I don't believe that multiplying the clock is totally straightforward, tho I believe people have found workarounds (there also appear to be some future operators brewing on a few threads which might aid this). Regarding clock division, you could in a line or 2 assign a variable to count to say 4 and only trigger script a script if the variable is 1.
As I write this, I'm realizing I've spent much of my time triggering teletype from external boxes where most of this kind of division or sequencing is handled by the other units. I'm inclined to say the trilogy or ansible modules are probably a little more straightforward for divisions (meadowphysics) or grid based step sequencing (WW), but the openendness of teletype could surely lend itself to some neat controlled or chaotic clocking systems.
That being said TT seems like a game of maximizing patterns/variables/scripts/commands/outputs in a way which is most valuable to you and I'm sure complex clocking scripts would be a cool use of TT's powers