1521/1520: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Icon =
| Name = pinkanberry
| Ratio = 1521/1520
| Color name = 19u3oog1, nuthothogu 1sn
| Monzo = -4 2 -1 0 0 2 0 -1
| Comma = yes
| Cents = 1.1386
| Name = pinkanberry comma
| Color name = 19u3oog1, nuthothogu unison
| Sound =  
}}
}}


'''1521/1520''', the '''pinkanberry comma''', is a [[19-limit]] unnoticeable comma and [[Essential tempering commas|essential tempering comma]], specifically of the 2.3.5.13.19 subgroup. Among other things, it is the difference between [[20/19]] and a stack of two [[40/39]]<nowiki/>s, as well as the difference between two other essential tempering commas, [[676/675]] and [[1216/1215]].  
'''1521/1520''', the '''pinkanberry''', is an [[unnoticeable comma|unnoticeable]] [[19-limit]] (also 2.3.5.13.19 [[subgroup]]) [[comma]] and [[19-odd-limit]] [[essential tempering comma]]. It is the amount by which a stack consisting of [[13/10]] and [[9/8]] exceeds [[19/13]]. It is also the difference between [[39/38]] and [[40/39]], as well as other relations detailed in the next section.  


It is named for the fact that the latter two commas define [[The Archipelago#Pinkan|pinkan]] temperament, making the tempering of 1521/1520 its most prominent "fruit", and thus tempering it out enables the '''pinkanberry chords'''. EDOs that support these include {{EDOs| 24, 27, 53, 77, 84, 111, 130, 137, 164, 190, 217, 243, 270, 323, 407, 460, and 513.}}
== Commatic relations ==
This comma is the difference between the following superparticular pairs:
* [[153/152]] and [[170/169]]
* [[169/168]] and [[190/189]]
* [[351/350]] and [[456/455]]
* [[676/675]] and [[1216/1215]] *
* [[936/935]] and [[2432/2431]]
* [[1001/1000]] and [[2926/2925]]
* [[1331/1330]] and [[10648/10647]]
* [[1445/1444]] and [[28900/28899]]


==See also==
It factors into the following superparticular pairs:
*[[Unnoticeable comma]]
* [[2376/2375]] and [[4225/4224]]
*[[List of superparticular intervals]]
* [[1729/1728]] and [[12636/12635]]
* [[1716/1715]] and [[13377/13376]]
* [[1701/1700]] and [[14365/14364]]
* [[1540/1539]] and [[123201/123200]]
 
<nowiki>*</nowiki> relation within the 2.3.5.13.19 subgroup
 
== Temperaments ==
Tempering out this comma enables [[pinkanberry chords]], and EDOs that support these include {{Optimal ET sequence| 24, 27, 53, 77, 80, 84, 104c, 111, 130, 137, 140, 164, 190, 217, 243, 270, 323, 407, 460, and 513 }}.
 
== Etymology ==
This comma is named for the fact that tempering out both 676/675 and 1216/1215 defines the [[The Archipelago #Pinkan|pinkan]] temperament, making the tempering of 1521/1520 its most prominent "fruit".
 
== See also ==
* [[Unnoticeable comma]]
* [[List of superparticular intervals]]


[[Category:19-limit]]
[[Category:Superparticular]]
[[Category:Unnoticeable comma]]
[[Category:Pinkanberry]]
[[Category:Pinkanberry]]
[[Category:Commas named for other reasons]]

Latest revision as of 10:38, 23 February 2025

Interval information
Ratio 1521/1520
Factorization 2-4 × 32 × 5-1 × 132 × 19-1
Monzo [-4 2 -1 0 0 2 0 -1⟩
Size in cents 1.138595¢
Name pinkanberry
Color name 19u3oog1, nuthothogu 1sn
FJS name [math]\displaystyle{ \text{d1}^{13,13}_{5,19} }[/math]
Special properties square superparticular,
reduced
Tenney height (log2 nd) 21.1407
Weil height (log2 max(n, d)) 21.1416
Wilson height (sopfr(nd)) 64
Comma size unnoticeable
S-expression S39
Open this interval in xen-calc

1521/1520, the pinkanberry, is an unnoticeable 19-limit (also 2.3.5.13.19 subgroup) comma and 19-odd-limit essential tempering comma. It is the amount by which a stack consisting of 13/10 and 9/8 exceeds 19/13. It is also the difference between 39/38 and 40/39, as well as other relations detailed in the next section.

Commatic relations

This comma is the difference between the following superparticular pairs:

It factors into the following superparticular pairs:

* relation within the 2.3.5.13.19 subgroup

Temperaments

Tempering out this comma enables pinkanberry chords, and EDOs that support these include 24, 27, 53, 77, 80, 84, 104c, 111, 130, 137, 140, 164, 190, 217, 243, 270, 323, 407, 460, and 513.

Etymology

This comma is named for the fact that tempering out both 676/675 and 1216/1215 defines the pinkan temperament, making the tempering of 1521/1520 its most prominent "fruit".

See also

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