All the elements you mentioned can be easily considered as variables that change based on each other. Yes, you can have the same beat for a song or you can have two different BPM, but other elements will change as you modify or increase the BPM. If you try to keep one value and change another, then the result won't be what you expect. For music and notes including beats, everything must be in a "symmetry" or you'll end with a totally different track.
For example, if you change tempo in a song, then other variables will change as well.