Wednesday, March 27, 2013

The Circle of Fifths in Relationship to Key Signatures

The circle of fifths is a useful tool to determine the relative major and minor key signatures, as well as the relationships between the number of sharps and flats, and the name of the key.

Relative Minor and Major Key Signatures

Relative minor and major keys are keys that share the same key signature. For instance, G Major has 1 sharp and E minor also has 1 sharp. Because they share the same number of sharps they are considered relative to each other.

To determine the relative minor of a major key, simply find the major key and match it with its minor equivalent. For instance, G major is the relative major of e minor because they have 1 sharp each. To find the relative major just go in the opposite direction. E minor is the relative minor of G major for the same reason.

Parallel Minor and Major Key Signatures

Parallel minor and major keys are keys that share the same tonic, or key name. For instance, D Major and d minor may have different relative key signatures, but they share the same tonic. Because of this D major is said to be parallel to d minor.

Given this information, you can easily see that D Major has 2 sharps while d minor has 1 flat. One easy way to determine the parallel major key signature from a minor key signature is to add 3 sharps. In the case of D minor, adding three sharps will give you 2 sharps in the key signature. As another example, e minor has 1 sharp, so it's parallel major must have 4 sharps. If you look at the circle of fifths, you will see that this is, in fact, correct.

To go from major to minor, simply add three flats. Let's try A Major:

A Major has 3 sharps, so we need to add 3 flats to get it's parallel minor key signature. 3 flats cancel out the 3 sharps and you are left with no sharps or flats. After checking with the Circle of Fifths, this is correct as the minor key with no sharps or flats is a minor.

Remember that a sharp cancels out a flat, and a flat cancels out a sharp.

The Order of Sharps and Flats

The final concept that the Circle of Fifths simplifies is determining the order of sharps and flats. This order is the order in which they appear in the key signature.

For sharps, you simply start with the key that has one sharp and work your way around moving in fifths:

F# C# G# D# A# E# B# (Note that I am referring to the actual key signatures in the circle of fifths and not the names of the keys.)

For flats you start with the key that has one flat and proceed by adding flats to the key signature:

Bb Eb Ab Db Gb Cb Fb

Notice that the order of flats is the order of sharps backwards and vice-versa. Note that with sharps you have to start with F# on the top line and keep each additional sharp as close to F# as possible as long as they stay within the staff. A# is placed lower because it would leave the staff if it was placed above. With flats, you have to start with Bb in the center of the staff and follow the same sort of logic.