Gentle region (extended version) - Revision history

Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot

2025-09-03T21:08:31Z

Moving from Category:Interval region to Category:Interval regions using Cat-a-lot

← Older revision		Revision as of 21:08, 3 September 2025
Line 396:		Line 396:

	[[Category:Gentle]]		[[Category:Gentle]]
	[[Category:Interval ~~region~~]]		[[Category:Interval regions]]
	[[Category:Tables]]		[[Category:Tables]]

ArrowHead294 at 15:16, 16 January 2025

2025-01-16T15:16:33Z

← Older revision		Revision as of 15:16, 16 January 2025
Line 6:		Line 6:
	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~~\|~~29edo]]~~, ~~[[46edo\|46edo]]~~, ~~[[75edo\|75edo]]~~, ~~[[104edo\|104edo]]~~, ~~[[109edo\|109edo]]~~, ~~[[121edo\|121edo]]~~, ~~[[145edo\|133edo]]~~, ~~[[155edo\|155edo]]~~, ~~[[162edo\|162edo]]~~, ~~[[167edo\|167edo]]~~, ~~[[179edo\|179edo]]~~, ~~[[191edo\|191edo]]~~, ~~[[201edo\|201edo]]~~, ~~[[213edo\|213edo]]~~, ~~[[225edo\|225edo]]~~ and ~~[[237edo\|237edo]]~~, plus ~~[[63edo\|63edo]]~~ and ~~[[80edo\|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.

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

ArrowHead294 at 15:15, 16 January 2025

2025-01-16T15:15:25Z

← Older revision		Revision as of 15:15, 16 January 2025
Line 15:		Line 15:
	! <span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"><span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">Half 8/7+ 1\3 7/6<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">1\3 8/7+ Half 7/6</span></span></span>		! <span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"><span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">Half 8/7+ 1\3 7/6<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">1\3 8/7+ Half 7/6</span></span></span>
	! 8/7+7/6		! 8/7+7/6
	!		! Notes
	\|-		\|-
	\| (7+10)\29		\| (7+10)\29

ArrowHead294 at 15:15, 16 January 2025

2025-01-16T15:15:11Z

Show changes

BudjarnLambeth: Categorised this uncategorised page

2023-04-26T01:14:09Z

Categorised this uncategorised page

← Older revision		Revision as of 01:14, 26 April 2023
Line 394:		Line 394:
	\|		\|
	\|}		\|}
			[[Category:Gentle]]
			[[Category:Interval region]]
			[[Category:Tables]]

Moremajorthanmajor at 18:52, 14 April 2021

2021-04-14T18:52:42Z

Show changes

CritDeathX: Added section from other article

2020-09-22T01:36:10Z

Added section from other article

← Older revision		Revision as of 01:36, 22 September 2020
Line 2:		Line 2:

	-----		-----
	[[Margo_Schulter\|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. 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\|29edo]], [[46edo\|46edo]], [[75edo\|75edo]], [[104edo\|104edo]], [[109edo\|109edo]], [[121edo\|121edo]], [[145edo\|133edo]], [[155edo\|155edo]], [[162edo\|162edo]], [[167edo\|167edo]], [[179edo\|179edo]], [[191edo\|191edo]], [[201edo\|201edo]], [[213edo\|213edo]], [[225edo\|225edo]] and [[237edo\|237edo]], plus [[63edo\|63edo]] and [[80edo\|80edo]] in the extended region.		[[Margo_Schulter\|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.)

			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\|29edo]], [[46edo\|46edo]], [[75edo\|75edo]], [[104edo\|104edo]], [[109edo\|109edo]], [[121edo\|121edo]], [[145edo\|133edo]], [[155edo\|155edo]], [[162edo\|162edo]], [[167edo\|167edo]], [[179edo\|179edo]], [[191edo\|191edo]], [[201edo\|201edo]], [[213edo\|213edo]], [[225edo\|225edo]] and [[237edo\|237edo]], plus [[63edo\|63edo]] and [[80edo\|80edo]] in the extended region.

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

CritDeathX: Added links to the Yahoo groups archive

2020-05-28T22:15:17Z

Added links to the Yahoo groups archive

Show changes

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>mbattaglia1: Imported revision 629084697 - Original comment:

2018-04-26T01:40:17Z

**Imported revision 629084697 - Original comment: **

← Older revision		Revision as of 01:40, 26 April 2018
Line 1:		Line 1:
	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:mbattaglia1\|mbattaglia1]] and made on <tt>2018-04-26 01:37:51 UTC</tt>.<br>		: This revision was by author [[User:mbattaglia1\|mbattaglia1]] and made on <tt>2018-04-26 01:40:17 UTC</tt>.<br>
	: The original revision id was <tt>~~629084659~~</tt>.<br>		: The original revision id was <tt>629084697</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
	<h4>Original Wikitext content:</h4>		<h4>Original Wikitext content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">//This is an extended version of the [[Gentle region]] article.//		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">//This is an extended version of the [[Gentle region]] article.//
	----		----
	[[@Margo Schulter]], in a [[@http://launch.groups.yahoo.com/group/tuning/message/38721\|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 [[@http://launch.groups.yahoo.com/group/tuning/message/105172\|amending that]] to from 1.49 to 3.04 cents sharp. 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\|133edo]], [[@155edo]], [[@162edo]], [[@167edo]], [[@179edo]], [[@191edo]], [[@201edo]], [[@213edo]], [[@225edo]] and [[@237edo]], plus [[@63edo]] and [[@80edo]] in the extended region.		[[@Margo Schulter]], in a [[@http://launch.groups.yahoo.com/group/tuning/message/38721\|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 [[@http://launch.groups.yahoo.com/group/tuning/message/105172\|amending that]] to from 1.49 to 3.04 cents sharp. 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\|133edo]], [[@155edo]], [[@162edo]], [[@167edo]], [[@179edo]], [[@191edo]], [[@201edo]], [[@213edo]], [[@225edo]] and [[@237edo]], plus [[@63edo]] and [[@80edo]] in the extended region.

	\|\|\|\|~ Generator \|\|~ Cents \|\|~ 2-3-7(b)-11-13(b) \|\|~ <span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"><span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">Half 8/7+ 1\3 7/6<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">1\3 8/7+ Half 7/6</span></span></span> \|\|~ 8/7+7/6 \|\|~ \|\|		\|\|\|\|~ Generator \|\|~ Cents \|\|~ 2-3-7(b)-11-13(b) \|\|\|\|~ <span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"><span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">Half 8/7+ 1\3 7/6<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">1\3 8/7+ Half 7/6</span></span></span> \|\|~ 8/7+7/6 \|\|~ \|\|
	\|\| (7+10)\29 \|\| \|\|= 289.655+413.793 \|\| < 29 46 81 100 107\| \|\|\|\|= 2\29+<span style="line-height: 1.5;">3\29</span>		\|\| (7+10)\29 \|\| \|\|= 289.655+413.793 \|\| < 29 46 81 100 107\| \|\|\|\|= 2\29+<span style="line-height: 1.5;">3\29</span>
	82.759+124.138 \|\|= 6\29+6\29		82.759+124.138 \|\|= 6\29+6\29
Line 116:		Line 116:
	225+270 \|\| Boundary of larger "gentle region" \|\|</pre></div>		225+270 \|\| Boundary of larger "gentle region" \|\|</pre></div>
	<h4>Original HTML content:</h4>		<h4>Original HTML content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gentle region (extended version)</title></head><body><em>This is an extended version of the <strong><a class="wiki_link" href="/Gentle%20region">Gentle region</a> article.</strong></em> <br />		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gentle region (extended version)</title></head><body><em>This is an extended version of the <strong><a class="wiki_link" href="/Gentle%20region">Gentle region</a> article.</strong></em><br />
	<hr />		<hr />
	<a class="wiki_link" href="/Margo%20Schulter" target="_blank">Margo Schulter</a>, in a <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/38721" rel="nofollow" target="_blank">tuning list posting</a>, defined the &quot;gentle region&quot; of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp; later <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/105172" rel="nofollow" target="_blank">amending that</a> to from 1.49 to 3.04 cents sharp. 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 <a class="wiki_link" href="/29edo" target="_blank">29edo</a>, <a class="wiki_link" href="/46edo" target="_blank">46edo</a>, <a class="wiki_link" href="/75edo" target="_blank">75edo</a>, <a class="wiki_link" href="/104edo" target="_blank">104edo</a>, <a class="wiki_link" href="/109edo" target="_blank">109edo</a>, <a class="wiki_link" href="/121edo" target="_blank">121edo</a>, <a class="wiki_link" href="/145edo" target="_blank">133edo</a>, <a class="wiki_link" href="/155edo" target="_blank">155edo</a>, <a class="wiki_link" href="/162edo" target="_blank">162edo</a>, <a class="wiki_link" href="/167edo" target="_blank">167edo</a>, <a class="wiki_link" href="/179edo" target="_blank">179edo</a>, <a class="wiki_link" href="/191edo" target="_blank">191edo</a>, <a class="wiki_link" href="/201edo" target="_blank">201edo</a>, <a class="wiki_link" href="/213edo" target="_blank">213edo</a>, <a class="wiki_link" href="/225edo" target="_blank">225edo</a> and <a class="wiki_link" href="/237edo" target="_blank">237edo</a>, plus <a class="wiki_link" href="/63edo" target="_blank">63edo</a> and <a class="wiki_link" href="/80edo" target="_blank">80edo</a> in the extended region.<br />		<a class="wiki_link" href="/Margo%20Schulter" target="_blank">Margo Schulter</a>, in a <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/38721" rel="nofollow" target="_blank">tuning list posting</a>, defined the &quot;gentle region&quot; of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp; later <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/105172" rel="nofollow" target="_blank">amending that</a> to from 1.49 to 3.04 cents sharp. 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 <a class="wiki_link" href="/29edo" target="_blank">29edo</a>, <a class="wiki_link" href="/46edo" target="_blank">46edo</a>, <a class="wiki_link" href="/75edo" target="_blank">75edo</a>, <a class="wiki_link" href="/104edo" target="_blank">104edo</a>, <a class="wiki_link" href="/109edo" target="_blank">109edo</a>, <a class="wiki_link" href="/121edo" target="_blank">121edo</a>, <a class="wiki_link" href="/145edo" target="_blank">133edo</a>, <a class="wiki_link" href="/155edo" target="_blank">155edo</a>, <a class="wiki_link" href="/162edo" target="_blank">162edo</a>, <a class="wiki_link" href="/167edo" target="_blank">167edo</a>, <a class="wiki_link" href="/179edo" target="_blank">179edo</a>, <a class="wiki_link" href="/191edo" target="_blank">191edo</a>, <a class="wiki_link" href="/201edo" target="_blank">201edo</a>, <a class="wiki_link" href="/213edo" target="_blank">213edo</a>, <a class="wiki_link" href="/225edo" target="_blank">225edo</a> and <a class="wiki_link" href="/237edo" target="_blank">237edo</a>, plus <a class="wiki_link" href="/63edo" target="_blank">63edo</a> and <a class="wiki_link" href="/80edo" target="_blank">80edo</a> in the extended region.<br />
Line 130:		Line 130:
	<th>2-3-7(b)-11-13(b)<br />		<th>2-3-7(b)-11-13(b)<br />
	</th>		</th>
	<th><span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"><span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">Half 8/7+ 1\3 7/6<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">1\3 8/7+ Half 7/6</span></span></span><br />		<th colspan="2"><span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"><span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">Half 8/7+ 1\3 7/6<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">1\3 8/7+ Half 7/6</span></span></span><br />
	</th>		</th>
	<th>8/7+7/6<br />		<th>8/7+7/6<br />

← Older revision		Revision as of 15:16, 16 January 2025
Line 6:		Line 6:
	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~~\|~~29edo]]~~, ~~[[46edo\|46edo]]~~, ~~[[75edo\|75edo]]~~, ~~[[104edo\|104edo]]~~, ~~[[109edo\|109edo]]~~, ~~[[121edo\|121edo]]~~, ~~[[145edo\|133edo]]~~, ~~[[155edo\|155edo]]~~, ~~[[162edo\|162edo]]~~, ~~[[167edo\|167edo]]~~, ~~[[179edo\|179edo]]~~, ~~[[191edo\|191edo]]~~, ~~[[201edo\|201edo]]~~, ~~[[213edo\|213edo]]~~, ~~[[225edo\|225edo]]~~ and ~~[[237edo\|237edo]]~~, plus ~~[[63edo\|63edo]]~~ and ~~[[80edo\|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.

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

Gentle region (extended version) - Revision history

Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot

ArrowHead294 at 15:16, 16 January 2025

ArrowHead294 at 15:15, 16 January 2025

ArrowHead294 at 15:15, 16 January 2025

BudjarnLambeth: Categorised this uncategorised page

Moremajorthanmajor at 18:52, 14 April 2021

CritDeathX: Added section from other article

CritDeathX: Added links to the Yahoo groups archive

Wikispaces>FREEZE at 00:00, 17 July 2018

Wikispaces>mbattaglia1: **Imported revision 629084697 - Original comment: **

Wikispaces>mbattaglia1: Imported revision 629084697 - Original comment: