For example say I'm analyzing the piece and I'm using C major as a reference and I realize that the composer plays a dominant chord 3rd inversion
Can I think of the dominant is 5-7-2-4 as well as keeping in mind that 5 is the root note of the dominant chord and 3 is the 7th of the dominant chord? if I want to figure out the 3rd inversion I see that the 7 and the 1 always appear in the same order and it is at the bottom so the shape of dominant chord 3rd inversion is (7(leading )tone-1(root)-3(major third)-5(fifth))*and also keep track of leading, root, maj 3 and fifth for all inversions
I can do this with secondary dominants as well like the V/IV is 1-3-5-b7. This way if I know the scale degree by heart, I can easily find my way through the key
I can also do it like this, were going to take the same chord. I can think of the dominant of as a change in key, so instead of thinking in C major, I think of G major 7th 1-3-5-b7 instead of 5-7-2-b4 but that means I have to have already memorize the scale degree of D major as well as all the other scales.
for now since I want to know the patterns after i memorize the scale degrees of the scales I can immediately apply the patterns in that scale
let me know if you guys need more clarification