Gentle region - Revision history

Lériendil: links; god, links

2025-06-02T00:26:12Z

links; god, links

← Older revision		Revision as of 00:26, 2 June 2025
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	''For an alternative version of the page, see: [[Gentle region (extended version)]].''		''For an alternative version of the page, see: [[Gentle region (extended version)]].''

	The '''gentle region''' refers to the set of tuning systems generated by fifths in the region between the fifths of 29edo (~703.4c) and 17edo (~705.9c), which generate [[neogothic]] (specifically, neomajor and neominor) thirds. The region was defined by [[Margo Schulter]] in a [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105200.html#105202 tuning list posting], originally defined as the region between 1.49 to 2.65 cents sharp of a just fifth (~703.4 to ~704.6 cents), before being [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_106239.html#106239 revised] to 1.49 to 3.04 cents sharp (~703.4 to 705 cents). The tuning range shown on this page shows tunings as sharp as 17edo.		The '''gentle region''' refers to the set of tuning systems generated by fifths in the region between the fifths of [[29edo]] (~703.4c) and [[17edo]] (~705.9c), which generate [[neogothic]] (specifically, neomajor and neominor) thirds. The region was defined by [[Margo Schulter]] in a [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105200.html#105202 tuning list posting], originally defined as the region between 1.49 to 2.65 cents sharp of a just fifth (~703.4 to ~704.6 cents), before being [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_106239.html#106239 revised] to 1.49 to 3.04 cents sharp (~703.4 to 705 cents). The tuning range shown on this page shows tunings as sharp as 17edo.

	Gentle tuning systems are thus "mild" (or, as the name says, "gentle") versions of tuning systems like [[Superpyth]] temperament. They allow harmony in the style of medieval Pythagorean harmony, usable for neogothic harmony systems; besides, they are possible temperament frameworks for [[Arabic music\|Arabic]] and [[Turkish music\|Turkish]] tuning systems, with the special property of delivering a common framework for both, differing in the degree of tempering.		Gentle tuning systems are thus "mild" (or, as the name says, "gentle") versions of tuning systems like [[Superpyth]] temperament. They allow harmony in the style of medieval Pythagorean harmony, usable for neogothic harmony systems; besides, they are possible temperament frameworks for [[Arabic music\|Arabic]] and [[Turkish music\|Turkish]] tuning systems, with the special property of delivering a common framework for both, differing in the degree of tempering.
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	When the tempering of the fifth is "very gentle"/near-just as in 29edo, the interval notated as C-Fb in standard sheet notation (8 fifths down) will be close to a 5/4 major third (implying [[schismic]] temperament), as used in Turkish music; sharper tempering as in 17edo will give this interval the character of a neutral third, as important in Arabic music. (The interval notated as C-E will have the character of a pythagorean or neomajor third.)		When the tempering of the fifth is "very gentle"/near-just as in 29edo, the interval notated as C-Fb in standard sheet notation (8 fifths down) will be close to a 5/4 major third (implying [[schismic]] temperament), as used in Turkish music; sharper tempering as in 17edo will give this interval the character of a neutral third, as important in Arabic music. (The interval notated as C-E will have the character of a pythagorean or neomajor third.)

	We can consider the ~~first~~ region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of {{EDOs\| 29, 46, 75, 104, 109, 121, 145, 155, 162, 167, 179, 191, 201, 213, 225 and 237, plus 63 and 80 }} in the extended region.		We can consider the originally-defined gentle region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of {{EDOs\| 29, 46, 75, 104, 109, 121, 145, 155, 162, 167, 179, 191, 201, 213, 225 and 237, plus 63 and 80 }} in the extended region.

	The extended gentle region is further divided into two subregions:		The extended gentle region is further divided into two subregions:

Lériendil: added back link to the extended version

2025-06-02T00:25:11Z

added back link to the extended version

← Older revision		Revision as of 00:25, 2 June 2025
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	\| ja =		\| ja =
	}}		}}
			''For an alternative version of the page, see: [[Gentle region (extended version)]].''

	The '''gentle region''' refers to the set of tuning systems generated by fifths in the region between the fifths of 29edo (~703.4c) and 17edo (~705.9c), which generate [[neogothic]] (specifically, neomajor and neominor) thirds. The region was defined by [[Margo Schulter]] in a [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105200.html#105202 tuning list posting], originally defined as the region between 1.49 to 2.65 cents sharp of a just fifth (~703.4 to ~704.6 cents), before being [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_106239.html#106239 revised] to 1.49 to 3.04 cents sharp (~703.4 to 705 cents). The tuning range shown on this page shows tunings as sharp as 17edo.		The '''gentle region''' refers to the set of tuning systems generated by fifths in the region between the fifths of 29edo (~703.4c) and 17edo (~705.9c), which generate [[neogothic]] (specifically, neomajor and neominor) thirds. The region was defined by [[Margo Schulter]] in a [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105200.html#105202 tuning list posting], originally defined as the region between 1.49 to 2.65 cents sharp of a just fifth (~703.4 to ~704.6 cents), before being [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_106239.html#106239 revised] to 1.49 to 3.04 cents sharp (~703.4 to 705 cents). The tuning range shown on this page shows tunings as sharp as 17edo.

VectorGraphics at 00:22, 2 June 2025

2025-06-02T00:22:22Z

← Older revision		Revision as of 00:22, 2 June 2025
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	\| ja =		\| ja =
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	''~~This is~~ the ~~version~~ of ~~Oct 30~~, ~~2012~~. ~~For an alternative version see:~~ [[~~Gentle~~ region (~~extended version~~)]~~]''~~		The '''gentle region''' refers to the set of tuning systems generated by fifths in the region between the fifths of 29edo (~703.4c) and 17edo (~705.9c), which generate [[neogothic]] (specifically, neomajor and neominor) thirds. The region was defined by [[Margo Schulter]] in a [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105200.html#105202 tuning list posting], originally defined as the region between 1.49 to 2.65 cents sharp of a just fifth (~703.4 to ~704.6 cents), before being [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_106239.html#106239 revised] to 1.49 to 3.04 cents sharp (~703.4 to 705 cents). The tuning range shown on this page shows tunings as sharp as 17edo.

	~~-----~~		Gentle tuning systems are thus "mild" (or, as the name says, "gentle") versions of tuning systems like [[Superpyth]] temperament. They allow harmony in the style of medieval Pythagorean harmony, usable for neogothic harmony systems; besides, they are possible temperament frameworks for [[Arabic music\|Arabic]] and [[Turkish music\|Turkish]] tuning systems, with the special property of delivering a common framework for both, differing in the degree of tempering.
	[[~~Margo Schulter~~]], ~~in a~~ [~~https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105200.html#105202~~ tuning ~~list posting]~~, ~~defined~~ the ~~"gentle region"~~ of ~~temperaments with~~ a ~~fifth as generator as that~~ of ~~fifths about 1.49 to 2.65 cents sharp; later [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_106239.html#106239 amending that] to from 1.49 to 3.04 cents sharp~~.

	Gentle-tempered tone systems are thus "mild" (or, as the name says, "gentle") versions of [[Superpyth]] temperament. They allow harmony in the style of medieval Pythagorean harmony, usable for "Neo-gothic" harmony systems; besides, they are possible temperament frameworks for [[Arabic, Turkish, Persian\|middle-eastern (Arabic, Turkish, Persian)]] tuning systems, with the special property of delivering a common framework for both Arabic and Turkish music, differing in the degree of tempering. When the tempering of the fifth is "very gentle"/near-just, the interval notated as C-Fb in standard sheet notation (8 fifths down) will be close to a 5/4 major third, as used in Turkish music; ~~while~~ sharper tempering will give this interval the character of a neutral third, as important in ~~arabic~~ music. (The interval notated as C-E will have the character of a ~~larger Pythagorean -~~ or ~~super-Pythagorean - major~~ third.)		When the tempering of the fifth is "very gentle"/near-just as in 29edo, the interval notated as C-Fb in standard sheet notation (8 fifths down) will be close to a 5/4 major third (implying [[schismic]] temperament), as used in Turkish music; sharper tempering as in 17edo will give this interval the character of a neutral third, as important in Arabic music. (The interval notated as C-E will have the character of a pythagorean or neomajor third.)

	We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of {{EDOs\| 29, 46, 75, 104, 109, 121, 145, 155, 162, 167, 179, 191, 201, 213, 225 and 237, plus 63 and 80 }} in the extended region.		We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of {{EDOs\| 29, 46, 75, 104, 109, 121, 145, 155, 162, 167, 179, 191, 201, 213, 225 and 237, plus 63 and 80 }} in the extended region.

ArrowHead294 at 15:05, 16 January 2025

2025-01-16T15:05:35Z

← Older revision		Revision as of 15:05, 16 January 2025
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	Gentle-tempered tone systems are thus "mild" (or, as the name says, "gentle") versions of [[Superpyth]] temperament. They allow harmony in the style of medieval Pythagorean harmony, usable for "Neo-gothic" harmony systems; besides, they are possible temperament frameworks for [[Arabic, Turkish, Persian\|middle-eastern (Arabic, Turkish, Persian)]] tuning systems, with the special property of delivering a common framework for both Arabic and Turkish music, differing in the degree of tempering. When the tempering of the fifth is "very gentle"/near-just, the interval notated as C-Fb in standard sheet notation (8 fifths down) will be close to a 5/4 major third, as used in Turkish music; while sharper tempering will give this interval the character of a neutral third, as important in arabic music. (The interval notated as C-E will have the character of a larger Pythagorean - or super-Pythagorean - major third.)		Gentle-tempered tone systems are thus "mild" (or, as the name says, "gentle") versions of [[Superpyth]] temperament. They allow harmony in the style of medieval Pythagorean harmony, usable for "Neo-gothic" harmony systems; besides, they are possible temperament frameworks for [[Arabic, Turkish, Persian\|middle-eastern (Arabic, Turkish, Persian)]] tuning systems, with the special property of delivering a common framework for both Arabic and Turkish music, differing in the degree of tempering. When the tempering of the fifth is "very gentle"/near-just, the interval notated as C-Fb in standard sheet notation (8 fifths down) will be close to a 5/4 major third, as used in Turkish music; while sharper tempering will give this interval the character of a neutral third, as important in arabic music. (The interval notated as C-E will have the character of a larger Pythagorean - or super-Pythagorean - major third.)

	We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of ~~[[29edo]]~~, ~~[[46edo]]~~, ~~[[75edo]]~~, ~~[[104edo]]~~, ~~[[109edo]]~~, ~~[[121edo]]~~, ~~[[145edo]]~~, ~~[[155edo]]~~, ~~[[162edo]]~~, ~~[[167edo]]~~, ~~[[179edo]]~~, ~~[[191edo]]~~, ~~[[201edo]]~~, ~~[[213edo]]~~, ~~[[225edo]]~~ and ~~[[237edo]]~~, plus ~~[[63edo]]~~ and ~~[[80edo]]~~ in the extended region.		We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of {{EDOs\| 29, 46, 75, 104, 109, 121, 145, 155, 162, 167, 179, 191, 201, 213, 225 and 237, plus 63 and 80 }} in the extended region.

	The extended gentle region is further divided into two subregions:		The extended gentle region is further divided into two subregions:
	* "~~lower~~ gentle": 703.4¢ (near 17\29) to 704.3¢ (near 27\46)		* "Lower gentle": 703.4{{c}} (near 17\29) to 704.3{{c}} (near 27\46)
	* "~~upper~~ gentle": 704.3¢ to 705.0¢ (near 10\17, or more accurately 47\80).		* "Upper gentle": 704.3{{c}} to 705.0{{c}} (near 10\17, or more accurately 47\80).
	[[46edo]] is effectively the boundary between lower and upper neogothic.		[[46edo]] is effectively the boundary between lower and upper neogothic.

	{\| class="wikitable"		{\| class="wikitable"
			\|-
	! colspan="4" \| EDO Generator		! colspan="4" \| EDO Generator
	! Fifth		! Fifth

AthiTrydhen at 08:09, 13 December 2022

2022-12-13T08:09:15Z

← Older revision		Revision as of 08:09, 13 December 2022
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	\| 372.416		\| 372.416
	\|		\|
			\|-
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			\|703.711
			\|370.312
			\|Margo Schulter's MET-24 fifth
	\|-		\|-
	\|		\|

Xenwolf: makes no sense. Undo revision 76315 by Moremajorthanmajor (talk)

2021-08-16T05:54:09Z

makes no sense. Undo revision 76315 by Moremajorthanmajor (talk)

← Older revision		Revision as of 05:54, 16 August 2021
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	~~{{Infobox MOS\|Equalized=1\|Pattern=LLs Ls Ls LLs Ls Ls LLs Ls Ls Ls LLs Ls Ls LLs Ls Ls Ls\|Periods=1\|nLargeSteps=17\|nSmallSteps=12}}~~{{interwiki		{{interwiki
	\| de = Gentle		\| de = Gentle
	\| en = Gentle region		\| en = Gentle region

Moremajorthanmajor at 18:13, 15 August 2021

2021-08-15T18:13:50Z

← Older revision		Revision as of 18:13, 15 August 2021
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	{{interwiki		{{Infobox MOS\|Equalized=1\|Pattern=LLs Ls Ls LLs Ls Ls LLs Ls Ls Ls LLs Ls Ls LLs Ls Ls Ls\|Periods=1\|nLargeSteps=17\|nSmallSteps=12}}{{interwiki
	\| de = Gentle		\| de = Gentle
	\| en = Gentle region		\| en = Gentle region

Fredg999: Categories

2021-08-14T19:19:05Z

Inthar at 03:52, 17 May 2021

2021-05-17T03:52:31Z

← Older revision		Revision as of 03:52, 17 May 2021
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	We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of [[29edo]], [[46edo]], [[75edo]], [[104edo]], [[109edo]], [[121edo]], [[145edo]], [[155edo]], [[162edo]], [[167edo]], [[179edo]], [[191edo]], [[201edo]], [[213edo]], [[225edo]] and [[237edo]], plus [[63edo]] and [[80edo]] in the extended region.		We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of [[29edo]], [[46edo]], [[75edo]], [[104edo]], [[109edo]], [[121edo]], [[145edo]], [[155edo]], [[162edo]], [[167edo]], [[179edo]], [[191edo]], [[201edo]], [[213edo]], [[225edo]] and [[237edo]], plus [[63edo]] and [[80edo]] in the extended region.

	The gentle region is further divided into two subregions:		The extended gentle region is further divided into two subregions:
	* "lower ~~neogothic~~": 703.4¢-704.2¢		* "lower gentle": 703.4¢ (near 17\29) to 704.3¢ (near 27\46)
	* "upper ~~neogothic~~": 704.~~6¢-~~705.0¢		* "upper gentle": 704.3¢ to 705.0¢ (near 10\17, or more accurately 47\80).
	[[46edo]] is ~~near~~ the boundary between lower and upper neogothic.		[[46edo]] is effectively the boundary between lower and upper neogothic.

	{\| class="wikitable"		{\| class="wikitable"

Inthar: had a discussion with margo schulter

2021-05-17T03:47:58Z

had a discussion with margo schulter

← Older revision		Revision as of 03:47, 17 May 2021
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	We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of [[29edo]], [[46edo]], [[75edo]], [[104edo]], [[109edo]], [[121edo]], [[145edo]], [[155edo]], [[162edo]], [[167edo]], [[179edo]], [[191edo]], [[201edo]], [[213edo]], [[225edo]] and [[237edo]], plus [[63edo]] and [[80edo]] in the extended region.		We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of [[29edo]], [[46edo]], [[75edo]], [[104edo]], [[109edo]], [[121edo]], [[145edo]], [[155edo]], [[162edo]], [[167edo]], [[179edo]], [[191edo]], [[201edo]], [[213edo]], [[225edo]] and [[237edo]], plus [[63edo]] and [[80edo]] in the extended region.

			The gentle region is further divided into two subregions:
			* "lower neogothic": 703.4¢-704.2¢
			* "upper neogothic": 704.6¢-705.0¢
			[[46edo]] is near the boundary between lower and upper neogothic.

	{\| class="wikitable"		{\| class="wikitable"

← Older revision		Revision as of 19:19, 14 August 2021
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	[[Category:Fifth]]		[[Category:Fifth]]
	[[Category:Gentle]]		[[Category:Gentle]]
	~~[[Category:Sharpness]]~~