Qian's small comma: Difference between revisions

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#redirect [[Qian's small comma]]
{{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
}}
}}
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''' 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.  


==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 />

Latest revision as of 13:49, 20 January 2025

Interval information
Factorization 2485 × 3-306
Monzo [485 -306⟩
Size in cents 1.769735¢
Names Qian's small comma,
sasktel comma,
306-comma
Color name s44w30, lequadsawa 30th
FJS name [math]\displaystyle{ \text{43d30} }[/math]
Special properties reduced,
reduced subharmonic
Tenney height (log2 nd) 969.999
Weil height (log2 max(n, d)) 970
Wilson height (sopfr(nd)) 1888
Comma size unnoticeable
Open this interval in xen-calc

Qian's small comma, also known as the sasktel comma or 306-comma, is an unnoticeable 3-limit comma with a monzo of [485 -306⟩, and a size of 1.7697 cents. It is the difference between 306 just perfect fifths and 179 octaves, in other words 2179/(3/2)306. It is also the amount by which a Pythagorean comma exceeds a stack of six Mercator's commas, or the amount by which a 41-comma exceeds a stack of five Mercator's commas.

Temperaments

This comma is 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[1]. 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[2]. It is unclear how this name was coined.

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
  2. ↑ See Small comma (Revision as of 18:47, 4 July 2011 by Wikispaces>genewardsmith).
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