Say I'm given the notes like this.

enter image description here

How do I determine whether it's already in root, 1st, 3rd, or 7th inversion?


I'm going to disagree with Tim (he removed his answer, in case you are wondering what I am referring to). I think it is safe to assume this is an F dominant seventh (f-a-c-e♭). (I don't know the names for chords with sevenths in English.) To determine which inversion a chord is, one should always look at 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. There are not so many chords with major seconds, so I think the safest assumption is the F dominant seventh. I personally do associate all above inversions with this chord.

As for the lowest note: I already argued this is an F chord. So the root chord would look like this, from low to high (obviously, the root note comes first in the root chord): F-A-C-E♭. Then we just count these notes, starting at zero:

0 1 2 3

And we see A maps to 1 => first inversion. I think this rule that the lowest note determines which inversion a chord is is somewhat counterintuitive, but that is how it is. (You need some rule as soon as there are octaves (or huge intervals) in the chord to be identified.)

  • 2
    F major + minor 7th = F dominant 7th (F7). – Bradd Szonye Jun 19 '14 at 20:14
  • I agree that the note values are A, Eb, C, and F, in ascending order. I agree that these notes construct a dom7 chord (major triad + minor 7th). I would not call it the first inversion because it was not originally in root ascending order; the Eb was out or order. If this was the first inversion, then the Eb and F would be a major 2nd apart. – Kirk A Jun 19 '14 at 20:17

Your example is an F dominant seventh in 6/5 position (first inversion).

Steps for determining the inversion of a chord:

  1. Use your ear to try to detect a particular character (is it major? minor? Tristan chord?)
  2. Write down (or think of) all possible voicings. It often helps to pack the notes into as small an ambitus as possible, and/or to arrange it as a stack of thirds.
  3. Does one of the voicings match the character you detected in step 1? If so, that's the root position, now figure out the inversion (determined solely by which is the lowest note).
  4. If you have multiple good answers or can't determine the character by ear, examine the harmonic context. (Is the chord a massive, imposing feature of the music, or simply a quick way to get from one place to another? The latter type may not have well-defined inversions, as it may contain suspensions or chromatic alterations.) Also consider the spelling of the chord. (In your example, if you had E# instead of F - weird, I know - you'd have Adim(#12) in root position rather than F dominant seventh in first inversion. This issue becomes a lot more relevant when dealing with, for instance, fully diminished seventh chords, which have several equivalent spellings. A convenient tool here is to simply remove all accidentals, changing the notes to naturals, and see if you get a chord you understand.)
  5. If all else fails, try to find any triad within the notes (if multiple triads, the one that sounds the most like the original) and base your analysis on that triad, calling everything else an extraneous addition.

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