Qian's large comma - Revision history

Godtone: make clear the relation as it occurred to me that should be necessary when editing the other page

2026-04-04T15:29:15Z

make clear the relation as it occurred to me that should be necessary when editing the other page

← Older revision		Revision as of 15:29, 4 April 2026
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	== See also ==		== See also ==
	* [[Qian's small comma]]		* [[Qian's small comma]]
	* [[Satanic comma]] (aka. 665-comma)		* [[Satanic comma]] (aka. 665-comma, via 306 + 359 = 665)

	== Notes ==		== Notes ==
	[[Category:Commas named after polymaths]]		[[Category:Commas named after polymaths]]

Godtone: relevant as 306 + 359 = 665

2026-04-04T15:27:31Z

relevant as 306 + 359 = 665

← Older revision		Revision as of 15:27, 4 April 2026
Line 14:		Line 14:
	== See also ==		== See also ==
	* [[Qian's small comma]]		* [[Qian's small comma]]
			* [[Satanic comma]] (aka. 665-comma)

	== Notes ==		== Notes ==
	[[Category:Commas named after polymaths]]		[[Category:Commas named after polymaths]]

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

2026-04-04T15:22:34Z

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 15:22, 4 April 2026
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	== Etymology ==		== Etymology ==
	According to a 2009 paper by Chen Yingshi, this comma as well as the [[306-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 Huangzhong (黄钟) and Anyun (安运).		According to a 2009 paper by Chen Yingshi, this comma as well as the [[306-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 Huangzhong (黄钟) and Anyun (安运).

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

	== Notes ==		== Notes ==

	[[Category:Commas named after polymaths]]		[[Category:Commas named after polymaths]]

FilterNashi: Undo revision 216349 by FilterNashi (talk)

2025-11-07T08:37:21Z

Undo revision 216349 by FilterNashi (talk)

← Older revision		Revision as of 08:37, 7 November 2025
Line 10:		Line 10:

	== Etymology ==		== 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 Huangzhong (黄钟) and Anyun (安运).		According to a 2009 paper by Chen Yingshi, this comma as well as the [[306-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 Huangzhong (黄钟) and Anyun (安运).

	== Notes ==		== Notes ==

	[[Category:Commas named after polymaths]]		[[Category:Commas named after polymaths]]

FilterNashi: /* Etymology */

2025-11-07T08:36:19Z

Etymology

← Older revision		Revision as of 08:36, 7 November 2025
Line 10:		Line 10:

	== Etymology ==		== Etymology ==
	According to a 2009 paper by Chen Yingshi, this comma as well as the [[~~306~~-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 Huangzhong (黄钟) and Anyun (安运).		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 Huangzhong (黄钟) and Anyun (安运).

	== Notes ==		== Notes ==

	[[Category:Commas named after polymaths]]		[[Category:Commas named after polymaths]]

FloraC: Cleanup and rework

2025-01-20T13:54:59Z

Cleanup and rework

← Older revision		Revision as of 13:54, 20 January 2025
Line 4:		Line 4:
	\| Comma = yes		\| Comma = yes
	}}		}}
	~~{{monzo\|-569 359}}, called~~ '''Qian's large comma''', is an [[unnoticeable comma\|unnoticeable]] [[3-limit]] [[comma]] with a size of 1.845 cents. ~~Which~~ is the amount by which 359 [[perfect fifth]]s exceed 210 [[octave]]s, in other words (3/2)<sup>359</sup>/2<sup>210</sup>. It is also the amount by which a [[Mercator's comma]] exceeds a [[~~Qianlezhi's small comma\|~~Qian's small comma]].		'''Qian's large comma''', or the '''359-comma''', is an [[unnoticeable comma\|unnoticeable]] [[3-limit]] [[comma]] with a [[monzo]] of {{monzo\|-569 359}} and a size of 1.845 cents. It is the amount by which 359 [[perfect fifth]]s exceed 210 [[octave]]s, in other words (3/2)<sup>359</sup>/2<sup>210</sup>. It is also the amount by which a [[Mercator's comma]] exceeds a [[Qian's small comma]].

	==~~Etymology~~==		== Temperaments ==
	~~The~~ comma is ~~discovered~~ by the ~~ancient Chinese theorist~~, ~~Qian Lezhi（钱乐之，390—462~~, ~~pronounces as ch'ien lo-chih）, see~~ [https://kns.cnki.net/kcms2/article/abstract?v=oIAaYX6OCNIVGHOUBDvBdqAJyVAgMN-zl7gj0MMjQ567l1DriSpw6d29XAsML4Khkg1NyaNVX4Aar610z0PLa23h_Od2OPgd2u25apJJzoRVYL5HAXRdq2efCwOmyBy9V84FKOwwUeOgTxcVT5XG3rMmw1gYqIig&uniplatform=NZKPT Qian's 360 pitches].		This comma is [[tempering out\|tempered out]] in [[359edo]] and any edo that is divisible by 359 and has its best perfect fifth as the same perfect fifth in 359edo ([[718edo]], [[1077edo]], [[1436edo]], etc).

	In Qian's 360 ~~pitches~~, this comma can be described as the interval between ~~Huangzhong（黄钟）~~ and ~~Anyun（安运）~~.		== Etymology ==
			According to a 2009 paper by Chen Yingshi, this comma as well as the [[306-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 Huangzhong (黄钟) and Anyun (安运).

	==~~Temperaments~~==		== Notes ==
	~~[[359edo]]~~

	~~[https://sintel.pythonanywhere.com/result?subgroup=2%2C3&reduce=on&weights=weil&target=&edos=&commas=%5B-569+359%3E&submit_comma=submit see]~~		[[Category:Commas named after polymaths]]

	~~==Ratio==~~
	~~1934329451767021421190980423006270754962252499447372679942534652297789463068718331568475476554301659845788554312924531179306109686817232569946089263295619210341718686733067~~

	~~/1932268761508629172347675945465993672149463664853217499328617625725759571144780212268096883290961288981231808015751088588682539330521493827871454336733540374348490407411712~~

	~~==Old pages==~~
	~~Qianlezhi's large comma[https://en.xen.wiki/index.php?title=Qianlezhi%27s_large_comma&action=history]~~

	~~==See also==~~
	*[[Unnoticeable comma]]
	*[[Qian's small comma]]

	~~[[Category:Commas named after mathematicians]]~~
	[[Category:Commas named after ~~music theorists~~]]

FilterNashi: fixing

2025-01-20T05:35:43Z

fixing

← Older revision		Revision as of 05:35, 20 January 2025
Line 1:		Line 1:
	{{Infobox Interval		{{Infobox Interval
	\| Monzo = -569 359		\| Monzo = -569 359
	\| Name = ~~Qianlezhi~~'s large comma, 359-comma		\| Name = Qian's large comma, 359-comma
	\| Comma = yes		\| Comma = yes
	}}		}}

FilterNashi: Created page with "{{Infobox Interval | Monzo = -569 359 | Name = Qianlezhi's large comma, 359-comma | Comma = yes }} {{monzo|-569 359}}, called '''Qian's large comma''', is an unnoticeable co..."

2025-01-20T05:24:39Z

Created page with "{{Infobox Interval | Monzo = -569 359 | Name = Qianlezhi's large comma, 359-comma | Comma = yes }} {{monzo|-569 359}}, called '''Qian's large comma''', is an unnoticeable co..."

New page

{{Infobox Interval
| Monzo = -569 359
| Name = Qianlezhi's large comma, 359-comma
| Comma = yes
}}
{{monzo|-569 359}}, called '''Qian's large comma''', is an [[unnoticeable comma|unnoticeable]] [[3-limit]] [[comma]] with a size of 1.845 cents. Which is the amount by which 359 [[perfect fifth]]s exceed 210 [[octave]]s, in other words (3/2)<sup>359</sup>/2<sup>210</sup>. It is also the amount by which a [[Mercator's comma]] exceeds a [[Qianlezhi's small comma|Qian's small comma]].

==Etymology==
The comma is discovered by the ancient Chinese theorist, Qian Lezhi（钱乐之，390—462, pronounces as ch'ien lo-chih）, see [https://kns.cnki.net/kcms2/article/abstract?v=oIAaYX6OCNIVGHOUBDvBdqAJyVAgMN-zl7gj0MMjQ567l1DriSpw6d29XAsML4Khkg1NyaNVX4Aar610z0PLa23h_Od2OPgd2u25apJJzoRVYL5HAXRdq2efCwOmyBy9V84FKOwwUeOgTxcVT5XG3rMmw1gYqIig&uniplatform=NZKPT Qian's 360 pitches].

In Qian's 360 pitches, this comma can be described as the interval between Huangzhong（黄钟） and Anyun（安运）.

==Temperaments==
[[359edo]]

[https://sintel.pythonanywhere.com/result?subgroup=2%2C3&reduce=on&weights=weil&target=&edos=&commas=%5B-569+359%3E&submit_comma=submit see]

==Ratio==
1934329451767021421190980423006270754962252499447372679942534652297789463068718331568475476554301659845788554312924531179306109686817232569946089263295619210341718686733067

/1932268761508629172347675945465993672149463664853217499328617625725759571144780212268096883290961288981231808015751088588682539330521493827871454336733540374348490407411712

==Old pages==
Qianlezhi's large comma[https://en.xen.wiki/index.php?title=Qianlezhi%27s_large_comma&action=history]

==See also==
*[[Unnoticeable comma]]
*[[Qian's small comma]]

[[Category:Commas named after mathematicians]]
[[Category:Commas named after music theorists]]