Qian's large comma: Difference between revisions

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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)<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]]

Revision as of 13:54, 20 January 2025

Interval information
Factorization 2-569 × 3359
Monzo [-569 359⟩
Size in cents 1.845311¢
Names Qian's large comma,
359-comma
FJS name [math]\displaystyle{ \text{51d}{-35} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 1138
Weil norm (log2 max(n, d)) 1138
Wilson norm (sopfr(nd)) 2215
Comma size unnoticeable
Open this interval in xen-calc

Qian's large comma, or the 359-comma, is an unnoticeable 3-limit comma with a monzo of [-569 359⟩ and a size of 1.845 cents. It is the amount by which 359 perfect fifths exceed 210 octaves, in other words (3/2)359/2210. It is also the amount by which a Mercator's comma exceeds a Qian's small comma.

Temperaments

This comma is 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).

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[1]. In Qian's 360-tone tuning, this comma can be described as the interval between Huangzhong (黄钟) and Anyun (安运).

Notes

  1. ↑ Chen Yingshi. "Three Kinds of Tone Difference in 'Qian's 360 temperament'", Journal of Nanjing Arts Institute (Music & Performance), 2009. CNKI (simplified Chinese) archive
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