Thanks @Aaronwith2dots
I’m glad you’re enjoying it and coming back for more. Cheers. 
Great article! I’ve tried to understand the Circle of Fifths and it just never made sense, until now. This breaks it down nicely for my analytical mind and really illustrated how all the scales flow together. I look forward to the other articles.
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Thanks Dean, I appreciate you taking your time to read and digest this. Hopefully the further sections will prove interesting and useful too.
Second read through since last week. Very neat to see how you’ve derived it out. The overlap bit is news to me and the whole is interesting for a more fundamental understanding.
So with the circle done, what about a Mobius next? Perhaps that requires micro tones … 
thanks!
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The Circle of Fifths Part 2 - isn’t it the same as the circle of fourths?
The Circle of Fifths is our main focus.
Categorically, absolutely, without a shadow of a doubt.
We are here to learn about and consider the Circle of Fifths.
Yet it would be remiss of me not to mention that it has two names and can be viewed in two ways. Many musicians know it and refer to it as the Circle of Fourths.
We saw how the overlapping four-note clusters, when read from left-to-right, connected to a matching partner, and then transformed to leading around a circular arrangement in a clockwise direction yielded the 12 notes of the Circle of Fifths.
The 5th notes were seen where the next major scale in the clockwise direction started. The 5ths were where the four-note clusters joined together. Consider that when two things connect and a join is made, there are two sides to the join. Two parts that meet up, that connect and are bonded. On one side of our join we have the 5ths. On the other side, self evidently, we have the 4ths.
Let us suppose then that it was the 4ths that determined the order of successive major scales. Just as C major led to G major which in turn led to D major when reading clockwise from the 5ths, we will now consider what would result if the successive major scales were rooted on the 4ths not the 5ths.
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We would see the major scales connect and lead to this succession of scales.
C major to F major
F major to Bb major
Bb major to Eb major
Eb major to Ab major
Ab major to Db major
Db major to Gb major
F# major to B major
B major to E major
E major to A major
A major to D major
D major to G major
G major to C major
We are reading the topmost major scale from left to right until we reach the 4th note of the scale. That 4th note gives the start of the next major scale which is shown below. The overlaps clearly show the matching clusters of four notes between each pair of scales.
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Taken as individual notes based on the major scale root notes we have this order of twelve notes.
We would see the major scales connect and lead to this succession:
C → F → Bb → Eb → Ab → Db → Gb / F# → B → E → A → D → G → C
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Hang on.
That looks familiar.
We have seen that somewhere before haven’t we?
Mmmh.
Pauses for reflection and consideration.
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Got it.
Oh wow!
That series of twelve notes built on the 4ths matches exactly the twelve notes on the Circle of Fifths … BUT … when reading anticlockwise around the circle.
We have created The Circle of Fourths
C → F → Bb → Eb → Ab → Db → Gb / F# → B → E → A → D → G → C
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The Circle of Fifths is, simultaneously, the Circle of Fourths. Depending on whether we read around the circle in a clockwise or an anticlockwise direction.
Note:
Some musicians prefer their reference to be the viewpoint of the Circle of Fourths and place that clockwise around the circle, meaning on such circles the fifths read anticlockwise. That is all down to preference and usage. There is no inherent difference between them apart from their circular direction.
Some musicians spend their lives playing in keys with lots of flat notes and they may prefer to view it as the Circle of Fourths. Not guitarists of course - ask a guitarist to play in the key of Ab and they might just choke on their own horror!
Anyway, after this little sojourn, the next part will take us nicely back to the Circle of Fifths, in a clockwise direction.
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All good stuff Richard and a timely review. Will have to park your latest excursions, until the family are back in Blighty. Keep up the good work.
Cheers
Toby
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I’m curious about this. I know certain instruments have preferred keys, or that certain keys are more suited to certain instruments.
Obviously, on guitar C, G, D, A and E (circle of 5ths!) are the most common keys. I think Bb and Eb (?) are associated with horns (trumpet, sax). For example, I’ve heard that Johnny B. Goode was pitched in Bb to accomodate the horn section (wait, are there horns on Johnny B. Goode?)
Also, I think I read somewhere that expert piano players prefer to play on the black keys, does anybody know if that is true? I’d be curious to find out which keys are “typical” of which instruments and why.
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Yes, a standard trumpet is tuned to Bb (with a limited range of about two octaves) and a piccolo trumpet to Eb.
I don’t know any technical reasons and am no piano player so this is my imagination answering - the black keys present a changing landscape (two together then three together) so give the player some points of interest and waymarkers to keep them alert and able to navigate, rather than the flatlands of the unbroken white keys.
The Circle of Fifths Part 3 - where does it go? [a] major scales
The next instalment of our story will take us to places where the Circle of Fifths begins to reveal some of its uses and usefulness.
We have seen where it comes from, now … where does it go?
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The first, perhaps most obvious, start would be to mention that the twelve notes around the Circle of Fifths are the twelve notes of western music, the twelve notes around the note circle, the twelve key signatures. There are no duplicates. All notes / key signatures are represented, once each. Clearly, they do not follow one another in alphabetical order. As mentioned earlier, the arrangement derives from another source, not the alphabet.
It must follow that if all notes are represented then all notes of all major scales can be found somewhere around the Circle of Fifths. Not only is this necessarily true, it is also spectacularly true that all seven notes of any major scale can be found grouped in succession, all adjacent to each other with no gaps.
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Hopefully everyone reading this knows that the C major scale contains only natural notes, no flats or sharps. Let us look at the Circle of Fifths. Let us find seven notes that are all natural, containing no sharps or flats, the seven notes that make up the C major scale in fact.
You should be able to identify these seven adjacent notes:
They all sit happily alongside one another, friendly neighbours around the circle.
The root note C is not in any obvious position, it does not conveniently come first when reading the notes clockwise for instance. It happens to be in second position from that perspective. Nor, as has been mentioned several times, do the notes appear in alphabetical order. But these inconveniences are really not that at all. Merely minor surprises or small deviations away from any expectation we may have had. And they will reveal some hidden patterns and order soon enough.
Look at the notes again, knowing that they all belong in the C major scale:
We could reasonably ask whether there be any logic or sequence to the ordering of the scale degrees when we read them on the Circle of Fifths.
That seems rather ad hoc and random, certainly nothing to raise any hopes of an exciting or revealing pattern as yet.
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Let us look at a different major scale.
What about Ab major? A real favourite key … said no guitarist, ever haha!
Can we find all of those seven notes somewhere in adjacent positions on the Circle of Fifths?
Aha!
That’s interesting – once again the root note is in the second position when reading clockwise. Let us rearrange to match the clockwise order on the Circle of Fifths.
4, 1, 5, 2, 6, 3, 7 – we saw that with the scale degrees of the C major scale also.
Is that just coincidence?
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