(Circle of 5ths Diagram)

A.
Rearrangement of notes in Circle of Fifths order :

1. G - C - F - Bb - Eb - Ab - Db - Gb - B

2. G# - C# - F# - B - E - A - D - G

3. D - G - C - F - A# - D# - G# - C# - F# - B

4. E - A - D - G - C - F - Bb - Eb - Ab

B.
1.Tones at opposite points of the Circle of Fifths are exactly halve an octave (and augmented 4th, or diminished 5th, or 6 semitones or 3 whole tones or a tritone) apart.
For example :

• C - F#(Gb)
• F - B
• Bb - E

2. The white notes on the keyboard form an uninterrupted segment on the Circle of Fifths (B - E - A - D - G - C - F), and so do therefore the black notes (Bb - Eb - Ab - Db - Gb).
Knowing this may help you remember the Circle of Fifths order.

3. The Circle of Fifths can be seen as two interlocking whole-tone scales
C - D - E - Gb - Ab - Bb - C
G - A - B - Db - Eb - F - G

C.
The Perfect Cadence represents a downstream movement on the Circle of Fifths.

Plagal Cadence represents a upstream movement on the Circle of Fifths.

D.
The number of sharps or flats in each key signature :

From C going clockwise ----> increasing SHARPS in the key signatures.

From C going anti-clockwise ------> increasing FLATS in the key signatures.

E.
The Circle of 5ths segments in the Mystery tune are :

F - F#dim - (Gm7 - C7) - (Am7 - Dm7 - Gm7 - C7 - F) - F#dim -

(Gm7 - C7) - (Am7 - Dm7 - Cm7 - F7 - Bb) - (Abm7 - Db7 - Gbmaj7) -

(Em7 - A7 - Dmaj7) - (Abm7 - Db7 - Gbmaj7) - (Gm7 - C7 - F) - F#dim -

(Gm7 - C7) - Bb7 - (Am7 - D7 - Gm7 - C7 - F) - (Dm7 - Gm7 - C7 - F).

There are only five chords in the above progression that do not belong to a Circle segment.
These isolated chords (F#dim and Bb7) function in this song as passing chords that connect one Circle segment to the next.