Minor Keys
Songs in minor keys are relatively rare in modern popular music, but aren't uncommon in folk, rock, and other older genres of music. Understanding how chords and numbers work in minor keys starts with a look at the minor scale.
The minor scale is built off the 6th degree (or note) of a major scale/key, shares the same notes and is referred to as the relative minor of that major scale/key. For example, the 6th degree of the C major scale is A minor. A minor's scale notes are (A, B, C, D, E, F, G, A) and it is referred to as relative to C major. A song can be completely in a minor key or one section in a minor key and another part in its relative major.
A few more examples:
D minor is relative to F major (D is the 6th degree of an F major scale) . The D minor scale shares notes with the F major scale, only starting on D (D, E, F, G, A, Bb, C, D).
G major's relative minor is E minor (E, F#, G, A, B, C, D, E).
G minor is relative to Bb major and share's Bb's key signature (G, A, Bb, C, D, Eb, F, G).
D major is relative to B minor (B, C#, D, E, F#, G, A, B).
The minor scale in numbers looks like this
1, 2, b3, 4, 5, b6, b7, 1
Chords built off the minor scale look quite a bit different than what we're used to:
1m, 2˚, b3, 4m, 5m, b6, b7, 1m
The minor scale lacks something important found in major scale harmony: a leading tone. The leading tone, or L.T., are the 1/2 steps in the major scale between scale degrees 3/4 and 7/8 (In C major: E/F and B/C). These scale degrees strongly have a tendency to resolve (7 wants strongly to resolve up to 1, 4 wants strongly to resolve down to 3).
The most important instance of this in a major key is in the progression 5 to 1 (scale degree 7 in the 5 chord resolving to 1 in the 1 chord). This is such an important aspect of harmony that some argue that most music effectively boils down to 5 going to 1 (more can be read about this in the harmonic function guide). Because of the power of the leading tone, the minor scale often comes with a raised 7th degree to create the same effect.
The minor scale in numbers with a raised 7th (leading tone).
1, 2, b3, 4, 5, b6, 7, 1
With a raised 7th, the minor scale's chords change: the 5 chord becomes major and the 7 becomes diminished. Most importantly, a proper 5 to 1 is possible with just as much pull as with a major scale.
1m, 2˚, b3, 4m, 5, b6, 7˚, 1
The major 5 strongly helps a song to firmly sound in a minor key. Without the major 5, a minor key's chords are shared with its relative major and is a bit more ambiguous to whether it's in a minor key or the relative major. With the major 5, the 1 minor is strongly tonicized, or successfully made to sound like our home key.
For example:
I: 6m 6m 4 4 / 6m 6m 4 4
V: 6m 6m 4 4 / 6m 6m 4 4 / 1 1 4 4 / 1 1 4 4
C: 6m 6m 4 4 / 6m 6m 4 4
This song has chords entirely from C major but really rests and sounds like it's in A minor.
By contrast:
The Rolling Stones, Paint it Black (Em)
V: 1m 1m 5 5 / 1m 1m 5 5
C: (1m b7) (b3 b7) 1m 1m / (1m b7) (b3 b7) 4 5
Paint it Black sounds firmly in the key of Em because of the major 5. Even though the 7th isn't raised in the b7 chord, it's just a passing chord in-between the bigger details (minor 1 and major 5) and a good example of how these elements can mix. The major 4 (normally minor in a minor key) can be thought of as a bit of mode mixture.