1521/1520

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]\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
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.2112 bits
Comma size	unnoticeable
S-expression	S39
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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:

• 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

It factors into the following superparticular pairs:

• 2376/2375 and 4225/4224
• 1729/1728 and 12636/12635
• 1716/1715 and 13377/13376
• 1701/1700 and 14365/14364
• 1540/1539 and 123201/123200

* 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

• Unnoticeable comma
• List of superparticular intervals