Qian's small comma: Difference between revisions

(3 intermediate revisions by 2 users not shown)

Line 1:

{{Infobox Interval

| Monzo = 485 -306

| Name = sasktel comma

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

| Color name = s44w30, lequadsawa 30th

| 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 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 ==

~~''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~~.

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.

== Notes ==

''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]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | Monzo = 485 -306
-| Name = sasktel comma
+| Name = Qian's small comma, sasktel comma, 306-comma
 | Color name = s<sup>44</sup>w30, lequadsawa 30th
 | 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.
+== 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 ==
-''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.
+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.
-== Notes ==
+''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 />