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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

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You seem to be overthinking all of it!

The way I look at this is that each chord has its own dominant 7th, which is the dominant of that chord - the V of the chord I. So, looking at, say, Amaj. The dominant is going to be E7 (having only notes that belong to A).

The big difference with V7 chords is that they contain a note which is not in their own key. It's the b7, which needs to be flattened from its own key in order to make it a dominant 7th.

Example - in C. Dominant of C > G7. G B D F all notes belonging to key C. When Cdom7 arrives, it has the notes belonging to F: C E G Bb. I only ever think 1,3,5,b7 of the chord itself, because the rest is irrelevant. If I start thinking 5,7,2,4, I just mess up. Stick with the root of the chord in question as being called 1. Otherwise, you'll likely get number-bound.

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    " Stick with the root of the chord in question as being called 1." - the other historical option was to call the bass note of the chord 1. That gave 7-5-3 for root position, 6-5-3 for first inversion, 6-4-3 for second, and 6-4-2 for third. Figured bass notation conventionally abbreviated those to 7, 6-5, 4-3, and 4-2. if the OP wants "a system based on intervals," he/she might as well learn something that some musicians still actually use, and is included in some advanced music theory exams - e.g. ABRSM. – user19146 Jul 22 '17 at 22:02
  • @alephzero - yes, that works for some, though I have never found use for it. I think the OP is already confused, so I tried to simplify the situation. Using figured bass at the OP's level may cause explosion of the brain! Perhaps save figured bass till it's needed in an advanced theory exam? – Tim Jul 23 '17 at 5:26
  • In my Royal Conservatory of Music Harmony lessons, inversions like V 4/3 were introduced in Grade 3 Harmony (above Grade 2 Theory, but Grade 2 Theory still taught pretty basic stuff). At least according to RCM, figured bass is not an "advanced theory" concept--maybe intermediate at most. – Dekkadeci Aug 11 '17 at 13:51

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