Say a 555 is set up in astable mode such as this:

The frequency of that, with control voltage at the standard 2/3 V, is this:

Now, what if the control voltage isn't 2/3V? What would the new frequency formula be?

TIA!

 

The datasheet shows that the frequency changes and the duty-cycle of the output pulses also changes. It is called Pulse-Position-Modulation.

There is no formula but you might be able to figure it out.

 

It is pure RC math, available in every text book. Since Pin 5 is connected to the voltage set points you can easily vary off the 2/3 setup point.

It is a function of natural logs, which you know since you showed an atypical formula for this oscillator.