Some Uses for the Circle of Fifths, Part One

A. Use the circle of fifths to determine the quantity and quality of sharps and flats in any given key:
take a look at the circle of fifths below. Let's say you wanted to know which notes are flat in the key of Ab. 

First, by looking at the circle, we know that Ab contains four flats. To determine which notes are flat, start on the Bb note and move counter-clockwise four times. These four notes will be the flat notes in the key of Ab: Bb Eb Ab Db. Likewise, if you wanted to know which notes were flat for Bb you'd start on Bb and go counter-clockwise two times. For Db, you start on Bb and go around five times, etc.

To determine which notes are sharp we follow a similar process: Let's say you're interested in knowing which notes are sharp in D major. D has two sharps: start on the F note and move clock-wise, in the case of D, two times: F# and C#. Similarly, for the key of E we know that E contains 4 sharps: start on F and go around four times: F# C# G# D#

B. You can also use the circle of fifths to determine which notes are part of any major scale: start with any note, include the first counter-clockwise note + five clock- wise notes. So let's find the notes of the the G major scale: start with the G note, go left to the C, then go back to the right, include the G, then go 5 more notes to the right (clockwise). So, we end up with C G D A E B and F#

These are the notes of the G major scale. Just put them in the correct order as dictated by the musical alphabet: G A B C D E F#

C. Use the circle to find the chords for any major key: start with any note acting as the I chord. The first chords both counter- clockwise (IV) and clockwise (V) will be major chords, next three clockwise chords are minor (ii, vi, iii), and the final clockwise chord will be the diminished chord. For example, if we wanted to know what the chords were in the key of A we would start on the A and determine that it is the I maj chord. Go counter-clockwise one note to the D. The D represents what will be the IV major chord. Go back to the A and travel one note clockwise to the E. E represents the V chord. So the A and the notes on either side tell you thatA=I D=IV E=V

Now, to determine the remaining chords in A, start on the V cord (i.e., the E) and pick up the next three chords by moving in the clockwise direction from the V. Each will be minor chords: B F# Db/C#.
B=ii C#=iii F#=vi

The last remaining chord is the diminished vii. Simply go one more note clockwise from the last note (F#) and you'll find the diminished chord: Ab/G# A (I) B (ii) C# (iii) D (IV) E (V) F# (vi) G# (dim)

D. Reharmonizations and substitutions are easy with the circle of fifths: let's say you were tired of playing songs that used only primary chords (I IV and V). In the key of A the primarily chords are A D and E. You know already because by looking at the circle you found that the notes on either side of the "A" note represent the major chords (IV and V). Now, you want to find an alternative to the D or IV chord. Start on the D chord that you'd like to substitute and go three in the clockwise direction. You'll land on B (the ii) which is the functional equivalent to the IV. So try I ii V for a change. 

Likewise, let's say you want to substitute the V for something more interesting. Go "three from" the V chord in a counter-clockwise direction. Starting on E in this case, move three to the G which represents the b7 substitute for the V chord. In A, the vii chord is the diminished G#. A common jazz move is to lower the vii 1/2 step and make it a dominant (diminished chords are, for all practical purposes, dominant chords anyway) ... so we find the G# being lowered to G and transformed into a b7th chord. Now try I ii vii/V. If you examine the relationship between a chord and counter-clockwise motion three places you'll find other "three from" alternatives such as the ii is "three from" the IV and the vi is "three from" the I, etc. 
I = I, iii, and vi, IV= IV and ii, V= V and vii

This is known as "functional harmony"

Other simple reharmonizations are done by experimenting with adjacent chords in intervals of 4ths and 5ths.
In Part II, I'll cover more reharmonizations, substitutions, and modulations.