Inverting Intervals and Chords

To invert an interval, you take an interval and switch the order of the notes. In other words, if you have a low note and a high note, you can take the low note and play it an octave higher, and it will now be the high note.

Doing this introduces a large number of very interesting relationships. Let’s start with an example using the C major scale. Below, the C major scale is diagrammed, highlighting the E (a Major 3rd).

C to E is a third, and seeing as we are using the major scale, it is more specifically a major third. But what happens when we play E to C? We get a minor sixth in that case.

All major thirds become minor sixths. In fact, all intervals have a kind of partner. This partner is the interval that results from an inversion.

All Major intervals, when inverted, become minor. Similarly, all minor intervals when inverted become Major.

All perfect intervals remain perfect when inverted.

All Augmented intervals, when inverted, become diminished. Similarly, all diminished intervals when inverted become Augmented.

All 2nds, when inverted, become 7ths. Similarly, all 7ths when inverted become 2nds.

All 3rds, when inverted, become 6ths. Similarly, all 6ths when inverted become 3rds.

All 4ths, when inverted, become 5ths. Similarly, all 5ths when inverted become 4ths.

Ones become octaves, twos become sevens, threes become sixes, and fours become fives. It is very important to remember that these inversions work both ways. In other words, sixes become threes, fives become fours and so forth. Major will always become minor, and vice versa. Perfect will stay the same. Diminished will become augmented, and vice versa.

First, let's invert a perfect 5th from A.

Let's invert a 5th from G.

Let's invert a 2nd from F.

Let's invert a 2nd from B.

Before we go in depth, however, we must examine something called figured bass. Figured bass is an extension to the Roman numerals that you’ve already encountered.

Here is an example of figured bass: i6. This would represent an inverted one chord in minor. But what does the number six really mean? It means that there is an interval of a sixth above the bass note.

The bass note is the lowest sounding note of the chord. Let’s look at a basic one chord in the key of E minor, then look at a one chord in first inversion. The root note will be colored red.

There is an interval of a sixth above the bass note, which in this case is a G. This inversion is called first inversion.

For the sake of space, notice that this diagram STARTS on the fifth scale degree. This is for presentation only.

Chapter nine is going to describe types of chords that you have not yet encountered. One of these is the seventh chord. The seventh chord is comprised of four notes. Chords that have four notes can be inverted one more time yet.

Below you will find a diagram of a seventh chord in root position, the noninverted form, as well as third inversion.

Third inversion can be written as i6/4/2, or abbreviated as i2. Also note that first and second inversion will have different numbers involved if a seventh is in the chord. They go as follows: i6/5/3 for first inversion, and i6/4/3 for second inversion. Don’t worry about doing an exercise for this one yet; you’ll have plenty of opportunity to try this inversion in the chapters to come.