Say I'm given the notes like this.
How do I determine whether it's already in root, 1st, 3rd, or 7th inversion?
Music: Practice & Theory Stack Exchange is a question and answer site for musicians, students, and enthusiasts. It only takes a minute to sign up.Sign up to join this community
This is an F dominant seventh chord. The inversion is determined entirely by the lowest note, so here it would be first inversion.
How I identified the chord: I recognised F-A-C as an F Major chord. But even if we ignore that, when going up from A (A-C-E♭-F), C (C-E♭-F-A) or E♭ (E♭-F-A-C) we get a major second every time. A chord, by definition, is a stack of thirds, so you have to reorder them until you get rid of the second. (Exception: incomplete chords skip thirds.)
To find out the inversion, we just have to list the notes in the order in which they are all a third apart: F-A-C-E♭. Then we just count these notes, starting at zero:
F-A-C-E♭ 0 1 2 3
And we see A maps to 1 for first inversion.
Your example is an F dominant seventh in 6/5 position (first inversion).
Steps for determining the inversion of a chord: