No one has yet found the mathematical formulae to predict the tides.

What we use these days is a computed transformation of the Doogson gearbox that incorporates a value for all the astronomical phenomena that go into making such a prediction. The numerical values are not yet known. (One wonders what Einstien wasted his time on when there was something useful he might have worked on.)

The value of these influences varies from place to place. In the UK for instance you can work out the local tide if you know the predictions for anywhere else on the coast merely adding or subtracting the time it takes for the pulse to travel around the coast.

Where this pulse meets at the Solent in the middle of the English Channel there is a double high tide and double low.

Sometimes the constant can be worked out from one port to another in different countries.

It's mostly based on observation. To answer your question, the phase and the apse are involved in the "calculations." Some other things are the distance to the sun and the declinations of both the sun and moon.