Inversion
An inversion is the same chord with its notes stacked in another order, so that a note other than the root is at the bottom. The C major triad C–E–G inverted becomes E–G–C or G–C–E.
A triad has three positions. Root position: the root at the bottom – C, E, G. Move the C up an octave: E, G, C. That is the first inversion, or sixth chord, because from the bottom E to the top C is a sixth. Move the E up as well: G, C, E. That is the second inversion, or six-four chord: from G to C is a fourth, from G to E a sixth.
The bottom note tells you which position it is: C, E or G. On the staff, in root position the notes sit tight – three lines or three spaces in a row. In an inversion a wider gap opens between two of the notes.
Why invert chords at all? So the hand does not have to jump. In the progression C–F–G in root positions the hand moves a lot; with inversions – C–E–G, C–F–A, B–D–G – the fingers shift by a key or two, and the chords join more smoothly.
What it sounds like
All three positions are the same chord, so they sound alike. Root position sounds the most solid; the inversions sound lighter and brighter, because the root is not at the bottom.
Where it is taught: the studio’s interactive textbook, chapter 11, “Triad inversions and the dominant seventh”.