28561/28560

Interval information

Ratio	28561/28560
Factorization	2-4 × 3-1 × 5-1 × 7-1 × 134 × 17-1
Monzo	[-4 -1 -1 -1 0 4 -1⟩
Size in cents	0.06061638¢
Name	Pisanoisma
Color name	suquadtho-arugu 1sn
FJS name	[math]\text{dd1}^{13,13,13,13}_{5,7,17}[/math]
Special properties	square superparticular, reduced
Tenney height (log2 nd)	29.6035
Weil height (log2 max(n, d))	29.6035
Wilson height (sopfr(nd))	92
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.19985 bits
Comma size	unnoticeable
S-expression	S169
open this interval in xen-calc

28561/28560 is an unnoticeable 17-limit comma of about 0.06 ¢. It is a superparticular with a fourth power as its numerator, in this case 13⁴ = 169² so that this comma is expressible as S169 and as the difference between 169/168 and 170/169. Its denominator decomposes as (13² - 1)(13² + 1), which, as 13 is a member of the Fibonacci sequence, by a property of that sequence is equal to 5*8*21*34, the product of the four nearest members of the sequence to 13. This is responsible for the comma belonging to a relatively low prime limit for the size of its numerator and denominator, though the same Fibonacci property also applies to the scintillisma, S441 = S(21²). Therefore, this comma has been given the name of the pisanoisma, in reference to Leonardo Pisano, the discoverer of the Fibonacci sequence.

Commatic relations

It factors into

• 37180/37179 and 123201/123200
• 31213/31212 and 336141/336140