1/2-comma meantone - Revision history

FloraC: Mistuning -> error

2024-11-07T14:27:32Z

Mistuning -> error

← Older revision		Revision as of 14:27, 7 November 2024
Line 21:		Line 21:
	[[Tuning map]]: {{val\| 1200 1891.2019 2764.8074 3350.4316 }}		[[Tuning map]]: {{val\| 1200 1891.2019 2764.8074 3350.4316 }}

	[[~~Mistuning~~ map]]: {{val\| 0 -10.7531 -21.5063 -18.3944 }}		[[Error map]]: {{val\| 0 -10.7531 -21.5063 -18.3944 }}

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

CompactStar: Readd historical because of Fogalino or whoever it was proposing it in the 1500s

2024-08-08T01:16:36Z

Readd historical because of Fogalino or whoever it was proposing it in the 1500s

← Older revision		Revision as of 01:16, 8 August 2024
Line 24:		Line 24:

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

FloraC: Adopt flattertone mapping

2024-08-07T10:54:03Z

Adopt flattertone mapping

← Older revision		Revision as of 10:54, 7 August 2024
Line 3:		Line 3:
	In this system, the major thirds are exactly [[100/81]] or approximately 365 [[cent]]s, thus bordering on neutral thirds. The fifths of this temperament fall between those of [[26edo]] and [[33edo]], but closer to 33, which is the best small number candidate for a closed system approximating this meantone. If you want more precision, [[125edo]] using the bb [[val]] flat 5th is audibly indistinguishable from a closed system of half-comma meantone, with an error measured in thousandths of a cent.		In this system, the major thirds are exactly [[100/81]] or approximately 365 [[cent]]s, thus bordering on neutral thirds. The fifths of this temperament fall between those of [[26edo]] and [[33edo]], but closer to 33, which is the best small number candidate for a closed system approximating this meantone. If you want more precision, [[125edo]] using the bb [[val]] flat 5th is audibly indistinguishable from a closed system of half-comma meantone, with an error measured in thousandths of a cent.

	For a tuning with so flat a fifth, the 7-limit [[extension]] is [[~~flattone~~]] ~~instead of~~ septimal meantone~~, or~~ [[7/6]] and [[8/7]] ~~would swap their~~ sizes.		For a tuning with so flat a fifth, the 7-limit [[extension]] that preserves [[7-odd-limit]] [[diamond monotone]] is [[flattertone]]. Otherwise the septimal meantone mapping has the sizes of [[7/6]] and [[8/7]] swapped, and the flattone mapping has the sizes of [[7/5]] and [[10/7]] swapped.

	== Tuning profile ==		== Tuning profile ==
Line 10:		Line 10:
	{\| class="right-all"		{\| class="right-all"
	\|-		\|-
	\| [⟨ \|\| 1 \|\| 2 \|\| 4 \|\| -1 \|\| ]		\| [⟨ \|\| 1 \|\| 2 \|\| 4 \|\| 10 \|\| ]
	\|-		\|-
	\| ⟨ \|\| 0 \|\| -1 \|\| -4 \|\| 9 \|\| ]		\| ⟨ \|\| 0 \|\| -1 \|\| -4 \|\| -17 \|\| ]
	\|-		\|-
	\| ⟨ \|\| 0 \|\| 1/2 \|\| 2 \|\| -9/2 \|\| ]		\| ⟨ \|\| 0 \|\| 1/2 \|\| 2 \|\| 17/2 \|\| ]
	\|-		\|-
	\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| ]]		\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| ]]
	\|}		\|}

	[[Tuning map]]: {{val\| 1200 1891.2019 2764.8074 ~~3379~~.~~1833~~ }}		[[Tuning map]]: {{val\| 1200 1891.2019 2764.8074 3350.4316 }}

	[[Mistuning map]]: {{val\| 0 -10.7531 -21.5063 ~~+10~~.~~3574~~ }}		[[Mistuning map]]: {{val\| 0 -10.7531 -21.5063 -18.3944 }}

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

CompactStar: I don't think this is a historical system like third-comma or less eccentric, it's very xen

2024-02-28T23:14:34Z

I don't think this is a historical system like third-comma or less eccentric, it's very xen

← Older revision		Revision as of 23:14, 28 February 2024
Line 24:		Line 24:

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

FloraC: +tuning profile

2023-11-21T04:44:45Z

+tuning profile

@@ Line 1: / Line 1: @@
-In '''1/2-comma [[meantone]]''' temperament, each perfect fifth is tempered by a half of a [[syntonic comma]] from its just value of [[3/2]]. This results in minor sevenths being exactly [[9/5]] (and major seconds being exactly [[10/9]]).
+'''1/2-comma meantone''' is the tuning of [[meantone]] temperament in which each perfect fifth is tempered by a half of a [[syntonic comma]] from its just value of [[3/2]]. This results in minor sevenths being exactly [[9/5]] (and major seconds being exactly [[10/9]]).
-In this system, the "major thirds" are exactly [[100/81]] or approximately 365 [[cent]]s, thus bordering on neutral thirds. The fifths of this temperament fall between those of [[26edo]] and [[33edo]], but closer to 33, which is the best small number candidate for a closed system approximating this meantone. If you want more precision, [[125edo]] using the bb val flat 5th is audibly indistinguishable from a closed system of half comma meantone, with an error measured in thousandths of a cent.
+In this system, the major thirds are exactly [[100/81]] or approximately 365 [[cent]]s, thus bordering on neutral thirds. The fifths of this temperament fall between those of [[26edo]] and [[33edo]], but closer to 33, which is the best small number candidate for a closed system approximating this meantone. If you want more precision, [[125edo]] using the bb [[val]] flat 5th is audibly indistinguishable from a closed system of half-comma meantone, with an error measured in thousandths of a cent.
 [[Category:Meantone]]
 [[Category:Historical]]

FloraC: FloraC moved page 1/2 syntonic comma meantone to 1/2-comma meantone: Syntonic comma is assumed

2023-09-30T07:07:32Z

FloraC moved page 1/2 syntonic comma meantone to 1/2-comma meantone: Syntonic comma is assumed

← Older revision	Revision as of 07:07, 30 September 2023
(No difference)

BudjarnLambeth: Added to category "historical"

2023-04-27T01:11:23Z

Added to category "historical"

← Older revision		Revision as of 01:11, 27 April 2023
Line 4:		Line 4:

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

Yourmusic Productions: Expand on convergent math.

2021-02-19T10:39:26Z

Expand on convergent math.

← Older revision		Revision as of 10:39, 19 February 2021
Line 1:		Line 1:
	In '''1/2-comma [[meantone]]''' temperament, each perfect fifth is tempered by a half of a [[syntonic comma]] from its just value of [[3/2]]. This results in minor sevenths being exactly [[9/5]] (and major seconds being exactly [[10/9]]).		In '''1/2-comma [[meantone]]''' temperament, each perfect fifth is tempered by a half of a [[syntonic comma]] from its just value of [[3/2]]. This results in minor sevenths being exactly [[9/5]] (and major seconds being exactly [[10/9]]).

	In this system, the "major thirds" are exactly [[100/81]] or approximately 365 [[cent]]s, thus bordering on neutral thirds. The fifths of this temperament fall between those of [[26edo]] and [[33edo]], but closer to 33, which is the best small number candidate for a closed system approximating this meantone.		In this system, the "major thirds" are exactly [[100/81]] or approximately 365 [[cent]]s, thus bordering on neutral thirds. The fifths of this temperament fall between those of [[26edo]] and [[33edo]], but closer to 33, which is the best small number candidate for a closed system approximating this meantone. If you want more precision, [[125edo]] using the bb val flat 5th is audibly indistinguishable from a closed system of half comma meantone, with an error measured in thousandths of a cent.

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

Inthar at 21:49, 2 July 2020

2020-07-02T21:49:08Z

← Older revision		Revision as of 21:49, 2 July 2020
Line 1:		Line 1:
	In '''1/2-comma [[meantone]]''' temperament, each perfect fifth is tempered by a half of a [[syntonic comma]] from its just value of [[3/2]]. This results in minor sevenths being exactly [[9/5]] (and major seconds being exactly [[10/9]]).		In '''1/2-comma [[meantone]]''' temperament, each perfect fifth is tempered by a half of a [[syntonic comma]] from its just value of [[3/2]]. This results in minor sevenths being exactly [[9/5]] (and major seconds being exactly [[10/9]]).

	In this system, the "major thirds" are exactly [[100/81]] or approximately 365 [[cent]]s, thus bordering on neutral thirds. The fifths of this temperament fall between those of [[26edo]] and [[33edo]], but closer to 33, which is the best small number candidate for a closed system approximating this ~~meantoneaaa~~.		In this system, the "major thirds" are exactly [[100/81]] or approximately 365 [[cent]]s, thus bordering on neutral thirds. The fifths of this temperament fall between those of [[26edo]] and [[33edo]], but closer to 33, which is the best small number candidate for a closed system approximating this meantone.

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

Inthar: typo

2020-07-02T21:48:59Z

typo

← Older revision		Revision as of 21:48, 2 July 2020
Line 1:		Line 1:
	In '''1/2-comma [[meantone]]''' temperament, each perfect fifth is tempered by a half of a [[syntonic comma]] from its just value of [[3/2]]. This results in minor sevenths being exactly [[9/5]] (and major seconds being exactly [[10/9]]).		In '''1/2-comma [[meantone]]''' temperament, each perfect fifth is tempered by a half of a [[syntonic comma]] from its just value of [[3/2]]. This results in minor sevenths being exactly [[9/5]] (and major seconds being exactly [[10/9]]).

	In this system, the "major thirds" are exactly [[100/81]] or approximately 365 [[cent]]s, thus bordering on neutral thirds. The fifths of this temperament fall between those of [[26edo]] and [[33edo]], but closer to 33, which is the best small number candidate for a closed system approximating this ~~meantime~~.		In this system, the "major thirds" are exactly [[100/81]] or approximately 365 [[cent]]s, thus bordering on neutral thirds. The fifths of this temperament fall between those of [[26edo]] and [[33edo]], but closer to 33, which is the best small number candidate for a closed system approximating this meantoneaaa.

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