Philip Jackson - The Circle of Fifths: visual tools for musicians

The Circle of Fifths

visual tools for musicians

Philip Jackson

The Circle of Fifths

Philip Jackson

ePub Edition

Le Theron Publishing

Copyright 2019 Philip Jackson

All rights reserved.

No part of this publication may be
reproduced in any form or by any
means without the prior written
permission of this publisher.

Preface

When I was learning to play a musical instrument and the associated musical theory, the mass of factual detail given to me concerning intervals, scales, chords and harmony did not always seem to form a coherent entity. The relationships between the various elements were not always evident.

Naturally, that reflected mainly on my inability to understand all those relationships arriving in too short a space of time. Perhaps too, the teachers were treading a well worn and familiar path which did not fit well with my aspirations.

Later when I moved towards techniques of improvisation, I found difficulty in assembling these many facts into a structure which would enable rapid recall. I could often remember where to find the facts rather than the facts themselves. It appeared that my visual memory was dominant.

The circle of fifths came to be the visual crutch I needed and on which I could rely as a basis for seeing the structural coherence of multiple aspects of music. Time after time, I found that I was able to associate a series of facts with the circular representation of fourths or fifths.

I have assembled these ideas into a small tool-kit which I hope will help many others with their learning and understanding of musical theory and its application in performance. This book is not intended as a basic course in music theory and it is expected that the reader will already be acquainted with scales, intervals, chords and chord progressions.

Please take and adapt for your own use those ideas that you find most useful.

Philip Jackson

Table of Contents

Our intention is to make this book a practical kit of tools for visualizing those aspects of music where the brain (of some of us) can get easily left behind and overwhelmed by the task at hand. It is expected that these tools will be of especial interest to musicians involved in improvisational musical genres, jazz, jazz-folk fusions.

To make the best use of this book, the reader should have an understanding of scales, chords and intervals but in most cases a small recap of such material is provided where thought relevant.

We will not hesitate to simplify and this will the most often be evidenced by the re-spelling of note names : C# will become Db, Bbb will become A, F## will become G. These are but a few examples of simplification which might shock theorists but eases the job of the practising musician. Key and scale may well be used interchangeably more practical.

• The perfect major triad will be represented simply by the letter name of the root note. C major triad will be simply written as C
• Minor triads will be represented like this : Cm

• Augmented triads will be represented as : Caug
• Diminished triads will be represented as : Cdim

• Major seventh chords will be represented like this : Cmaj7
• Dominant seventh chords will be shown as : C7
• Minor seventh chords : Cm7
• The minor triad with major seventh : Cm.maj7

• the augmented triad with major seventh : Caug.maj7, Cmaj7#5 , Caug9
• the augmented triad with minor seventh (altered chords) : C7#5
• the half-diminished seventh : C or as Cm7b5
• the diminished seventh : Cdim7

We shall use the major scale as the point of reference for all scales and modes and for harmonic analysis, the degrees of the major scale will be represented by Roman Numerals using upper case to represent notes having a diatonic major third and lower case for notes having a diatonic minor third.

Using C Major as an example of the harmonization of the major scale, we have :

This concurs with the accepted harmonization of major scales.

When deriving a chord or another scale, we shall respect the convention of using as the point of departure the major scale commencing with the same tonic note name. In this case, we shall use arabic numerals. Some examples are listed below :

C major triad consisting of notes C - E - G will have a melodic analysis based on the C Major scale :

1 3 5

C minor triad consisting of notes C - Eb - G will have a melodic analysis based on the C Major scale :

1 b3 5

C dominant seventh chord consisting of notes C - E - G - Bb will have a melodic analysis based on the C Major scale :

1 3 5 b7

C major pentatonic scale consisting of notes C D E G A will have a melodic analysis based on the C Major scale :

1 2 3 5 6

The circle of fifths is also known as the cycle of fifths or the circle / cycle of fourths. The interval of a fourth is, of course, the inversion of the fifth. The circle can be found drawn with flats on the left-hand side and sharps on the right or the other way round.

In earlier periods when much of musical harmony was triad based, the cycle of fifths was perhaps a more appropriate name in the sense that it referred to a progression or motion to and from the primary triads constructed on the first, fourth and fifth degrees of a major scale. This motion acted as a cadential element serving to establish the tonal context or color of the music. The fourth degree is a fifth below the tonic and the fifth degree is a fifth above the tonic. So, these degrees can be viewed as bracketing the tonic in a cycle of fifths and indeed, on our circle of fifths they are either side of the tonic.

For this book, I have adopted the convention of naming it the 'circle of fifths' and drawing it with sharps increasing in the clockwise sense. Fear not ! Once you have worked with the circle for a little time, you will not have any difficulty drawing it the other way round or even visualizing it either way in your mind's eye.

So we will consistently show the circle as you see it below, in Figure 1.1, with a series of ascending fifths (or descending fourths) in the clockwise sense and descending fifths (or ascending fourths) in the anti-clockwise sense. We will also consistently place C at the 12 o'clock position, whether it is the tonic of the scale or not.

In earlier times, the succession of twelve perfect fifths did not cause the circle to close on itself. There was a small excess of approximately a quarter of a semitone and this was known as the Pythagorean comma. The 'circle' was more precisely a first turn of a helix. The adverse effect of transposing a piece of music into remote keys could be clearly heard.

Over the centuries, many ways were tried to eliminate this problem and these culminated in our equal tempered system where the octave is maintained as a doubling of the sound's frequency between notes of the same name and the 'frequency space' between these two notes is split into twelve equal intervals. The size of each semitone is thus equal and defined by the factor 2 1/12 .

The result is that the Pythagorean comma has been eliminated, the circle has been flattened and is no longer a first turn of a helix but the price to be paid is that each of our equally tempered fifths is very slightly flat compared with the natural ratio of 3:2. The advantage is that we now have no difficulty in transposing a piece of music into any key and having it sound right.