4225/4224: Difference between revisions
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'''4225/4224''', the '''leprechaun comma''', is an unnoticeable [[13-limit]] [[superparticular]] interval. | '''4225/4224''', the '''leprechaun comma''', is an unnoticeable [[13-limit]] [[superparticular]] interval. This comma is the difference between the following pairs: | ||
* [[65/64]] and [[66/65]] | * [[65/64]] and [[66/65]] | ||
* [[169/168]] and [[176/175]] | * [[169/168]] and [[176/175]] | ||
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* [[2080/2079]] and [[4096/4095]] | * [[2080/2079]] and [[4096/4095]] | ||
* [[3025/3024]] and [[10648/10647]] | * [[3025/3024]] and [[10648/10647]] | ||
It factors into [[4375/4374]] and [[123201/123200]]. | |||
== Temperaments == | == Temperaments == | ||
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{{Val list|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 }} | {{Val list|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 == | |||
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>. | |||
== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
* [[Unnoticeable comma]] | * [[Unnoticeable comma]] | ||
== Notes == | |||
[[Category:Leprechaun]] | [[Category:Leprechaun]] | ||
Revision as of 11:42, 8 March 2023
| Interval information |
reduced
4225/4224, the leprechaun comma, is an 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.
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:
[⟨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
Etymology
The leprechaun comma was named by Margo Schulter in 2012[1].