4225/4224: Difference between revisions

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{{Infobox Interval

~~| Ratio = 4225/4224~~

~~| Monzo = -7 -1 2 0 -1 2~~

~~| Cents = 0.40981~~

| Name = leprechaun comma

| Color name =

| Color name = 3oo1uyy1, thotholuyoyo unison

| ~~FJS name~~ =

| Comma = yes

}}

'''4225/4224''', the '''leprechaun comma''', is an unnoticeable [[13-limit]] [[superparticular]] interval. It 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]]

Line 13:

Line 10:

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

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

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

== Temperaments ==

Tempering it out 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 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 it out also splits the~~ [[33/32]] ~~Alpharabian quarter-tone~~ in ~~two~~, ~~each part corresponding to 65~~/~~64 and 66~~/65.

[[Subgroup]]: 2.3.5.7.11.13

[[Mapping]]: <br>

{| class="right-all"

|-

| [⟨ || 1 || 0 || 0 || 0 || 1 || 4 || ],

|-

| ⟨ || 0 || 1 || 0 || 0 || 1 || 1 || ],

|-

| ⟨ || 0 || 0 || 1 || 0 || 0 || -1 || ],

|-

| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || ],

|-

| ⟨ || 0 || 0 || 0 || 0 || 2 || 1 || ]]

|}

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

{{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 }}

== Etymology ==

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]]

~~[[Category:13-limit]]~~

== Notes ==

~~[[Category:Unnoticeable commas]]~~

~~[[Category:Superparticular]]~~

[[Category:Leprechaun]]

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

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 4225/4224
-| Monzo = -7 -1 2 0 -1 2
-| Cents = 0.40981
 | Name = leprechaun comma
-| Color name =
+| Color name = 3oo1uyy1, thotholuyoyo unison
-| FJS name =
+| Comma = yes
 }}
-'''4225/4224''', the '''leprechaun comma''', is an unnoticeable [[13-limit]] [[superparticular]] interval. It 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]]
@@ Line 13: / Line 10: @@
 * [[2080/2079]] and [[4096/4095]]
 * [[3025/3024]] and [[10648/10647]]
+It factors into [[4375/4374]] and [[123201/123200]].
 == Temperaments ==
-Tempering it out 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 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 it out also splits the [[33/32]] Alpharabian quarter-tone in two, each part corresponding to 65/64 and 66/65.
+[[Subgroup]]: 2.3.5.7.11.13
+[[Mapping]]: <br>
+{| class="right-all"
+|-
+| [⟨ || 1 || 0 || 0 || 0 || 1 || 4 || ],
+|-
+| ⟨ || 0 || 1 || 0 || 0 || 1 || 1 || ],
+|-
+| ⟨ || 0 || 0 || 1 || 0 || 0 || -1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 2 || 1 || ]]
+|}
+: mapping generators: ~2, ~3, ~5, ~7, ~65/48
+{{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 }}
+== Etymology ==
+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]]
-[[Category:13-limit]]
+== Notes ==
-[[Category:Unnoticeable commas]]
-[[Category:Superparticular]]
 [[Category:Leprechaun]]
+[[Category:Commas named after mythology or literature]]