A Simple View of the Circle of Fifths
Draw outer Circle with C on top and F#/Gb on botom; the keys go left to right, C, G, D, A, E, B, F#/Gb, Db, Ab, Eb, Bb, F. Break the circle between F and Bb and between Db and B having F#/Gb open. Draw an inner circle with numbers Starting with C location 0, 1, 2, 3, 4, 5, 6, 5 ,4 ,3 ,2 ,and end with 1 on F. make a note on F as First # and Bb as First b. Follow the explaination below. It is the first time the circle of fifths made sense.
The left side of the circle lists keys containing flats. The right side lists keys containing sharps. At the top of the circle is the key of C Major which has no sharps or flats. At the bottom of the circle is the key of F# Major or Gb Major which contains six sharps or six flats respectively.
The numbers inside the circle tell you how many sharps or flats (depending on which side of the circle you are on) a given key contains. For example, on the right side of the circle, the key of G Major has 1 sharp, the key of D Major has two sharps etc. On the left side, the key of F Major has 1 flat nd the key of Bb major has 2 flats etc.
The circle of fifths will also tell you which notes are sharped or flatted in each key.
For sharp keys, start with the number 1 sharp F# and count the required number Clockwise. Thus the key of E Major has four sharps, F#, C#, G#, and D#.
For flat keys, start with the number 1 flat Bb and count the required number Counter-Clockwise. Thus the key of Ab Major for example, has four flats, Bb, Eb, Ab, and Db.
Nice job on the circle of fifths but i do have some comments. Personally I think your ding a bit too much work. lol. The circle of fifths is easy if you know your key signitures. Lets have a look:
It starts with the Key of C on the tope and goes left to right "C, G, D, A, E, B, F#, C#" for the sharp scales (Not looking at the flat yet). wonder why they call it the circle of fifths? because the fifth note of the key of C is G. C-D-E-F-G-A-B-C. you count the tonic (first note) so you get G as the fifth note. well the key of G has one sharp.... F#. why? because in the Major sharp scales the Leading tone or the note leading to the tonic is sharped because it needs to be one half step away from the tonic (in the key of G the tonic is G, key of C it would be C... and so on.) So the key of G is G-A-B-C-D-E-F#-G.
You keep the sharps as you go. so the Key of D has two sharps, F# and C#. Now the pattern for the major scale ( should have put it earlier but here it is) is Whole-Whole-Half-Whole-Whole-Whole-Half. now put numbers to that. THere is a whole step between 1 and 2, 2 and 3. but between notes 3 and 4 there is a half step, in the Keyof C its already there (E-f) In G as well ( B-C) but in D the F# is kept and creates the needed half step. D-E-F#-G...... the patern keeps repeating itself but thgen you get into Double sharps... triple sharps which are just other scales but those arent used much.. so you just really for the Circle of fifths stop at C#.
For the Flats, you go Back 5 notes, but its easir to go ahead 4 notes i.e. The fourth note in the key of c is???? you guessed it F! The raised leading tone doesnt apply here but what happends is you still need the half steps in the appropriat places. so its F-G-A-Bb-C-D-E-F. now as for enharmonics the Bb would be an A#. It still makes the half step between the 3rd and 4th notes, and the E-f makes the half step between the leading tone and tonic (7 and 8). you keep the flats and they fill in the spaces as well. the trick to the flat keys is that the last note in the key signature is the next flat scale ( Not a rule because your still counting 5 notes down or 4 notes up, just coincidence) i.e. the flat scales go F-Bb-Eb-Ab-Db-Gb and the key signiture for F is Bb, and Bb is the next scale. the key signature for Bb is Bb- Eb. then there is Eb which has the key signiture of Bb Eb Ab. the pattern keeps repeating.
that is the simplest way the circle works that will allow you o now the most about it. this way you know all your key signitures and how they are related. This is especially important in techniques for chord progressions such as Modulation, which allows a song to change key. but that is getting more advanced than what this is about right now.
Hope I helped!
Thanks Bstguitarist, You do know your theory, and you can still say Potato and I will say POTATO. As long as we all can use the info to play and write music to fit our needs. I believe in th KISS principle. As a further explaination of the easy circle of fifths, All you have to do is memorize the circle keys and the coresponding # and you can then know which notes are getting the flats/sharps in the scale of things. The one I posted makes it so you don't have to think of the Tonic, the half steps etc and you correctly pointed out. That is the hard way- way to much thinking to get to the same point if you use my posting of the simple circle of keys.