For some reason, classical guitarists, more than any other genre of guitar, think of chords in root position. Root position means that the root note (or tonic) of the chord is the lowest pitch of the chord.
An example would be playing E Major and having the E in the bass, the open 6th string. Or playing a C Major chord and having the C in the bass (3rd fret 5th string). These chords would both be in root position. It doesn’t matter how the other notes of the chord are arranged above that low note, it will still be in root position.
Now, let’s say you play that C Major chord again, but this time you don’t play the fifth string and just play from the E note on the fourth string. That would mean that the chord is no longer in root position, because the lowest note is not the root, but rather it is in an inversion. In this case, it would be the first inversion.
The C Major triad has three notes in it. C, E and G. The C as we have discussed, is the root note and the triad is ordered in such a way that the notes are stacked closely together. If the bass note is not the root note, but the next note along, that is called the first inversion. If it is the third note in the triad ( in the case of C Major that would be the G note) it is in second inversion. And, yes, if the chord had four notes there would be the possibility of having a third inversion but after that we usually stop naming the inversions and just say what note is in the bass.
In Level 1, Chords 1 we looked at why it is important to recognize and identify chords in the repertoire. It helps us with sight reading and understanding the larger harmonic movement of a piece. By incorporating inversions we will start to see those harmonies even more clearly because the root note is not always in the bass!
Oh if life were only that simple.
Playing chords in different inversions give them quite a different sound and it is for this reason that a composer might use an inversion. That, and it could provide good voice leading from one chord to the next.
To study this technique in-depth you can take the comprehensive Technique & Musicianship Course Level 2. Over 3 hours of video and more than 20 worksheet downloads will guide you through a structured and focused course of study.