [[cent]]s sharper.)

			[[Category:Meantone]]