23: Inverting Triads

Just like we inverted intervals, we can invert chords. But unlike standalone intervals, what inversion a chord is in has a great deal to do with how it comes across, so knowing how to recognize them (and ultimately write with them) is vitally important. You have seen inverted chords before—I just haven’t yet mentioned that I am inverting them.
               Let’s begin, as we always have, looking at something that applies to all chords by looking at the simplest case: triads. Triads, since they have three notes, naturally have 3 possible states they can be in (6 if you count all mathematically possible states, but beyond one condition, we don’t care, so 6 arrangements boils down to 3 that we care about).
               If the root of the chord is in its lowest voice, then the chord is said not to be inverted at all, or to exist in “root position.” It does not matter where the other voices in the chord are. Any chord, so long as the note it’s named after is in the lowest voice, is in “root position.”
               Next, we can, in a sense, flip the root way up and out of the way—moving it up an octave so that it is no longer the lowest note in a chord. If we stack in thirds in root position, then the next note up for candidacy as the bass member is the third of the chord. If this is true, again, irrespective of what any of the other voices are doing, the chord is in what’s known as “first inversion.”
               Finally, among triads, we can have the fifth in the bass. If this is the case—as before, it does not matter what the other voices are doing—then the triad is said to be in “second inversion.” One must be especially careful about where and how these chords are used—so much so that (I haven’t decided exactly how many) at least a few articles will be devoted exclusively to the use of these kinds of chords.
               The quality of the chord—major, minor, augmented, diminished—does not affect this at all. Inversions are counted exactly the same way (that is, exclusively dependent on which of the notes of a triad is in the bass) for any quality type.
               Let’s look at some chords in each inversion, starting here with some in root position. All eight of these, regardless of whatever other shenanigans I wrote into them, are in root position because all eight have a C in their bass and they are C major triads:
A drawing of a rectangular object AI-generated content may be incorrect. 
Likewise, all of the following F major triads are in first inversion since they all have As in their bass voices:
A diagram of a math problem AI-generated content may be incorrect.

And finally, all of the following E major triads are in second inversion given they all have Bs in their bass voices:
A black and white sheet music AI-generated content may be incorrect.

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