Interval Inversions and Compound Intervals

Introduction

In this article, we'll further our understanding of intervals by learning about how to expand out past an octave, as well as learning how to manipulate intervals.

What is an interval inversion?

First, consider the following interval.

The answer is a minor sixth. Why? Well, B to G is a sixth, and G shows up in the key of B minor.

Now, what would happen if we kept the same notes, but instead put the B on top? Well, we get this interval.

If you said a major third, that's right! It's because in G major, B appears as the third note. Thus, this is a major third.

The operation we just performed is called an interval inversion. In other words, we simply inverted how the interval is written. Another way of thinking about it is that we simply divided the octave between the lower and upper B by inserting a G. This created two smaller intervals, a minor 6th and a major 3rd.

So, what else can we learn about interval inversions from this example? Well, we see that the sum of the size of the two intervals we generated is nine (6 + 3). This will always be true! Additionally, we saw that the minor interval, when inverted, became a major interval, and vice versa. This is also always true!

What would happen for diminished intervals? How about perfect intervals?

If you guessed that diminished intervals invert to augmented ones, and vice versa, you'd be right! And perfect intervals stay the same.

Come up with two examples that exemplify these rules to be true.

Answer: For example, we could invert a diminished 7th (enharmonic to a major sixth) to become an augmented 2nd (enharmonic to a minor third), and vice versa. We could also invert a perfect fifth to become a perfect fourth.

Compound intervals

Up until now, we have only focused on intervals smaller than (or equal to) an octave. We call these simple intervals. But in reality, while these are the most common, there are actually an infinite number of intervals. Why? Well, intervals can be larger than the octave of course! If we add an octave to a simple interval, we get a corresponding larger interval called a compound interval.

For example, consider the major third above, reprinted below in treble clef.

Now, what would happen if we added an octave between the two notes? We'd get this:

These two intervals contain the same pitches, it's just that one pitch is sounding in a different octave between the two intervals. Thus, these two intervals, one simple, and the other its corresponding compound interval, sound similar.

What other compound intervals should we know?

Here's a handy chart that outlines all of them: