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The circle of fifths lays out the 12 tones in a circle, moving clockwise in fifths. If C is 12 o'clock, its fifth, G, is 1 o'clock. G's fifth, D, is two o'clock. And so on.
==Inter-relation of Keys==
So far we've really only talked about C Major and A minor, which are composed of the 7 white keys per octave on the piano. But scales can be built upon any of the 12 tones in the chromatic scale. We know the whole-half patterns of the major and minor scales, so we can figure out what notes any scale has, but what about the interrelation between scales? This is where the circle of fifths helps to keep things in perspective.
The full circle only consists of the 12 tones, which can be arranged like the hours on an analog clock. The points opposite each other (12 vs. 6, 3 vs. 9, 11 vs. 5, etc.) are the least related, while the points nearest each other (12 and 1, 1 and 2, etc.) are most related. As we go right or clockwise, we sharp the 4th of the current key to get the next key. For example in C Major, sharping the 4th (F) gives us the scale of G Major. As we left or counter-clockwise, we flatten the 7th of the current key to get the next key. For C Major, we flat the B to get F Major.
So each movement is a single note difference. Note that the major scale has two half-steps, which means two notes right next to each other. Every other major or natural minor scale has to contain at least one of these notes, since the largest movement between neighboring notes is a whole step. So the least related scales will share 2 notes.
== Full Circle ==
Let's find all 12 tones in order of fifths, going both ways from C:
C
Gb - Db - Ab - Eb - Bb - F - C - G - D - A - E - B - F#
F# is the same pitch as Gb, which means we've completed the circle. If we keep going, we still get unique key names, but the pitches will match other keys already in the circle. For example, continuing left (counter-clockwise), we reach Cb, which is the same as B. Going right (clockwise), we reach C#, which is the same as Db.
{| class="wikitable"
|-
! Key !!Cb !! Gb !! Db !! Ab !! Eb !! Bb !! F !! C !! G !! D !! A !! E !! B !! F# !! C#
|-
| Flats/Sharps||7 b's||6 b's || 5 b's || 4 b's || 3 b's || 2 b's || 1 b's || 0 b/#'s || 1 #'s || 2 #'s || 3 #'s || 4 #'s || 5 #'s || 6 #'s || 7 #'s
|-
! Unison ||Cb || Gb || Db || Ab || Eb || Bb || F || C || G || D || A || E || B || F# || C#
|-
| 2nd ||Db || Ab|| Eb || Bb || F || C || G || D || A || E|| B || F#|| C# || G# || D#
|-
| 3rd ||Eb || Bb || F || C || G || D || A || E || B || F# || C# || G#|| D# || A# || E#
|-
! 4th ||Fb || Cb || Gb || Db || Ab || Eb || Bb || F || C || G || D || A|| E || B || F#
|-
| 5th ||Gb || Db || Ab || Eb || Bb || F || C || G || D || A || E|| B|| F# || C# || G#
|-
| 6th ||Ab || Eb || Bb || F || C || G || D || A || E || B || F#|| C#|| G# || D# || A#
|-
! 7th ||Bb || F || C || G || D || A || E || B || F# || C# || G#|| D#|| A# || E# || B#
|-
| Oct ||Cb || Gb || Db || Ab || Eb || Bb || F || C || G || D || A|| E|| B || F# || C#
|}
{| class = "wikitable"
|-
!Common Notes !! Diatonic Keys !! Non-Diatonic Keys
|-
|6 || P4, P5 ||
|-
|5 || M2 || D7
|-
|4 || M6 || m3
|-
|3 || M3 || m6
|-
|2 || M7 || m2, d5
|}