Qian's small comma: Difference between revisions

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~~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).

{{Infobox Interval

| Monzo = 485 -306

| Name = Qian's small comma, sasktel comma, 306-comma

| Color name = s44w30, lequadsawa 30th

| Comma = yes

}}

'''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 2179/(3/2)306. 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 ==

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==

[[Category:Commas with unknown etymology]]

[[Category:Commas named after polymaths]]

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-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).
+{{Infobox Interval
+| Monzo = 485 -306
+| Name = Qian's small comma, sasktel comma, 306-comma
+| Color name = s<sup>44</sup>w30, lequadsawa 30th
+| Comma = yes
+}}
+'''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 ==
+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==
+[[Category:Commas with unknown etymology]]
+[[Category:Commas named after polymaths]]
+<references />