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In Search of the Perfect Custom Bass, Part 3 - Stick Your Neck Out | Inverted Intervals

Inverted Intervals

by Stefon Pizzuto

Welcome back, bass colleagues. In our last two sessions, we discussed the modes of harmonic minor and the modes of jazz minor, respectively. This time, I thought we'd change the pace and delve into a subject that is not often taught in classrooms or theory books - the concept of inverted intervals.

Before beginning this exercise, make sure you have a thorough understanding of the twelve basic intervals and how they are arranged on the fretboard. Many theory publications such as books and magazines can show you how to play all of the intervals on the bass. I would like to stress that if you have never studied the intervals or have no experience playing them, it will be very difficult to fully comprehend this exercise. If you do feel confident with the basic intervals and how they are arranged on the fingerboard, the concept of inverted intervals should not be too difficult to grasp. Inverted intervals are simply the mirror image of intervals.

In most interval studies, the intervals are located above the root, meaning they always sound higher in pitch than the starting note. Inverted intervals allow us the opportunity to find any given interval below the root, so that the note sounds lower in pitch than the note on which we began. With the aid of inverted intervals, we will now have a 360 degree view of the fretboard.

There are several different ways to view inverted intervals. In order to avoid confusion, we will first begin by studying the chart below and memorizing the pattern they follow. Then, we will move ahead to their explanation and see how they apply to the instrument.

minor 2nd	inverts to	major 7th
major 2nd	inverts to	minor 7th
minor 3rd	inverts to	major 6th
major 3rd	inverts to	minor 6th
perfect 4th	inverts to	perfect 5th
tritone	inverts to	tritone
perfect 5th	inverts to	perfect 4th
minor 6th	inverts to	major 3rd
major 6th	inverts to	minor 3rd
minor 7th	inverts to	major 2nd
major 7th	inverts to	minor 2nd
octave	inverts to	unison

As you can see, major and minor are always the inversions of one another. For example, the first interval, the minor 2nd, inverts to the major 7th while the next interval, the major 2nd, inverts to the minor 7th. This holds true for every major and minor interval. Any time you have a major interval, its inversion will always be minor, and vice versa.

The other pattern that inverted intervals follow is that the sum of the interval plus its inversion must equal nine. This means that 2nds and 7ths, 3rds and 6ths, 4ths and 5ths, and octave and unison, will always invert to one another. The remaining interval, the tritone, will always invert to itself, meaning it will not change. If you would like to apply the idea of nine to the tritone, remember, the tritone is between the fourth and fifth. In mathematics, the number that falls between four and five is four and one-half. Adding four and one-half plus four and one-half gives you nine.

Since the explanation of how inverted intervals apply to the fingerboard can be rather lengthy, we will choose only one interval to use for the example below. This formula will apply to every interval and its inversion, though, so make sure you take all of them through the entire cycle before moving on to the next section.

Randomly, let's choose the interval major 6th and its inversion, the minor 3rd, for our study. As a root, let's use the note A at the fifth fret on the E string. Again, you could choose any note on the fingerboard for this exercise and the outcome would always be the same. In this case, A was chosen simply because it is the first note of the chromatic scale.

There are basically two ways to view inverted intervals. The first way uses the root note A as a sort of "pivot point". Playing a major 6th above A brings us to the note F# at the 4th fret on the D string. We can find its inversion simply by playing down a minor 3rd, or three frets, from A to the note F# at the second fret on the E string. Therefore, playing a major 6th above A or a minor 3rd below A will both bring us to the pitch of F#, although the notes are an octave apart.

The other way of applying inverted intervals to the fretboard is by using the second note, the major 6th, as the pivot point. We will still begin on the root note A at the fifth fret on the E string and play up a major 6th to the note F#. This time, however, we will play up a minor 3rd from the F# (major 6th) to the note A at the seventh fret on the D string, returning us to the original pitch of A, but one octave higher. By doing this, we have come full circle, further enforcing the rule that the notes A and F# will always be either a major 6th or minor 3rd away from one another.

As we stated above, the purpose for inverting intervals is to give us a 360 degree view of the fretboard. Inverted intervals, in many cases, provide a type of shortcut for helping us find an interval quicker and easier. For example, if you have a note that is functioning as the major 7th and you want to find its root, instead of counting back a major 7th to find the starting note, you can go up a minor 2nd and get the same result. The more confident you are with the positioning of all the intervals on the fingerboard, the easier you will be able to manipulate the fretboard.

Try this with all of the intervals and their inversions in every key from every position on the neck until you feel comfortable with how they are arranged on the fingerboard. Keep in mind, once you learn the intervals and their inversions in any given key, the same fingerings will apply to the remaining eleven keys, so you will only need to work these exercises in one key before transposing them through the rest.

I hope this exercise has helped you gain a better understanding of fretboard theory. If you have any questions or comments, please feel free to contact me via my website www.stefonpizzuto.com. If you would like to explore the world of intervals further, pick up a copy of my book, Scales and Arpeggios for Electric Bass, available from www.bassbooks.com. Thank you for joining us today and I look forward to seeing everyone in August.

Stefon Pizzuto