It is important to make mention of the possibility that both of these lists could take one further step downwards. Both Gb and F# contain one natural note that does not yet have an accidental.
Following Gb could be the scale of Cb major which reads: Cb, Db, Eb, Fb, Gb, Ab, Bb, Cb [with the upper cluster of four notes matching the lower cluster of Gb, of course].
Following F# would be the scale of C# major which reads: C#, D#, E#, F#, G#, A#, B#, C# [with the lower cluster matching the upper cluster of F#].
If Gb and F# are the ground-floor level of our structure then Cb and C# exist in the cellar. It is somewhat dark, damp and dusty down there. The light bulb flickers, there are many spiders and webs and it is too easy to fall over the many trip hazards. It is safer not to go exploring there for too long, unaccompanied.
It’ll end in tears - as my Dad used to say.
I have deliberately not selected these. My choice to exclude these was not accidental (pardon the pun). Not only are they down in the cellar, they are not needed for where we are going. So, having acknowledged them, we move on.
Notice that both left and right sides start with C major at the upper position.
Note too that both sides terminate at the enharmonic equivalent keys of Gb major and F# major. This is a crucial concept to understand. We need to ensure that this equivalence makes sense. This equivalence of the two scales at the lower reach of our arrangement creates a hidden join at the bottom. The two major scales of Gb and F# are not disconnected – as their physical appearance and written nomenclature would suggest – but actually connected. They are, sonically speaking, in exactly the same musical space. If you are occupying the space of Gb major, you are simultaneously occupying the space of F# major.
Look at the eight notes across the octave span of Gb and F#. They are all equivalent.
Gb = F#
Ab = G#
Bb = A#
Cb = B
Db = C#
Eb = D#
F = E#
Gb = F#
This musical equivalence can allow us to view two separate columns and begin to understand that there is just one continuous, connected flow of scales around which a freely flowing, uninterrupted path can be traced. We can envisage being able to start at the top – with C major - journey down the right side, back up the left side, and return to the start point of C major. We would be following a satisfying circuit of connectivity. Equally, if we were to start at the bottom and journey up from Gb to C then back down to F# we would also be back where we started (as Gb = F# enharmonically).
There are, of course, other ways in which we could arrange and view the twelve major scales all linked together with the overlapping clusters driving the arrangements. All of which can be viewed, interpreted and enjoyed in their own right. Here are two possible arrangements.
Note - please do not spend too long looking at these. They are merely a digression and will not be referred to or used beyond this point.
These arrangements are logical, systematic and entirely linear in design. That is no bad thing. However, we do not easily see that there are connections at both extremes. These arrangements show no visual continuity of flow. They do not illustrate how the scales of Gb major and F# major have us standing in the same place. They do not give us simple visualisation of being able to travel a single route with no need to change lanes. They also imply that there are only two start and finish points. So they may be pleasing and of interest as design arrangements but they do not help us move forwards in our study here.
To do justice to the entirety of all, we need a different visual system, a non-linear representation, a map that depicts the wholeness of the major scale landscape. We need to adopt the same conclusion that those inspired inventors of the wheel reached many centuries ago - that for certain jobs a circle is the best possible option.
Let us run with that idea of circularity. Let us take the straight rows of overlapping scales and bend them more to our needs. We will take the F, C and G major scales and wrap them around one another, curling together and forming an arc.
To do this, to save on duplicate writing and clutter in representation, where there are overlapping letters, two will be morphed into one. Because each scale is depicted as two clusters of four notes, essentially what will happen through this process is that all scales will connect together in a chain where each link is made up of such a cluster.
For every overlapping cluster pair, we will morph the two separate groups of four notes in to one group. We will do this for all twelve scales whose overlaps we have already found. Then we will daisy chain these morphed groups together to make one, long continuous linked group. This chain will comprise twelve clusters.
Now we get to work with our forge, our bellows, our anvil, our tongs and our hammer. We take steely-straight rows of clustered-notes, we heat them, we beat them, we bend and we shape them. We round them off like the iron rim of a cart wheel. We make a circle.
Note, a left-to-right reading of the clusters in a straight line will lead to a clockwise reading in the circle.
Note also that there are fourteen clusters listed above. The first two are the Gb major scale and the final two are the F# major scale. Working at our forge we will not only bend and shape these clusters, we will also take the Gb and F# and meld them together to become one arc that is an alloy of both. This will give us a circle with twelve sections, matching the twelve keys of music.
Each cluster is shown as before containing four notes. If we select any two adjacent clusters and read them, from the first note, in a clockwise direction, we will have found an octave span of a major scale. Let us pause and test that for a moment.
1] Can you find the D major scale? (the note D will be first and eighth across two clusters respectively).
2] Can you find two adjacent clusters whose fourth and fifth notes are Ab and Bb? What major scale is that?
3] Can you find which major scale has three sharp notes (one in the first cluster and two in the second cluster)?
4] Reading clockwise, B major follows E major. Which scale follows B major?
Click here to read the hidden answers ...
1] Look for D E F# G A B C# D at the right side of the circle
For improved clarity, here is the entire circle with major scales marked from their first root note with arrows indicating the clockwise direction to read them.
Circle of Four-Note Clusters with Major Scales shown
We have just one more step to take before the Circle of Fifths is revealed.
Let us return to the four-note clusters with overlaps shown in full, not morphed together. Let us analyse their overlaps and where that happens. We will do this with three examples. For each, we will be reading notes and clusters from left to right. This is equivalent to reading clockwise around the circle of clustered notes above.
F major to C major
Starting at the F major scale, we can see that the C major scale begins at the first note of the second cluster. Another way to describe this is to state that C major starts at the fifth note of F major.
C major to G major
Starting at the C major scale, we can see that the G major scale begins at the first note of the second cluster. Another way to describe this is to state that G major starts at the fifth note of C major.
E major to B major.
Starting at the E major scale, we can see that the B major scale begins at the first note of the second cluster. Another way to describe this is to state that B major starts at the fifth note of E major.
B major to F# major
Starting at the B major scale, we can see that the F# major scale begins at the first note of the second cluster. Another way to describe this is to state that F# major starts at the fifth note of B major.
Ab major to Eb major.
Starting at the Ab major scale, we can see that the Eb major scale begins at the first note of the second cluster. Another way to describe this is to state that Eb major starts at the fifth note of Ab major.
Eb major to Bb major
Starting at the Eb major scale, we can see that the Bb major scale begins at the first note of the second cluster. Another way to describe this is to state that Bb major starts at the fifth note of Eb major.
Notice that fifth has been written in italics for all examples!
What we have found in these examples holds true for all adjacent major scales when grouped in continuous manner around a circle as we have done. Reading clockwise, every next four-note cluster brings the first note of a new major scale.
Every new major scale begins on the fifth note of the previous major scale.
We have a system of arranging all twelve major scales around a circle. All twelve scales connect together in a single, unbroken chain. The chain is made of twelve four-note clusters. Each cluster contains half an octave span of a major scale. The first note of each cluster can be taken as the first note (root) of a major scale. Additionally, the first note of each cluster can be viewed as the fifth note of the major scale that precedes it when reading clockwise around the circle.
Put the other way round, the fifth note of any chosen major scale is simultaneously the first note (root) of the subsequent major scale when reading clockwise. Roots connected to fifths which become roots which then connect to fifths etc etc.
We no longer need twelve sets of four-note clusters. We no longer need to try to navigate and read a circle with forty-eight notes around its circumference. We no longer need the clutter of squeezing so much information in to a compact space.
We can pare it down to the bare essentials. All we need now are the first notes of each of the clusters. Everything else is surplus to requirements.
The first notes of all twelve clusters are simultaneously root notes and fifth notes of major scales.
Roots and fifths of major scales in a clockwise circuit that has no set entry or exit point, that carousels around and around no matter where we choose to hop aboard.
Circle of Clusters with each first note shown larger
The next and final step, an obvious one hopefully, is simply to erase all superfluous notes leaving just the prominent first / fifth notes to stand alone. Giving us …
The result of all this arranging, matching, pattern spotting, morphing and circling is that we have - quite literally - come full circle. We have reached the point where we have a circle of fifths in front of us. And, crucially, we know its origins, its formation, its essence. We know where it came from.
As a small reward for our efforts so far, here is the coloured circle of fifths again.
In hopes of clarity and good understanding, in hopes of removing any remaining confusion, what follows are further depictions of adjacent major scales with their 1st (root) notes and their 5th notes marked above them.
Compare each of these with the full circle of clusters and the twelve notes of the Circle of Fifths shown alongside.
These two major scales overlap and give us the note G on the Circle of Fifths. G is the fifth note in C major (and the root note of G major, our next scale moving clockwiswe).
These two major scales overlap and give us the note D on the Circle of Fifths. D is the fifth note in G major (and the root note of D major, our next scale moving clockwise).
These two major scales overlap and give us the note A on the Circle of Fifths. A is the fifth note in D major (and the root of A major, our next scale moving clockwise).
These two major scales overlap and give us the note E on the Circle of Fifths. E is the fifth note in A major (and the root of E major, our next scale moving clockwise).
These two major scales overlap and give us the note B on the Circle of Fifths. B is the fifth note in E major (and the root of B major, our next scale moving clockwise).
These two major scales overlap and give us the note F# on the Circle of Fifths. F# is the fifth note in B major (and the root of F# major, our next scale moving clockwise).
Note: F# is the enharmonic equivalent of Gb. For the next comparison we convert and use the Gb major scale. This is because we need to recognise that we are moving to the section of the circle containing flat, not sharp, notes.
These two major scales overlap and give us the note Db on the Circle of Fifths. Db is the fifth note in Gb major (and the root of Db major, our next scale moving clockwise).
These two major scales overlap and give us the note Ab on the Circle of Fifths. Ab is the fifth note in Db major (and the root of Ab major, our next scale moving clockwise).
These two major scales overlap and give us the note Eb on the Circle of Fifths. Eb is the fifth note in Ab major (and the root of Eb major, our next scale ).
These two major scales overlap and give us the note Bb on the Circle of Fifths. Bb is the fifth note in Eb major (and the root of Bb major, our next scale moving clockwise).
These two major scales overlap and give us the note F on the Circle of Fifths. F is the fifth note in Bb major (and the root of F major, our next scale moving clockwise).
These two major scales overlap and give us the note C on the Circle of Fifths. C is the fifth note in F major (and the root of C major, our next scale moving clockwise … and also the scale at which we started meaning we have gone full circle).
