One of the most fabled artifacts in the Music Theory world is the Circle of Fifths. Do you know it? IS IT MEMORIZED?? Not to worry, you don’t need to memorize it but rather know how it works. The circle of fifths is a useful organizational tool that helps you figure out what your sharps and flats are within a key based off it’s position in the circle.
The Circle of Fifths codifies a pattern that naturally occurs in keys related a fifth apart. With C major as the starting key (no sharps, no flats), a fifth away (G) will provide you with a key that has one additional sharp on the 7th scale degree. This pattern continues as you go a fifth higher, keeping the previous sharps valid in an additive fashion. The reason is as follows:
The formula to create a major scale is intervallically whole whole half whole whole whole half (WWHWWWH). When applied to C, this works perfectly because there is a natural half step between E and F as well as B and C.
When any other note is used as the starting note, because of the natural disposition of whole steps to half steps (with only the B and C and E and F relations containing half steps), the required whole steps and half steps formula for the Major Scale will cause sharps to occur. The fifth relationship gives the order of the sharps in consecutive order, thus making it easier to understand. For example, the next scale would be:
We keep the previous sharp valid (for sake of ease, the major scale formula would correct it if we didn’t as you will see there is a whole step between E and F where there would naturally be a half step) and continue a fifth higher than G, which would be D major scale
This pattern continues to give you the order of the sharps, each a fifth away from each other:
F# C# G# D# A# E# B#
For flat Keys; one can think of the circle of fifth in two ways. You can travel counter clockwise in fourths (which, according to the rule of 9 is an inversion of a fifth), or think of the previous key being the starting point at which you are now a fifth away. Since C has no sharps or flats, and traveling clockwise on the circle of fifths provides a sharp on the seventh scale degree, it is safe to assume that starting a fifth below C will give rise to the first flat. Using the major scale formula on F (a fifth previous to C, or a fourth ahead)
Much like the pattern in the order of sharps (keep the previous sharp valid, raise the 7th), there is a pattern for flats. Keep the previous flat valid and lower the 4th. Continuing to the next key:
This pattern will give you the order of the flats, each a fourth away from each other (or like I’ve mention, a fifth away from the previous note)
Bb Eb Ab Db Gb Cb Fb
Below is a video where we explain part 1 of the Circle of Fifths. Part 2 soon to come!