Inversions

What an inversion is

A triad has three notes, and any of them can lie at the bottom. With the root at the bottom it is called root position; move the root up an octave and you have the first inversion, once more and the second. It is always the same three notes — only in a different order.

What it is for

The usual explanation says what happens. More interesting is what for. Here is I–V–vi–IV in C major, once in root positions throughout and once with the nearest inversion each time. Underneath is how far the fingers move, counted in semitones.

All in root position

37 semitones of movement

With inversions

9 semitones of movement

That is the whole reason. Not every progression gets shorter — where the bass already walks down step by step, root positions are already the shortest path. But for the common four-chord loops it saves the jumping, and that is exactly why every pianist plays them this way.