# Circle of Fifths

# Circle of Fifths

Since major scales
are constructed of two tetrachords
linked by a whole-step
(or 2 half-steps),
each major scale has two parts - an upper tetrachord and a lower tetrachord.
In the C major scale, for example, the *upper tetrachord* is **C-D-E-F** and
the *lower tetrachord* is **G-A-B-C**. In the G major scale
the *upper tetrachord* is **G-A-B-C** and the *lower tetrachord* is **D-E-F#-G**.
Notice the *lower tetrachord* of the C major scale is identical to the *upper tetrachord*
of the G major scale. Due to this upper/lower tetrachord matching,
the major scales form an interlocking series known as the circle of fifths. The
chart below shows this series starting from the F major scale and continuing through B major.
If the chart continued on from B major in the same fashion it would loop (or circle) back
to F major again.

Recall that a perfect fifth is two notes separated by seven. Therefore a perfect fifth above F is C, a perfect fifth above C is G, and so on. The tetrachord matching of major scales naturally falls on the fifth interval of each scale. Hence the name circle of fifths.

# Key Signatures and the Circle of Fifths

The circle of fifths arranges the major scale key signatures in order according to the number of sharps or flats. See the diagram below.

A common mnemonic for memorizing the circle of fifths is **F**uzzy
**C**ats **G**et **D**irty **A**fter **E**very **B**ath.

The number of sharps or flats in a major scale can be easily calculated by going around the circle clockwise starting from C. For example, to find out how many sharps are in E major count: G-1, D-2, A-3, E-4. E major has 4 sharps. To find out how many flats Eb major has count from C in reverse order: F-1, Bb-2, Eb-3. Eb major has 3 flats.

# Circle of Fourths

Reversing the order of the circle of fifths produces the circle of fourths. That is, by reading the circle counterclockwise. Recall a perfect fourth is two notes separated by five half-steps. Therefore a perfect fourth above G is C. A perfect fourth above C is F, and so on. Notice the pattern on the diagram above.

The circle of fifths demonstrate three important musical concepts:

- the perfect fourth above a note,
- the perfect fifth above a note,
- the number of sharps or flats in a scale.