FizzBuzz, and the 3:5 Polyrhythm

There's this old children's game meant to teach kids about division, called FizzBuzz; It's quite simple. You audibly count upwards, and if a number is divisible by 3, you say "Fizz" instead of the number. If it's divisible by 5, you say "Buzz". If divisible by both, you say "FizzBuzz". A round could look like this:

1, 2, Fizz, 4, Buzz, Fizz, 7, 8, Fizz, Buzz, 11, Fizz, 13, 14, FizzBuzz.

A week ago, in a random free period in school, I was trying to play a 3:5 polyrhythm. Then, I remembered Fizz Buzz; A while back, in an English Lesson a year ago, I found out that a polyrhythm of x : y could be written as a "number line" of the length: (x and y's LCM), where you could note down (LCM / x = y's interval) or (LCM / y = x's interval) for each hit. For example, a 2:3 polyrhythm looks like this:

x     x     x   | 6 / 3 = Every 2 "ticks"

-  -  -  -  -  - |

o        o       | 6 / 2 = Every 3 "ticks

Coming back to the free period, I realised that this is just a really complicated game of FizzBuzz! Take the 3:5 polyrhythm as example

x           x          x          x               x              | x represents the hits for 3, or Fizz

0  1  2  3  4  5  6  7  8  9  10  11  12  13  14 |

o                  o                   o                          | o represents the hits for 5, or Buzz

This is the FizzBuzz pattern!!! It just loops at the end! This is FizzBuzz mod 15!!!!!!!

--- (FB) 1 2 F 4 B F 7 8 F B 11 F 13 14 --- mod(15)

Isn't it crazy??? I think it's crazy!!

In this regard, a 3:5 polyrhythm (And to a larger extent, all polyrhythms) can be thought of as an altered version of FizzBuzz!

This also lends itself to a neat discovery about FizzBuzz; The pattern just repeats over and over again after 15. I'm not sure what I expected. It makes complete sense. Basic prime factorization. But I think its neat to see this come to fruition unexpectedly, as opposed to in an assigned task or in a lesson.

Idk! It's not important knowledge, but it's cool. A little intersection between Computer Science, Music, and Obscure Children's Games. If you have any comments on this, I'd love to hear