Qian's small comma - Revision history

MisterShafXen at 21:23, 27 May 2026

2026-05-27T21:23:54Z

← Older revision		Revision as of 21:23, 27 May 2026
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	According to a 2009 paper by Chen Yingshi, this comma as well as the [[359-comma]] was discovered by the ancient Chinese theorist Qian Lezhi (Simplified Chinese: 钱乐之, 390–462, also romanized as Ch'ien Lo-chih), hence the name<ref>Chen Yingshi. "Three Kinds of Tone Difference in 'Qian's 360 temperament'", ''Journal of Nanjing Arts Institute (Music & Performance)'', 2009. [https://kns.cnki.net/kcms2/article/abstract?v=oIAaYX6OCNIVGHOUBDvBdqAJyVAgMN-zl7gj0MMjQ567l1DriSpw6d29XAsML4Khkg1NyaNVX4Aar610z0PLa23h_Od2OPgd2u25apJJzoRVYL5HAXRdq2efCwOmyBy9V84FKOwwUeOgTxcVT5XG3rMmw1gYqIig&uniplatform=NZKPT CNKI (simplified Chinese)] [https://ia904506.us.archive.org/28/items/360-temp/%E2%80%9C%E9%92%B1%E4%B9%90%E4%B9%8B%E4%B8%89%E7%99%BE%E5%85%AD%E5%8D%81%E5%BE%8B%E2%80%9D%E4%B8%AD%E7%9A%84%E4%B8%89%E7%A7%8D%E9%9F%B3%E5%B7%AE.pdf archive]</ref>. In Qian's 360-tone tuning, this comma can be described as the interval between Yizhao (亿兆) and Qinghuangzhong (清黄钟), or between Kezhong (克终) and Zhishi (执始), etc.		According to a 2009 paper by Chen Yingshi, this comma as well as the [[359-comma]] was discovered by the ancient Chinese theorist Qian Lezhi (Simplified Chinese: 钱乐之, 390–462, also romanized as Ch'ien Lo-chih), hence the name<ref>Chen Yingshi. "Three Kinds of Tone Difference in 'Qian's 360 temperament'", ''Journal of Nanjing Arts Institute (Music & Performance)'', 2009. [https://kns.cnki.net/kcms2/article/abstract?v=oIAaYX6OCNIVGHOUBDvBdqAJyVAgMN-zl7gj0MMjQ567l1DriSpw6d29XAsML4Khkg1NyaNVX4Aar610z0PLa23h_Od2OPgd2u25apJJzoRVYL5HAXRdq2efCwOmyBy9V84FKOwwUeOgTxcVT5XG3rMmw1gYqIig&uniplatform=NZKPT CNKI (simplified Chinese)] [https://ia904506.us.archive.org/28/items/360-temp/%E2%80%9C%E9%92%B1%E4%B9%90%E4%B9%8B%E4%B8%89%E7%99%BE%E5%85%AD%E5%8D%81%E5%BE%8B%E2%80%9D%E4%B8%AD%E7%9A%84%E4%B8%89%E7%A7%8D%E9%9F%B3%E5%B7%AE.pdf archive]</ref>. In Qian's 360-tone tuning, this comma can be described as the interval between Yizhao (亿兆) and Qinghuangzhong (清黄钟), or between Kezhong (克终) and Zhishi (执始), etc.

	''Sasktel comma'' was first attested on this wiki in 2011<ref>See [https://en.xen.wiki/index.php?title=Small_comma&oldid=13530 ''Small comma'' (Revision as of 18:47, 4 July 2011 by Wikispaces>genewardsmith)].</ref>. ~~It is unclear how this~~ name was coined.		''Sasktel comma'' was first attested on this wiki in 2011<ref>See [https://en.xen.wiki/index.php?title=Small_comma&oldid=13530 ''Small comma'' (Revision as of 18:47, 4 July 2011 by Wikispaces>genewardsmith)].</ref>. The name was most likely coined because the area code for telephone numbers in Saskatchewan, Canada is 306.

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

Godtone: relevant as 306 + 359 = 665

2026-04-04T15:28:26Z

relevant as 306 + 359 = 665

← Older revision		Revision as of 15:28, 4 April 2026
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	== See also ==		== See also ==
	* [[Qian's large comma]]		* [[Qian's large comma]]
			* [[Satanic comma]] (aka. 665-comma, via 306 + 359 = 665)

	== Notes==		== Notes==

Godtone: these pair together as the ratio of the cents of the pyth comma to the mercator comma is almost exactly 6.5 and making it so implies 665edo

2026-04-04T15:24:43Z

these pair together as the ratio of the cents of the pyth comma to the mercator comma is almost exactly 6.5 and making it so implies 665edo

← Older revision		Revision as of 15:24, 4 April 2026
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	''Sasktel comma'' was first attested on this wiki in 2011<ref>See [https://en.xen.wiki/index.php?title=Small_comma&oldid=13530 ''Small comma'' (Revision as of 18:47, 4 July 2011 by Wikispaces>genewardsmith)].</ref>. It is unclear how this name was coined.		''Sasktel comma'' was first attested on this wiki in 2011<ref>See [https://en.xen.wiki/index.php?title=Small_comma&oldid=13530 ''Small comma'' (Revision as of 18:47, 4 July 2011 by Wikispaces>genewardsmith)].</ref>. It is unclear how this name was coined.

			== See also ==
			* [[Qian's large comma]]

	== Notes==		== Notes==

	[[Category:Commas with unknown etymology]]		[[Category:Commas with unknown etymology]]
	[[Category:Commas named after polymaths]]		[[Category:Commas named after polymaths]]

	<references />		<references />

FloraC at 13:49, 20 January 2025

2025-01-20T13:49:24Z

← Older revision		Revision as of 13:49, 20 January 2025
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	{{Infobox Interval		{{Infobox Interval
	\| Monzo = 485 -306		\| Monzo = 485 -306
	\| Name = sasktel comma		\| Name = Qian's small comma, sasktel comma, 306-comma
	\| Color name = s<sup>44</sup>w30, lequadsawa 30th		\| Color name = s<sup>44</sup>w30, lequadsawa 30th
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''Qian's small comma''', also known as the '''sasktel comma''', is an [[unnoticeable comma\|unnoticeable]] [[3-limit]] [[comma]] with a [[monzo]] of {{monzo\| 485 -306 }}, and a size of 1.7697 [[cent]]s. It is the difference between 306 just [[3/2\|perfect fifths]] and 179 [[2/1\|octaves]], in other words 2<sup>179</sup>/(3/2)<sup>306</sup>. It is also the amount by which a [[Pythagorean comma]] exceeds a stack of six [[Mercator's comma]]s, or the amount by which a [[41-comma]] exceeds a stack of five [[Mercator's comma]]s.		'''Qian's small comma''', also known as the '''sasktel comma''' or '''306-comma''', is an [[unnoticeable comma\|unnoticeable]] [[3-limit]] [[comma]] with a [[monzo]] of {{monzo\| 485 -306 }}, and a size of 1.7697 [[cent]]s. It is the difference between 306 just [[3/2\|perfect fifths]] and 179 [[2/1\|octaves]], in other words 2<sup>179</sup>/(3/2)<sup>306</sup>. It is also the amount by which a [[Pythagorean comma]] exceeds a stack of six [[Mercator's comma]]s, or the amount by which a [[41-comma]] exceeds a stack of five [[Mercator's comma]]s.

	== Temperaments ==		== Temperaments ==

FloraC: FloraC moved page Sasktel comma to Qian's small comma: This name came earlier and has a clearer historical root, so setting it as main

2025-01-20T13:46:59Z

FloraC moved page Sasktel comma to Qian's small comma: This name came earlier and has a clearer historical root, so setting it as main

← Older revision	Revision as of 13:46, 20 January 2025
(No difference)

FloraC: Incorporate stuff from the new page, with improved referencing and linking

2025-01-20T13:44:02Z

Incorporate stuff from the new page, with improved referencing and linking

← Older revision		Revision as of 13:44, 20 January 2025
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	~~#redirect [[Qian's small comma]]~~
	{{Infobox Interval		{{Infobox Interval
	\| Monzo = 485 -306		\| Monzo = 485 -306
Line 6:		Line 5:
	\| Comma = yes		\| Comma = yes
	}}		}}
	~~The~~ '''sasktel comma''' is an [[unnoticeable comma\|unnoticeable]] [[3-limit]] [[comma]] with a [[monzo]] of {{monzo\| 485 -306 }}, and a size of 1.7697 [[cent]]s. It is the difference between 306 just [[3/2\|perfect fifths]] and 179 [[2/1\|octaves]]. It is ~~tempered in~~ [[~~306edo~~]] ~~and any edo that is divisible by 306 and has its best perfect fifth as the same perfect fifth in 306edo (~~[[~~612edo~~]], [[~~918edo~~]], [[~~1224edo~~]]~~, etc)~~.		'''Qian's small comma''', also known as the '''sasktel comma''', is an [[unnoticeable comma\|unnoticeable]] [[3-limit]] [[comma]] with a [[monzo]] of {{monzo\| 485 -306 }}, and a size of 1.7697 [[cent]]s. It is the difference between 306 just [[3/2\|perfect fifths]] and 179 [[2/1\|octaves]], in other words 2<sup>179</sup>/(3/2)<sup>306</sup>. It is also the amount by which a [[Pythagorean comma]] exceeds a stack of six [[Mercator's comma]]s, or the amount by which a [[41-comma]] exceeds a stack of five [[Mercator's comma]]s.

	==Etymology==		== Temperaments ==
	''Sasktel comma'' was first attested on this wiki in 2011<ref>See [https://en.xen.wiki/index.php?title=Small_comma&oldid=13530 ''Small comma'' (Revision as of 18:47, 4 July 2011 by Wikispaces>genewardsmith)].</ref>. It is unclear how this ~~comma~~ was ~~named~~.		This comma is [[tempering out\|tempered out]] in [[306edo]] and any edo that is divisible by 306 and has its best perfect fifth as the same perfect fifth in 306edo ([[612edo]], [[918edo]], [[1224edo]], etc).

			== Etymology ==
			According to a 2009 paper by Chen Yingshi, this comma as well as the [[359-comma]] was discovered by the ancient Chinese theorist Qian Lezhi (Simplified Chinese: 钱乐之, 390–462, also romanized as Ch'ien Lo-chih), hence the name<ref>Chen Yingshi. "Three Kinds of Tone Difference in 'Qian's 360 temperament'", ''Journal of Nanjing Arts Institute (Music & Performance)'', 2009. [https://kns.cnki.net/kcms2/article/abstract?v=oIAaYX6OCNIVGHOUBDvBdqAJyVAgMN-zl7gj0MMjQ567l1DriSpw6d29XAsML4Khkg1NyaNVX4Aar610z0PLa23h_Od2OPgd2u25apJJzoRVYL5HAXRdq2efCwOmyBy9V84FKOwwUeOgTxcVT5XG3rMmw1gYqIig&uniplatform=NZKPT CNKI (simplified Chinese)] [https://ia904506.us.archive.org/28/items/360-temp/%E2%80%9C%E9%92%B1%E4%B9%90%E4%B9%8B%E4%B8%89%E7%99%BE%E5%85%AD%E5%8D%81%E5%BE%8B%E2%80%9D%E4%B8%AD%E7%9A%84%E4%B8%89%E7%A7%8D%E9%9F%B3%E5%B7%AE.pdf archive]</ref>. In Qian's 360-tone tuning, this comma can be described as the interval between Yizhao (亿兆) and Qinghuangzhong (清黄钟), or between Kezhong (克终) and Zhishi (执始), etc.

			''Sasktel comma'' was first attested on this wiki in 2011<ref>See [https://en.xen.wiki/index.php?title=Small_comma&oldid=13530 ''Small comma'' (Revision as of 18:47, 4 July 2011 by Wikispaces>genewardsmith)].</ref>. It is unclear how this name was coined.

	== Notes==		== Notes==

	[[Category:Commas with unknown etymology]]		[[Category:Commas with unknown etymology]]
			[[Category:Commas named after polymaths]]

	<references />		<references />

FilterNashi: redirection

2025-01-20T05:11:24Z

redirection

← Older revision		Revision as of 05:11, 20 January 2025
Line 1:		Line 1:
			#redirect [[Qian's small comma]]
	{{Infobox Interval		{{Infobox Interval
	\| Monzo = 485 -306		\| Monzo = 485 -306
Line 7:		Line 8:
	The '''sasktel comma''' is an [[unnoticeable comma\|unnoticeable]] [[3-limit]] [[comma]] with a [[monzo]] of {{monzo\| 485 -306 }}, and a size of 1.7697 [[cent]]s. It is the difference between 306 just [[3/2\|perfect fifths]] and 179 [[2/1\|octaves]]. It is tempered in [[306edo]] and any edo that is divisible by 306 and has its best perfect fifth as the same perfect fifth in 306edo ([[612edo]], [[918edo]], [[1224edo]], etc).		The '''sasktel comma''' is an [[unnoticeable comma\|unnoticeable]] [[3-limit]] [[comma]] with a [[monzo]] of {{monzo\| 485 -306 }}, and a size of 1.7697 [[cent]]s. It is the difference between 306 just [[3/2\|perfect fifths]] and 179 [[2/1\|octaves]]. It is tempered in [[306edo]] and any edo that is divisible by 306 and has its best perfect fifth as the same perfect fifth in 306edo ([[612edo]], [[918edo]], [[1224edo]], etc).

	== Etymology ==		==Etymology==
	''Sasktel comma'' was first attested on this wiki in 2011<ref>See [https://en.xen.wiki/index.php?title=Small_comma&oldid=13530 ''Small comma'' (Revision as of 18:47, 4 July 2011 by Wikispaces>genewardsmith)].</ref>. It is unclear how this comma was named.		''Sasktel comma'' was first attested on this wiki in 2011<ref>See [https://en.xen.wiki/index.php?title=Small_comma&oldid=13530 ''Small comma'' (Revision as of 18:47, 4 July 2011 by Wikispaces>genewardsmith)].</ref>. It is unclear how this comma was named.

	== Notes ==		== Notes==

	[[Category:Commas with unknown etymology]]		[[Category:Commas with unknown etymology]]

			<references />

BudjarnLambeth at 09:17, 3 November 2024

2024-11-03T09:17:00Z

← Older revision		Revision as of 09:17, 3 November 2024
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	== Notes ==		== Notes ==

			[[Category:Commas with unknown etymology]]

FloraC: First attested in 2011

2024-10-23T11:08:59Z

First attested in 2011

← Older revision		Revision as of 11:08, 23 October 2024
Line 6:		Line 6:
	}}		}}
	The '''sasktel comma''' is an [[unnoticeable comma\|unnoticeable]] [[3-limit]] [[comma]] with a [[monzo]] of {{monzo\| 485 -306 }}, and a size of 1.7697 [[cent]]s. It is the difference between 306 just [[3/2\|perfect fifths]] and 179 [[2/1\|octaves]]. It is tempered in [[306edo]] and any edo that is divisible by 306 and has its best perfect fifth as the same perfect fifth in 306edo ([[612edo]], [[918edo]], [[1224edo]], etc).		The '''sasktel comma''' is an [[unnoticeable comma\|unnoticeable]] [[3-limit]] [[comma]] with a [[monzo]] of {{monzo\| 485 -306 }}, and a size of 1.7697 [[cent]]s. It is the difference between 306 just [[3/2\|perfect fifths]] and 179 [[2/1\|octaves]]. It is tempered in [[306edo]] and any edo that is divisible by 306 and has its best perfect fifth as the same perfect fifth in 306edo ([[612edo]], [[918edo]], [[1224edo]], etc).

			== Etymology ==
			''Sasktel comma'' was first attested on this wiki in 2011<ref>See [https://en.xen.wiki/index.php?title=Small_comma&oldid=13530 ''Small comma'' (Revision as of 18:47, 4 July 2011 by Wikispaces>genewardsmith)].</ref>. It is unclear how this comma was named.

			== Notes ==

FloraC: Cleanup

2024-10-23T11:03:43Z

Cleanup

← Older revision		Revision as of 11:03, 23 October 2024
Line 5:		Line 5:
	\| Comma = yes		\| Comma = yes
	}}		}}
	The '''sasktel comma''' is a [[3-limit]] [[~~unnoticeable~~ comma]] with a monzo of [485 -~~306⟩~~, and a size of 1.7697 ~~cents~~. It is the difference between 306 just [[3/2\|perfect fifths]] and 179 [[2/1\|octaves]]. It is tempered in [[306edo]] and any ~~EDO~~ that is divisible by 306 and has its best perfect fifth as the same perfect fifth in 306edo ([[612edo]], [[918edo]], [[1224edo]], etc).		The '''sasktel comma''' is an [[unnoticeable comma\|unnoticeable]] [[3-limit]] [[comma]] with a [[monzo]] of {{monzo\| 485 -306 }}, and a size of 1.7697 [[cent]]s. It is the difference between 306 just [[3/2\|perfect fifths]] and 179 [[2/1\|octaves]]. It is tempered in [[306edo]] and any edo that is divisible by 306 and has its best perfect fifth as the same perfect fifth in 306edo ([[612edo]], [[918edo]], [[1224edo]], etc).