Is it a good idea to create fomulas for chords and secondary dominants?

[ayumilovexd]

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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

[jancivil]

Well, it seems like the impetus for conceiving it in those terms is located in keeping up with key.
To be honest, none of that does anything for me and it looks like a lot of stuff to think about that isn't crucial at all.

The tried-and-true pedagogy for this is, this is your '2 chord'. Short for 4/2 which is short for 6/4/2, the full figured bass representation of the harmony. The reason for this norm is that figured bass is an apt guide for voice-leading. The 2, the F and G, in, eg., key of C's V7 are pretty much predictably going to turn into a third (with the 5 of the key held as the other parts move).
Compare: The second inversion of I, your 6/4 E and C over the G bass are typically leading you to a 5 and 3, the I triad.
I really do think this area is where your thoughts are better located than to describe an inversion like it's other than the triad it is, as you do in your lingo there. The big reason for a choice of inversion tends to be you want a type of line in the bass. Let's proceed from the I6/4 to the V4/2: bass is G to F, and let's just resolve normally, E... here is a certain quality of line and a certain treatment of tensions that's different than a root position V7 will give.

So there is already formulaic stuff going on with conventional harmonies. Similarly, jazz harmony treatment focuses on 3rd and 7th and how they move to the harmonic goals; eg., 3rd of ii is 7th of V type. IE., our musical sentence is found to have certain loci by dint of the materials.

[jancivil]

...
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

Look, if you're headed to IV your target area has one new feature; rising fourth by circle of 5ths = one more flat. This frankly is something you need to have settled beforehand.

For formula, the 7th of the V/IV classically resolves to the 3rd of IV.
So [from 'key of C'] Bb to A should be second nature.