4225/4224: Difference between revisions

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Created page with "'''4225/4224''', the '''leprechaun comma''', is an unnoticeable 13-limit superparticular interval. == Theory == It is targeted in the abigail, newt, decoid, and donar tempera..."
 
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'''4225/4224''', the '''leprechaun comma''', is an unnoticeable 13-limit superparticular interval.
{{Infobox Interval
| Ratio = 4225/4224
| Monzo = -7 -1 2 0 -1 2
| Cents = 0.40981
| Name = leprechaun comma
| Color name =
| FJS name =
}}
'''4225/4224''', the '''leprechaun comma''', is an unnoticeable [[13-limit]] [[superparticular]] interval. It 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]]


== Theory ==
== Temperaments ==
It is targeted in the abigail, newt, decoid, and donar 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.
 
== See also ==
* [[List of superparticular intervals]]
* [[Unnoticeable comma]]
 
[[Category:13-limit]]
[[Category:Unnoticeable comma]]
[[Category:Superparticular]]
[[Category:Leprechaun]]

Revision as of 12:41, 15 February 2022

Interval information
Ratio 4225/4224
Factorization 2-7 × 3-1 × 52 × 11-1 × 132
Monzo [-7 -1 2 0 -1 2
Size in cents 0.409808¢
Name leprechaun comma
FJS name [math]\displaystyle{ \text{P1}^{5,5,13,13}_{11} }[/math]
Special properties square superparticular,
reduced
Tenney height (log2 nd) 24.0891
Weil height (log2 max(n, d)) 24.0895
Wilson height (sopfr(nd)) 64
Open this interval in xen-calc

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

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.

See also