I am learning about neighboring chords (prolongation) and I have hit a speed bump, basically it seems the only tone that needs to be consistent in an inversion of a chord is the root, all the others can be whatever chord tones you want? Can someone verify this or yell at me for being more dumber?
I think you are a bit dazzled about how chords work. Let's take C major for example and work on that one.
The notes are: C,E and G.
If you use the C (root of the chord) as the bass note, you have the chord in root position. It doesn't matter how you place the other notes on top of that, or which ones you duplicate (if you duplicate any).
If you use the E (third of the chord) as the bass note, you have the chord in first inversion. Similarly as before for the notes you stack on top of this note.
Lastly, if you use the G (Fifth of the chord) as the bass note, you have the chord in second inversion. Once again, the way you place the other notes on top of this, doesn't affect the inversion.
If you're asking what I think you're asking, yes it's the bottom note that tells us what inversion a chord is in. The remaining notes may be filled in above in any order, in an open or closed voicing.
Be careful about your use of the term 'root'. It doesn't mean 'the bottom note' when talking about chord inversions.
Not sure what you mean by 'prolongation'?
The root is the chord's main identifier, so yes, it should be there. This is also normally the bass note in the chord.
When coming to inversions, any note can in the bass, in major and minor chords, this can be the 3rd (called 1st inversion) or the 5th (called 2nd inversion). Third inversions is also possible in chords which consist of 4 notes.
Also note, the bass note in an inversion need not to be one of the notes in the chords, it can be any note, except the root