The Basics of Inversion

Assuming you now know a bit about chords, scales, and the like, it's time to explore inversions. If you think inversions have anything to do with rearranging a group of notes, then you're thinking on the right track. Inversion applies to chords, scales, modes, arpeggios, and any collection of notes, either melodic (played sequentially) or harmonic (played simultaneously).

The question you are asking at this point is probably "and why do I care?" The answer is that inversions allow the creation of music that is more sophisticated and complex. In addition to it being a useful concept to keep in mind for purely intellectual purposes, inversions are behind voice-leading with chords, different voicings of standard chords, and are also paramount for harmonizing (think, for example, a mode and one of its inversions played simultaneously). Want to learn more? Read on.

Part I - What is it?

Quite simply, inversion is the changing of register of a note in a pattern. You want it simpler? To invert a collection of notes, you move one note to a different octave, but keep the note value the same (i.e. move from middle C to the C an octave above). You don't just move any which note to any particular octave. It is done systematically.

For the sake of example, let us consider a Cmaj7 chord. For those of you that aren't too familiar with chords and scales, this would be a good time to brush up. So that we're all on the same page, this particular chord consists of a C in the root, followed by an E, a G, and a B (natural mind you). To make the whole inversion business easier, let us also say that we are in register 4 (so C3, E3, etc.). With each inversion, we will take the current root note, and move it up one octave.

The first inversion of Cmaj7 has the following notes in it: E3, G3, B3, C4.

The second inversion has the following notes: G3, B3, C4, E4.

The third and final possible inversion with this chord contains: B3, C4, E4, G4.

Note that if we were to invert again, we would get the root position Cmaj7 chord again, only one octave up...and we don't really care what octave it's in. It's not considered "inverted."

This same process applies to arpeggios (which after all are just chords played in sequence), modes, and scales.

Part II - Inverting scales (and modes)

The trick about inversion is that it was created around chords. So inverting scales and modes is not quite as straightforward as you think. Instead of simply taking the bottom note of the scale and sending it up to the next octave, inversions are measured in terms of what note is now the first note in the resulting scale.

Perhaps (and only perhaps) it will make it easier to think of a scale as a 13th chord. Remember, this means a chord with scale degrees 1, 3, 5, 7, 9, 11, and 13 (i.e. 7 distinct notes). To make it clear why we are doing this, "invert down" all the notes above 7: 9 becomes 2, 11 becomes 4, and 13 becomes 6. Thus you have 1 to 7. However, it is in the order of the chord's notes that inversions are declared:

An un-inverted scale (or anything for that matter) has the root as the first note.

The "1st" inversion of a scale, arpeggio, chord, etc. has the 3rd as the first note.

The "2nd" inversion always has the 5th as the first note.

Get it? In other words, a third inversion G major scale starts on F# (the 7th), not C (the 4rd). This is an incredibly useful concept for harmonizing lead lines. For example, if three guitars were to play the same sequence of scale degrees, but one was playing a root position scale/mode, and the other two were playing the first and second inversions respectively, you'd have a perfectly harmonized triad lead line!

Part III - Details and the "Slash" notation

Two final thoughts to get you on your way. First, it doesn't matter what the sequence of notes after the first is in a chord when determining it's inversion. I explained how to arrive at an inversion, and how the process of inversion works, but when it comes to the way things are notated, nobody really cares what follows the root. In other words, if a chord is played with the third as the lowest note, it is classified as a first inversion chord. Period.

Why? I'd imagine it's largely because the primary purpose of declaring a specific inversion of chord IN NOTATION is for the purpose of voice leading, usually in the bass line: i.e. the lowest note of the chord. Once that melodic line is in place with a specific note declared as the bass note of the chord, nothing else is really important. Obviously a better guitar player would choose the best chord voicings above the bass note to produce the cleanest, most fitting sequence of chords possible in the context, but it's not imperative to convey the musical line.

That said, when you read fake books or sheet music of any kind, generally speaking you won't see inverted chords referred to by their inversion. Instead, "slash" notation is used. Instead of saying "I want a third inversion G7 chord," the music will instead instruct you to play G with an F in the bass. This is annotated with a slash (hence the name of the notation) like so G/F. Sometimes, depending on who writes the music, it could look like any of the following as well: Gmaj/F, G7/F (redundant), or in a particularly hideous cause you may even see GM/F. Keep in mind it's <chord to play>/<bass note>, not the other way around.

Well that should get you started. Now go write some voice-leading chord progressions or something!