Intervals and Inversions

Before we dive into the rest of the intervals, we need to talk about a special relationship that exists between pairs of intervals. In the last post we looked at fourths, fifths and the tri-tone. Fourths and fifths are related to each other as inversions. The tri-tone is an inversion of itself (does that blow your mind?) Let’s see what that really means.

Let’s start with our handy-dandy A major scale chart:

A major scale

A major scale

The fourth above A is D. Now let’s look at a D major scale chart:

D major scale

D major scale

The fifth degree of the D major scale is A. Look at that? It’s the same two notes, but depending on which one is the root, we give it a different name. This relationship is what we call an inversion. Inversions aren’t just a little bit of mathematical trivia.

Inversions also share a similar sonic quality. Remember when we talked about consonance and dissonance? Fourths and fifths have very similar characteristics. They both sound pretty rocking on a distorted guitar because they have the same sonic qualities.

Let’s see how this inversion looks on the fretboard. Here’s the process of inverting a fifth to a fourth:

Inverting a fifth to a fourth

Inverting a fifth to a fourth

Here’s the process of going the other way:

Inverting a fourth into a fifth

Inverting a fourth into a fifth

Magic!

Now what about a tri-tone? Let’s look at it on the fretboard. Here’s the process of inverting a tri-tone:

Inverting a tri-tone

Inverting a tri-tone

Whaaa? Exactly. An inverted tri-tone results in another tri-tone. Crazy, huh?

Let’s think about this mathematically in terms of steps and frets. A tri-tone is 3 steps, or 6 frets. The chromatic scale has a total of 6 steps, or 12 frets. The tri-tone is exactly half of the chromatic scale.

As we dive into the other intervals, we’ll look further at the inversion relationships between them. Without giving too much away, here’s another way to think about inversions and intervals:

Inversion chart

Inversion chart

Since we’ve only looked at fourths, fifths and tri-tones, I’m keeping this little picture intentionally…uh…vague. Just get these points into your head:

  • Fourths and fifths are inversions of each other
  • A tri-tone is an inversion of another tri-tone

This stuff is important to understand. If you’ve looked at this for a while and it still doesn’t make sense, consider taking a very long walk and pondering this. You may have a “moment of zen” when it all connects.

Mastering inversions will help you really understand what’s going on in your music in terms of music theory. You’ll be able to give names to things you play and hear. This helps you communicate with other musicians. Inversions are also a crucial tool in breaking down the fretboard into more manageable chunks.

Next time, we’ll dive into thirds and sixths. Until then, keep rocking!