Relationships Between Keys - The Circle of Fifths
This is the circle of fifths. It shows all 12 major keys and 12 minor keys possible in the western system. The name "circle of fifths" comes from the fact that the tonic pitch of a key (which is the same as the name of the key) changes by a perfect 5th each time you add or remove an accidental: it goes up a 5th each time you add a sharp or remove a flat, and it goes down a fifth each time you add a flat or remove a sharp. That is, if we start at C, which has no sharps or flats, and go up a perfect 5th, we get G, and the key of G has one sharp. It should be noted that flats and sharps are always added in a specific order.
Just as there are 12 discreet pitches in the western system (and thus, in the chromatic scale), there are 12 major and 12 minor keys possible in the western system. On this particular circle of fifths, the major keys are listed on the outer circle, and the minor keys are on the inner circle. It is important to note that when discussing keys, if major or minor is not stated explicitly, the major key is assumed. That is, when something is described simply as being in the key of C, that is understood to mean that it is in the key of C major.
The keys at the bottom of the circle of fifths have two names because they are enharmonic equivalents. The principle of enharmonic equivalence is the same for keys and scales as it is for individual pitches. Enharmonic keys occur when the same set of pitches can be indicated with either sharps or flats. For example, the key of D-flat has 5 flats and the key of C-sharp has 7 sharps. Just as the pitch D-flat is the same as C-sharp, so are the sets of pitches in their respective keys. If we look at each note in the D-flat and C-sharp major scales, we can see that each scale degree is enharmonically equivalent.
|D-flat Major Scale:||D-flat||E-flat||F||G-flat||A-flat||B-flat||C||D-flat|
|C-sharp Major Scale:||C-sharp||D-sharp||E-sharp||F-sharp||G-sharp||A-sharp||B-sharp||C-sharp|
Parallel and Relative Keys
We learned about the concept of relative and parallel relationships in the section on scales, and these relationships apply equally to keys. In the circle of fifths above, the keys are aligned in slices according to their key signatures. Since two keys are considered relative if they share the same collection of pitches, the major and minor keys that are aligned in each slice are relative keys (examples: G major and E minor, E-flat major and C minor).
|Key Signature:||no sharps or flats||1 sharp||2 sharps||3 sharps||4 sharps||5 sharps or 7 flats||6 sharps or 6 flats||5 flats or 7 sharps||4 flats||3 flats||2 flats||1 flat|
|Major Keys:||C||G||D||A||E||B or C-flat||F-sharp or G-flat||D-flat or C-sharp||A-flat||E-flat||B-flat||F|
|Minor Keys:||A||E||B||F-sharp||C-sharp||G-sharp or A-flat||D-sharp or E-flat||B-flat or A-sharp||F||C||G||D|
Keys in the circle of fifths that have the same tonic pitch are parallel keys. In the table below, you will see the key signatures required to have a major or minor key for each tonic pitch.
|Tonic Pitch (Key Name):||C||G||D||A||E||B or
|F-sharp or G-flat||D-flat or C-sharp||G-sharp or A-flat||D-sharp or E-flat||B-flat or A-sharp||F|
|Key Signature for Major Key:||no sharps or flats||1 sharp||2 sharps||3 sharps||4 sharps||5 sharps or 7 flats||6 sharps or 6 flats||5 flats or 7 sharps||4 flats||3 flats||2 flats||1 flat|
|Key Signature for Minor Key:||3 flats||2 flats||1 flat||no sharps or flats||1 sharp||2 sharps||3 sharps||4 sharps||5 sharps or 7 flats||6 sharps or 6 flats||5 flats or 7 sharps||4 flats|