1521/1520
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Ratio | 1521/1520 |
Factorization | 2^{-4} × 3^{2} × 5^{-1} × 13^{2} × 19^{-1} |
Monzo | [-4 2 -1 0 0 2 0 -1⟩ |
Size in cents | 1.1385953¢ |
Name | pinkanberry |
Color name | 19u3oog1, nuthothogu 1sn |
FJS name | [math]\text{d1}^{13,13}_{5,19}[/math] |
Special properties | square superparticular, reduced |
Tenney height (log_{2} nd) | 21.1407 |
Weil height (log_{2} 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 |
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 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 (both of these commas are also within the 2.3.5.13.19 subgroup, while most others listed here are not)
- 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
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".