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]] | * [[65/64]] and [[66/65]] | ||
* [[169/168]] and [[176/175]] | * [[169/168]] and [[176/175]] | ||
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== Temperaments == | == 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 | [[Subgroup]]: 2.3.5.7.11.13 | ||
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== Etymology == | == 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 == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
== Notes == | == Notes == | ||
Revision as of 11:33, 5 November 2024
| 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
| [⟨ | 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: 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[1].