• How 7sus4 Chords And The Diminished Matrix Can Help You Master The Circle Of Fourths And Fifths

One of the best things that happened to me as an up and coming pianist was to master the circle of fourths and fifths.

In more occasions than one, our founder – Jermaine Griggs, has used this circle to teach the root movement of notes in chord progressions, how tritones, ditones, semitones, etc., relate to each other, and more. The importance of the circle of fourths and fifths in music cannot be overemphasized.

I’ll be sharing with you in this lesson, one of the smartest ways of learning and mastering the circle of fourths and fifths using 7sus4 chords and the diminished matrix.

Attention: Don’t worry, if those terms sounded unfamiliar or not-so-familiar to you because I’ll be giving you a detailed explanation of terms as we proceed.

Quick Insights On The Circle Of Fourths And Fifths

A good way to start this lesson is by answering the question below:

“What is the circle of fourths and fifths all about?”

The circle of fourths and fifths are interval cycles. An interval cycle is basically a sequence of notes (aka – “pitches“) starting from a given note, and going up [or down] by a stipulated interval until the original note is reached.

The circle of fourths and fifths are interval cycles that go up and down in perfect fourth and perfect fifth intervals respectively.

A perfect fourth interval is formed by the relationship between the first and fourth tones of the natural major scale, while a perfect fifth interval is formed by the relationship between the first and fifth tones of the natural major scale.

“Let Me Show You How The Circle Of Fourth Is Derived…”

Starting from any note (but let’s use C):

…and going up in perfect fourth intervals, we have…

C to F:

C-F to Bb:

C-F-Bb to Eb:

C-F-Bb-Eb to Ab:

C-F-Bb-Eb-Ab to Db:

C-F-Bb-Eb-Ab-Db to Gb:

…and it goes on [and on] to Cb:

…and other tones.

“Take A Look At How The Circle Of Fifths Is Derived…”

Also starting from C:

…and going up in perfect fifth intervals, we have…

C to G:

C-G to D:

C-G-D to A:

C-G-D-A to E:

C-G-D-A-E to B:

…and it goes on [and on] to F#:

…and other tones.

“Say Hello To The Circle Of Fourths And Fifths”

Here’s a pictorial representation of the circle of fourths and fifths:

Take note of the following:

• C is at the 12 o’clock position
• In the clockwise direction is the circle of fifths, which extends to the 7 o’clock position (C#.)
• In the counter-clockwise direction is the circle of fourths, which extends to the 5 o’clock position (Cb.)

Here’s One Of The Reasons Why Musicians Need To Learn The Circle Of Fourths/Fifths

The circle of fourths and fifths can be used as a guide to the mastery of root movements in cyclical progressions like the 2-5-1 chord progression. For example, C, F, and Bb:

…which are the first three notes in the circle of fourths (in the counter-clockwise direction) can either be played as the root movement of the 7-3-6 chord progression in the key of Db:

…or a 2-5-1 chord progression in the key of Bb:

“In The Key Of Db…”

Check out the 7-3-6 chord progression in the key of Db…

Chord 7:

Chord 3:

Chord 6:

Did you notice the C-F-Bb movement on the bass?

“In The Key Of Bb…”

Here’s a regular 2-5-1 chord progression in the key of Bb…

Chord 2:

Chord 5:

Chord 1:

That’s another C-F-Bb movement on the bass.

Attention: If you’re interested in learning how to endlessly find your way around the circle of fourths and fifths on the keyboard without looking at the pictorial illustration, read on.

I stopped looking at the pictorial illustration when I figured out a smarter way of memorizing the circle of fifths using two things:

• The 7sus4 chord
• The diminished matrix

…and I’ll be explaining them to you in the next segment.

A Short Note On 7sus4 Chords And The Diminished Matrix

Before I show you how to master the circle of fourths and fifths to a point where you’ll throw its pictorial illustration out of the window, let’s take a look at 7sus4 chords and the diminished matrix.

“What Are 7sus4 Chords?”

The 7sus4 chord is a dominant seventh chord with a suspended fourth. In the C dominant seventh chord:

…raising E (the third tone):

…by a half step (to F):

…produces the C7sus4 chord:

The fifth tone of the 7sus4 chord can still be omitted without changing the orientation of the chord. For example, here’s the C7sus4 without its fifth tone:

We’ll be using 7sus4 chords with omitted fifth tones in this lesson.

“Check them out in all twelve keys…”

C 7sus4:

C# 7sus4:

D 7sus4:

Eb 7sus4:

E 7sus4:

F 7sus4:

F# 7sus4:

G 7sus4:

Ab 7sus4:

A 7sus4:

Bb 7sus4:

B 7sus4:

The Diminished Matrix

The diminished matrix is a witty framework that can be used in the development of ideas. This framework is formed by the outline of the diminished seventh chord. In the key of C:

…where the diminished seventh chord:

…consists of the C, Eb, Gb, and Bbb (deliberately spelled as A), a diminished matrix can be formed by following the diminished seventh chord outline from C:

…to Eb:

…to Gb:

…to A:

In any key you’re in, you can develop an idea using the diminished matrix by following the diminished seventh chord outline in that key. For example in the key of E, a particular chord progression can be developed when it is played in several other keys following the diminished outline.

Using the E diminished seventh chord:

…we can figure out other keys that the chord progression can be played in, which are the keys of E:

…G:

…Bb:

…and Db:

Suggested reading: The Diminished Matrix: Who Else Wants To Connect The 2-5-1 Chord Progression?

How “7sus4 Chords In A Diminished Matrix” Can Make The Circle Of Fourths/Fifths A Walk-Over For You

Playing the 7sus4 chords we learned earlier in a diminished matrix creates a root movement identical to the circle of fourths.

In the C diminished matrix outlines C:

…Eb:

…Gb:

…and A:

Forming 7sus4 chord in those notes, we’ll have the C7sus4 chord:

…Eb7sus4 chord:

…F#7sus4 chord:

…A7sus4 chord:

Using the circle of fourths/fifths pictorial illustration:

…as a guide, check out how the 7sus4 chord in diminished can form an outline of the notes in the circle of fifths.

“Going Counter-Clockwise…”

The first three notes in the circle of fourths (C, F, and Bb) are the tones of the C7sus4 chord:

The next set of three notes in the circle of fourths (Eb, Ab, and Db) are the tones of the Eb7sus4 chord:

The next set of three notes in the circle of fourths (F#, B, and E) are the tones of the F#7sus4 chord:

The next set of three notes in the circle of fourths (A, D, and G) are the tones of the A7sus4 chord:

Altogether, the notes of the 7sus4 chord played in a diminished matrix are identical with the ones in the cycle of fourths/fifths.

Final Words

Whenever there’s need to cycle through the cycle of fourths/fifths, you can count on 7sus4 chords in a diminished matrix.

We’ll continue with our discussion in another lesson. See you then!

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Chuku Onyemachi

Head of Education at HearandPlay Music Group
Onyemachi "Onye" Chuku (aka - "Dr. Pokey") is a Nigerian musicologist, pianist, and author. Inspired by his role model (Jermaine Griggs) who has become his mentor, what he started off as teaching musicians in his Aba-Nigeria neighborhood in April 2005 eventually morphed into an international career that has helped hundreds of thousands of musicians all around the world. Onye lives in Dubai and is currently the Head of Education at HearandPlay Music Group and the music consultant of the Gospel Music Training Center, all in California, USA.

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1 Roo

Hi this subject is kind of hard for me to understand is there a whay to sumplfy it or sum thing that I need to learn be for I do this?

2 Roo

Hoo I understand now what is going on it toke me sum time but now I understand.
What needs to be done first take a diminished 7 cord and then take the first degry note for example if my cord is
C diminshed 7 so the first digry is C.
And naw creat the 7sus4 of C and you have the sercole of fifts just go to the next degry of the diminished C and that is Eb and do the same thing with the 4sus7 of that and you have a sercole of fifts.