Qian's large comma: Difference between revisions

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| Comma = yes

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~~{{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)359/2210. 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)359/2210. 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~~]]

@@ Line 4: / Line 4: @@
 | 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]]