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'''4225/4224''', the '''leprechaun comma''', is an unnoticeable 13-limit superparticular interval. | {{Infobox Interval | ||
| Name = leprechaun comma | |||
| Color name = 3oo1uyy1, thotholuyoyo unison | |||
| Comma = yes | |||
}} | |||
'''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]] | |||
* [[2080/2079]] and [[4096/4095]] | |||
* [[3025/3024]] and [[10648/10647]] | |||
== | It factors into [[4375/4374]] and [[123201/123200]]. | ||
It is | |||
== 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. | |||
[[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]] | |||
== Notes == | |||
[[Category:Leprechaun]] | |||
[[Category:Commas named after mythology or literature]] | |||