Building Blocks: The Circle of 5ths

 

    By now you should have all the information you need to find a major or minor scale starting on any note.  In this lesson we will learn an easier way to find any major or minor scale.  All the scales and keys are related in various ways, but the most important relationship to take note of is that all keys are related by 5ths.

    Remember that no two major scales/keys have the exact same notes.  Every major scale or key is different by at least one note.  In fact, the major scales can be put in an order that changes only one note of the previous scale.  Let's take a look at the C Major scale:

C  D  E  F  G  A  B  C

    If we take the 5th note of the C Major scale (G) and build another major scale starting from that note we get:

G  A  B  C  D  E  F#  G

    Notice that the 4th note from the C Major scale (F) moved up one half-step to F#, and is now the 7th note in the G Major scale.  Since no two scales share the exact same notes, we can say that the key with one sharp is G Major, since no other major scales will have only one sharp.  Now let's build a major scale from the 5th note of G Major, which is D:

D  E  F#  A  B  C#  D

    Again the 4th note of the scale we started with (the C from the G Major scale) was raised a half-step to C#, and is now the 7th note of the new scale (D Major).  We can say that the key with two sharps is D Major, since we know that no other major scale will have only two sharps in it.  

    So we can see that by building a major scale from the 5th note of another major scale, one sharp is added.  Another thing to notice is the distance between each added sharp.  Starting from C Major, we built a major scale from the 5th note (G) which added F#.  Then we built another major scale from the 5th note of G Major (D) which added C#.  The distance between these two sharps is also a 5th (F# to C# is a 5th because F = 1, G = 2, A = 3, B = 4, C = 5).  All these relationships continue in the same way every time we build a new major scale from the 5th note of another major scale!  To recap what we just learned:

• Whenever we build a major scale starting from the 5th note of any other major scale it adds one sharp to the scale
• The added sharp is always on the 4th note of the previous scale, and becomes the 7th note of the new scale
• The added sharp is always a 5th higher than the sharp that was added to make the previous scale

    Another interesting relationship is that the amount of 5ths we go up from C adds the same number of sharps to the scale.  For example, Going from C to G was one 5th and added one sharp, and going from C to D was going up two 5ths and added two sharps.  Remember that the added sharp is always a 5th higher than the sharp that was added to make the previous scale.  Let's take a look at what we end up with if we continue the pattern of building major scales from the 5th of the previous major scale:

C Major = 0 sharps

G Major = 1 sharp: F#

D Major = 2 sharps: F#, C#

A Major = 3 sharps: F#, C#, G#

E Major = 4 sharps: F#, C#, G#, D#

B Major = 5 sharps: F#, C#, G#, D#, A#

F# Major = 6 sharps: F#, C#, G#, D#, A#, E#

C# Major = 7 sharps: F#, C#, G#, D#, A#, E#, B#

    We could continue this cycle by going to G# Major next, but we would have to start using double sharps since all seven letters already have sharps, and that's not very practical, so we'll stop at C#.

    One thing that's super helpful to remember is the order in which the sharps appear.  This is called, you guessed it, the "order of sharps" which goes F - C - G - D - A - E - B.  As I already mentioned, these are all a 5th apart.  I find mnemonics useful for memorizing things, so here are a few for the order of sharps:

"Funky Chickens Get Down At Every Barnyard"

"Fidel Castro Gets Drunk At Every Bar"

"Fat Cats Get Drunk At Every Barbecue"

"Father Charles Goes Down And Ends Battle"

    Since the order of sharps never changes, we know that if a key has three sharps, those three sharps are going to be F#, C#, and G#, because those are the first three sharps in the order of sharps.  Similarly, we also know that if a key has five sharps, those five sharps are going to be F#, C#, G#, D#, and A#.  

    As you might have guessed, when we go down a 5th, we take a sharp away.  If we start with D Major (two sharps, F# and C#) and move down a 5th to G Major, we take away the last sharp (C#) leaving us with just F#.  Moving down another 5th to C Major, we take away the F#, leaving us with no sharps (C Major is all plain letters from the musical alphabet, remember?)

    Moving a 5th down from C Major, there are no more sharps to take away, so what do we do?  Well it turns out that taking away a sharp is the same as "adding a flat", but which flat do we add?  We know that there are up to seven sharps possible, and that those sharps are in a specific order.  Well there are also up to seven flats possible, and they are also in a specific order.  This order happens to be the reverse order of sharps!  Check it out:

order of sharps:  F - C - G - D - A - E - B

order of flats:  B - E - A - D - G - C - F

    So if we go down a 5th from C Major, we can see that it adds one flat to the scale (Bb).  Let's see what it looks like to continue going down in 5ths from C:

C Major = 0 flats

F Major = 1 flat: Bb

Bb Major = 2 flats: Bb, Eb

Eb Major = 3 flats: Bb, Eb, Ab

Ab Major = 4 flats: Bb, Eb, Ab, Db

Db Major = 5 flats: Bb, Eb, Ab, Db, Gb

Gb Major = 6 flats: Bb, Eb, Ab, Db, Gb, Cb

Cb Major = 7 flats: Bb, Eb, Ab, Db, Gb, Cb, Fb

    Because these patterns repeat themselves in a cycle, it is common to see the information displayed within a circle which we call the "circle of 5ths".  

    Typically we don't write out all these sharps and flats in actual music.  Instead we use a "key signature".  A key signature is a marking at the beginning of a piece of music that tells us which notes will be sharp or flat throughout the song.  We typically say things like "E Major has a key signature of 4 sharps", or "Db Major has a key signature of 5 flats", etc.  

    There are seven keys that use sharps and seven keys that use flats, for a total of 15 key signatures.  As I mentioned earlier, we could theoretically continue the pattern in either direction to get keys with double sharps or double flats, but these keys are not very practical so we don't have key signatures for them.  

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