Funny - cos I’m not a big fan!! I can see it has some uses but my opinion is that many times students spend too much time thinking about things like the Co5 when they should play more and worry less… but it certainly works for some people, and if it works for you then enjoy it!
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We need to have a chat about that haha!!
Or, you could always read my Circle of Fifths topic if you have a spare moment. 
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I came across this great presentation on Bill Keith’s circle of 5ths. Bill was a well-known banjo player, 3-finger style. It’s got a ton of info in it. I found it quite informative. Here’s the You Tube link: https://www.youtube.com/watch?v=4YdYdc3L3xg
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I’m also curious as to why the key of C# isn’t included in many circle of 5th presentations. I know it’s the same as Db, but F# and Gb are both listed.
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You’re gonna love my topic (if you like deep dive reading) JIm
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The C# major scale = C#, D#, E#, F#, G#, A#, B#
The Cb major scale = Cb, Db, Eb, Fb, Gb, Ab, Bb
Each is at the far extreme as it is possible to go from C natural major scale.
They provide no more than a curiosity.
@Richard_close2u I love a good challenge! I’ll take a look at it. Thanks!
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I recall asking Justin why a C# and a Db scale when the notes are the same during one of his topics on music theory I believe it was. He mentioned, and I agree, I’d rather play in Db than C#.
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The trouble in thinking in terms of C# is the naming of the notes; what do you call the 7th scale degree or the leading tone? It is the pitch of C, but you have to call it B#.
In Db, that note is given its more obvious and straightforward name: C.
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F#/Gb hits that inescapable point where you have either 6 sharps or 6 flats.
It’s the only key with this ‘problem’.
So, swapping to either enharmonic equivalent will still give you ’ messy’ notation, with 6 sharps or flats; and either an E# or a Cb.
Similarly with its relative minor, D# minor/ Eb minor, as they have the same notes.
This is why F#/Gb is notated on most Circle of Fifths diagrams.
Guitarists would prefer the key of F#. Other instruments may prefer to deal with Gb.
Once you pass this ‘6 accidentals problem’ into 7 accidentals, you can defer to its 5 accidental enharmonic to solve the messy notation issue.
ie Keys of C# / Db; and keys of Cb / B
Cheers, Shane
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@Richard_close2u Thanks for that. I got through part I this morning. A lot to digest, but easily understood so far. I can see you made a great math teacher. Reminded me of a book I read years ago I found interesting: Nature’s Numbers. If you haven’t read it, you might find it interesting as well. Here’s a link to a copy of it:
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