CIRCLE OF FIFTHS



This is a musical term.  It is not another version of the song 'ninety nine bottle of beer on the wall', or anything close.  I'm trying to figure out how we ended up with this concept.

The concept is rather simple.  It's an ordered set of notes, both ascending and descending from a C.  To get the next note in the ascending direction, you go up a perfect fifth.  To get the next note in a descending direction, you go down a perfect fifth.  The pattern looks like this:

G-flat, D-flat, A-flat, E-flat, B-flat, F, C, G, D, A, E, B, F#

Two notes are enharmonically the same when they are on the same pitch, but 'spelled' differently.  Note that in the circle of fifths shown here, the F# and G-flat are the same, enharmonically speaking.  So the circle of fifths will wrap back on itself, like a circular clock, enharmonically.

However, if you continue the pattern upwards, you get into fancier spellings for the same thing....

C#, G#, D#, A#, E#, B#

and descending, you get.....

A-double-flat, E-double-flat, B-souble-flat, F-flat, C-flat

and if you press the point, I suppose these notes do theoretically exist and I have seen some of them in written music over the years.  But they are enharmonically equivalent to simpler forms of the same notes.

At any rate, the basic series is:

F, C, G, D, A, E, B

But, why on earth is it useful  to put notes in order, spaced a perfect fifth apart?

One reason is that it helps you figure out what key some music is written in.  You count the number of sharps or flats and find that position in the circle of fifths, and that tells you the key the music is written in.  This rule varies between major keys and minor keys though, as follows.

For Major Keys......
Flats  7          6         5          4        3        2         1        0   1    2     3   4   5    6        7  Sharps
          C-flat, G-flat, D-flat, A-flat, E-flat, B-flat, F,      C,   G,   D,  A,  E,  B,    F#,  C#

For Minor Keys......
Flats  7          6         5          4    3    2    1    0   1   2   3   4   5     6    7  Sharps
         a-flat    e-flat    b-flat    f    c   g     d    a    e   b   f#   c#  g#  d#   a#


I have been trying to explain why the number of sharps required increases by one when you move from one key up a perfect fifth to another key, andwhy the number of flats required increases when you move from one key down a perfect fifth to another key.

First, assume we had no sharps and flats.  Based on the description of note spacing in the major, minor, and church modes (see Diatonic scales under Music Theory section, this web site)  we could play each type of scale only in one key, as follows:

Major
C
Dorian
D
Phrygian
E
Lydian
F
Mixolydian
G
Minor
A
unknown
B

The interval spacing pattern of the 'natural' notes is as follows:


|<--- M2 ---> |<--- M2 --->|<m2>|<--- M2 --->|<--- M2 --->|<--- M2 --->|<m2>|

Two major seconds, then a minor second, then three major seconds, then a minor second.

If you want to add just one note to the set of seven (a sharp or a flat) you need to know where in the pattern to insert  one additional note so you will be able to have the same pattern but starting on a different note.  So, you try sliding the pattern up-pitch and down-pitch until you find a point where there is only one more note required to form the same interval spacings of

M2, M2, m2, M2, M2, M2, m2.

And for some reason, that is consistantly a perfect fifth up or down from the previous point.

So far, so good.  But, then why when we slide the pattern up to begin on a G and see the need for another note between F and G, why call it F# instead of G-flat?  The only reason I can think of is that we don't need the F in the new pattern, but we do need the G, so we might as well call the new note by an unused letter name plus the modifier.

I hope this helps somewhat to understand the circle of fifths.  Somehow it doesn't give me a very warm fuzzy.

So, to round out this discussion, when you see some music with a certain number of sharps or flats in it, refmember the little chart from above, repeated here.....and look up the number of sharps or flats and that tells you what key the song is most likely in.  Remember to use the right chart though, because major is different than minor.

Or, if you are playing a song by ear and want to know what key it is in, observe the notes you are using.... you need all seven within an octave.... and count the number of sharps or flats, then refer to these charts to see what key you are most likely playing in.

For Major Keys......
Flats  7          6         5          4        3        2         1        0   1    2     3   4   5    6        7  Sharps
          C-flat, G-flat, D-flat, A-flat, E-flat, B-flat, F,      C,   G,   D,  A,  E,  B,    F#,  C#

For Minor Keys......
Flats  7          6         5          4    3    2    1    0   1   2   3   4   5     6    7  Sharps
         a-flat    e-flat    b-flat    f    c   g     d    a    e   b   f#   c#  g#  d#   a#

Now that you're familiar with the circle of fifths  the next step is to choose a key and determine the seven notes it should contain.

The Key of a Song                                                Music Theory