C major is the home key of Western common practice notation. It contains no sharps or flats in its key signature.
Major and minor keys can be related to each other in two ways. A parallel relationship is where the keys share the same tonic, or the same starting pitch. In this case, the two keys will have different key signatures. A relative relationship is where the keys share the same key signature. In this case, the two keys will have a different tonic. The relationship between major and minor keys on the circle of fifths is relative because they share key signatures but have different tonics.
You can always calculate the relative key by either descending three half steps from a major key to the relative minor or ascending three half steps from a minor key to the relative major. In the example, the relative minor of Bb major is G minor and vice versa.
Bb Major: Two Flats (Bb, Eb)
Bb Minor: Five Flats (Bb, Eb, Ab, Db, Gb)
The distance between relative keys is three half steps, in this case Bb Major and G minor.
In addition to memorizing the circle of fifths, there are two other methods for determining the name of any key. For sharp keys, find the last sharp of the key signature and go up one half step. This note is the name of the major key. For flat keys, find the second to last flat in the key signature, this is the name of the major key. To find the name of the minor key, go down three half steps from the name of the major key. This works for flat and sharp keys.
If the name of the key is known but the key signature isn’t, use the circle of fifths or work through these two methods in reverse to find the answer.
The last sharp in this key signature is D#. A half step above D# is E. Thus, E is the name of this major key signature.
For flat keys, find the second to last flat in the key signature, in this case, Db. This directly names the major key (Db Major).
Test your knowledge on this chapter’s material before moving on.
The Circle of Fifths
The order of sharps and flats can be represented by a diagram called the circle of fifths, so named because the distance between two adjacent positions on the circle are five letter names apart. Think of the circle as a clock face. Moving clockwise adds sharps to the key signature and moving counter-clockwise adds flats. C major, which has no sharps or flats in the key signature, is positioned at twelve o’clock. Moving one position clockwise ascends by a fifth or five letter names; C, D, E, F, G. Thus, G major is the next key in the circle of fifths and contains one sharp in the key signature. Moving to the next position in clockwise order ascends a fifth from G to D; G, A, B, C, D. Thus, D major has two sharps in the key signature. The next position is A, three sharps, then E, four sharps, etc., until the maximum number of seven sharps.
It is important to note that the distance of a fifth, or from one position on the circle to the next adjacent position, is precisely seven half steps. We can see why this is important when ascending from B to F#. If we simply ascended by five letters, we would arrive at F, which is not correct. But counting exactly seven half steps ensures we arrive at the correct pitch.
Moving counter-clockwise on the circle works exactly the same as ascending, just in reverse. Each position is a fifth, or seven half steps, below the previous position. For example, moving one position counter-clockwise from C is F; C, B, A, G, F. F major has one flat; Bb. The next position is Bb; F, E, D, C, Bb. Bb has two flats; Bb and Eb. We know that Bb is the correct answer and not B for two reasons: seven half steps below F is Bb, not B, and B has already been used as a sharp key. There are no duplicates on the circle of fifths. Continuing down the circle of fifths produces Eb, Ab, Db, Gb, and Cb. At the bottom of the circle there are three keys that have the same tonic, or sounding pitch, but are spelled differently. These are enharmonically equivalent keys; they sound the same but are spelled differently.
The circle works exactly the same for minor key signatures. The key positioned at twelve o’clock is A minor, which has no sharps or flats. Moving clockwise ascends by fifth to E minor, one sharp, then B minor, two sharps, etc. Moving counter-clockwise descends by fifth from A minor to D minor, one flat, then G minor, two flats, etc.
To help differentiate between major and minor, write minor with a lowercase m: For example, C major is written as C and C minor is written as Cm.