My understanding is that standard time signatures, e.g. the common 4/4 come with a definite pattern of dynamics for the beats. E.g. in the case of 4/4, the 1st beat must be the strongest, let's choose forte (f), the 2nd the weakest (i.e. let's choose mezzo piano or mp), the 3rd half-strong (mezzo forte or mf) and the 4th weak (again mp).
But given that a measure of 4/4 can be subdivided in many other ways from the standard one 1/4+1/4+1/4+1/4, e.g. something like 1/8+1/4+1/8+1/2, I wonder what velocity to assign to each of these notes. I agree the first 1/8th note should be forte (f), but what about the second 1/4 note, which plays between the first strong 1/4 and the second weak 1/4? Should that be strong, weak or half-strong? Same questions goes for the other notes in the example partition of the unity measure.
Are there some rules or everything is left to the sensitivity of the player? Can I start a 4/4 measure with an mp or even a p note for the first beat and increase the velocity on the second? If there aren't any rules, what is the purpose of time signatures? My understanding is that a time signature implies a definite dynamics.
As a composer, am I free to choose the velocity of each note as I wish? Standard notation does not provide a simple way to mark the velocity for every single note differently, so I thought there should be some implied patterns for each time signature. Am I right? Please shed a bit of light on this subject, since I am bit confused.