28561/28560: Difference between revisions
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m Text replacement - "[[Square superparticular|S" to "[[S-expression|S" |
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| Ratio = 28561/28560 | | Ratio = 28561/28560 | ||
| Comma = yes | | Comma = yes | ||
| Name = Pisanoisma | |||
| Color name = suquadtho-arugu 1sn | | Color name = suquadtho-arugu 1sn | ||
}} | }} | ||
'''28561/28560''' is an [[Unnoticeable comma|unnoticeable]] [[17-limit]] [[comma]] of about 0.06{{cent}}. | '''28561/28560''' is an [[Unnoticeable comma|unnoticeable]] [[17-limit]] [[comma]] of about 0.06{{cent}}. It is a superparticular with a fourth power as its numerator, in this case 13<sup>4</sup> = 169<sup>2</sup> so that this comma is expressible as [[S-expression|S]]169 and as the difference between [[169/168]] and [[170/169]]. Its denominator decomposes as (13<sup>2</sup> - 1)(13<sup>2</sup> + 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(21<sup>2</sup>). Therefore, this comma has been given the name of the '''pisanoisma''', in reference to Leonardo Pisano, the discoverer of the Fibonacci sequence. | ||
== Commatic relations == | == Commatic relations == | ||
It factors into | It factors into | ||
* [[37180/37179]] and [[123201/123200]] | * [[37180/37179]] and [[123201/123200]] | ||
* [[31213/31212]] and [[336141/336140]] | * [[31213/31212]] and [[336141/336140]] | ||
Latest revision as of 15:54, 21 May 2025
| Interval information |
reduced
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