The Smallest music note you'll likely see on sheet music is the 16th note.
2 connected 16th notes: Image
What if we went even further down the line of faster notes?
Planck time is defined as the time it takes for light to travel 1 Planck distance (L) or sec.
There are more units of planck time in a second than there are seconds since the big bang: image
I'll assume one half note is equal to 1 second, and that each further note takes half the time to play as the last. With this in mind I
get the equation:
That's a th note. Imagine a note with 144 flags on it!!!
a 64th note with 4 flags: image
We can go smaller and faster but it would make no difference since the human brain won't be able to determine beats faster than around a 32nd note.