4225/4224: Difference between revisions

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'''4225/4224''', the '''leprechaun comma''', is an unnoticeable [[13-limit]] [[superparticular]] interval. This comma is the difference between the following pairs:

'''4225/4224''', the '''leprechaun comma''', is an [[unnoticeable comma|unnoticeable]] [[13-limit]] [[superparticular]] interval. This [[comma]] is the difference between the following pairs:

* [[65/64]] and [[66/65]]

* [[169/168]] and [[176/175]]

* [[325/324]] and [[352/351]]

* [[385/384]] and [[847/845]]

* [[2080/2079]] and [[4096/4095]]

* [[3025/3024]] and [[10648/10647]]

It factors into [[4375/4374]] and [[123201/123200]].

== Temperaments ==

Tempering out this comma in the full 13-limit leads to the rank-5 '''leprechaun temperament'''. It is also tempered out in lower-rank temperaments including [[abigail]], [[newt]], [[decoid]], [[donar]], etc. Tempering it out also splits the [[33/32]] Alpharabian quarter-tone in two, each part corresponding to 65/64 and 66/65. You may find a list of good equal temperaments that support this temperament below.

[[Tempering out]] this comma in the full 13-limit leads to the rank-5 '''leprechaun temperament'''. It is also tempered out in lower-rank temperaments including [[abigail]], [[newt]], [[decoid]], [[donar]], etc. Tempering it out also splits the [[33/32]] Alpharabian quarter-tone in two, each part corresponding to 65/64 and 66/65. You may find a list of good equal temperaments that support this temperament below.

[[Subgroup]]: 2.3.5.7.11.13

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: mapping generators: ~2, ~3, ~5, ~7, ~65/48

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.0205{{c}}, ~3/2 = 701.9418{{c}}, ~5/4 = 386.2411{{c}}, ~7/4 = 968.7849{{c}}, ~65/48 = 524.6851{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9442{{c}}, ~5/4 = 386.2465{{c}}, ~7/4 = 968.7910{{c}}, ~65/48 = 524.6866{{c}}

{{Optimal ET sequence|legend=1| 41, 46, 53, 80, 87, 103, 121, 130, 183, 190, 217, 224, 270, 494, 684, 764, 935, 954, 1178, 1308, 1448, 1578, 1889, 2756, 2843, 3337, 4421f, 4915f, 7758cff, 10514cdff }}

[[Badness]] (Sintel): 0.244

== Etymology ==

~~The leprechaun~~ comma was named by [[Margo Schulter]] in 2012<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105598.html Yahoo! Tuning List | ''EDO alternatives, Leprechaun comma (4225/4224)'']</ref>~~. It was named as a tribute to [[George Secor]]’s 2002 short story ''A Bit O’ Blarney''~~.

This comma was named by [[Margo Schulter]] in 2012 as a tribute to [[George Secor]]’s 2002 short story ''A Bit O' Blarney''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105598.html Yahoo! Tuning List | ''EDO alternatives, Leprechaun comma (4225/4224)'']</ref>.

== See also ==

* [[List of superparticular intervals]]

* [[Unnoticeable comma]]

== ~~Notes~~ ==

== References ==

[[Category:Leprechaun]]

[[Category:Commas named ~~for other reasons~~]]

[[Category:Commas named after mythology or literature]]

@@ Line 4: / Line 4: @@
 | Comma = yes
 }}
-'''4225/4224''', the '''leprechaun comma''', is an unnoticeable [[13-limit]] [[superparticular]] interval. This comma is the difference between the following pairs:
+'''4225/4224''', the '''leprechaun comma''', is an [[unnoticeable comma|unnoticeable]] [[13-limit]] [[superparticular]] interval. This [[comma]] is the difference between the following pairs:
 * [[65/64]] and [[66/65]]
 * [[169/168]] and [[176/175]]
 * [[325/324]] and [[352/351]]
+* [[385/384]] and [[847/845]]
 * [[2080/2079]] and [[4096/4095]]
 * [[3025/3024]] and [[10648/10647]]
 It factors into [[4375/4374]] and [[123201/123200]].
 == Temperaments ==
-Tempering out this comma in the full 13-limit leads to the rank-5 '''leprechaun temperament'''. It is also tempered out in lower-rank temperaments including [[abigail]], [[newt]], [[decoid]], [[donar]], etc. Tempering it out also splits the [[33/32]] Alpharabian quarter-tone in two, each part corresponding to 65/64 and 66/65. You may find a list of good equal temperaments that support this temperament below.
+[[Tempering out]] this comma in the full 13-limit leads to the rank-5 '''leprechaun temperament'''. It is also tempered out in lower-rank temperaments including [[abigail]], [[newt]], [[decoid]], [[donar]], etc. Tempering it out also splits the [[33/32]] Alpharabian quarter-tone in two, each part corresponding to 65/64 and 66/65. You may find a list of good equal temperaments that support this temperament below.
 [[Subgroup]]: 2.3.5.7.11.13
@@ Line 32: / Line 33: @@
 |}
 : mapping generators: ~2, ~3, ~5, ~7, ~65/48
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0205{{c}}, ~3/2 = 701.9418{{c}}, ~5/4 = 386.2411{{c}}, ~7/4 = 968.7849{{c}}, ~65/48 = 524.6851{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9442{{c}}, ~5/4 = 386.2465{{c}}, ~7/4 = 968.7910{{c}}, ~65/48 = 524.6866{{c}}
 {{Optimal ET sequence|legend=1| 41, 46, 53, 80, 87, 103, 121, 130, 183, 190, 217, 224, 270, 494, 684, 764, 935, 954, 1178, 1308, 1448, 1578, 1889, 2756, 2843, 3337, 4421f, 4915f, 7758cff, 10514cdff }}
+[[Badness]] (Sintel): 0.244
 == Etymology ==
-The leprechaun comma was named by [[Margo Schulter]] in 2012<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105598.html Yahoo! Tuning List | ''EDO alternatives, Leprechaun comma (4225/4224)'']</ref>. It was named as a tribute to [[George Secor]]’s 2002 short story ''A Bit O’ Blarney''.
+This comma was named by [[Margo Schulter]] in 2012 as a tribute to [[George Secor]]’s 2002 short story ''A Bit O' Blarney''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105598.html Yahoo! Tuning List | ''EDO alternatives, Leprechaun comma (4225/4224)'']</ref>.
 == See also ==
 * [[List of superparticular intervals]]
-* [[Unnoticeable comma]]
-== Notes ==
+== References ==
 [[Category:Leprechaun]]
-[[Category:Commas named for other reasons]]
+[[Category:Commas named after mythology or literature]]