Music Theory: Building Chords That Work Together

My friend Denis emailed me the other day with some questions about music theory. Ever since I was finally able to digest the fundamentals of the subject in a way that made sense to me and was actually useful for songwriting/composition/performing, I've become quite keen about sharing it with others in case it becomes helpful in the same way it was to me. It's fun to talk about because it's sort of like math. I figured I might as well post this quick little tutorial since he said it cleared up a few things.

Below is a brief explanation about how to generate the 7 different diatonic chords in a major key. Simply put, these are the basic 7 chords that you can start off working with if you are writing a song in a certain key. Think of it as having a palette of 7 different colors, with which you can use to paint a picture. I don't know.

---------

Say you're in the key of C. All your chords are going to be built from the tones in that scale (C-D-E-F-G-A-B).

When you build a chord on any of those 7 different roots, you start with that root and take every 2nd tone after that until you have a triad (C-E-G for example, if you're doing the 1 chord). in the case of A minor (your 6 chord) it's going to be A-C-E.

Both of these chords, C major and A minor, are triads, but they have different sonorities. What creates the sonority is small differences in the structure of the triad.

To create a major sonority in a triad, you need two intervals: a major third followed by a minor third (for example, in C major, C-E is a major third (4 semitones) and E-G is a minor third (3 semitones). A minor chord is the other way around - minor third followed by major third. So in A minor, you've got A-C (3 semitones; minor 3rd) and C-E (major third).

In the same way that you need the right sequence of intervals to build a chord of a certain sonority, the same goes for scales. A major scale is constructed from a specific sequences of Whole Tones (2 semitones) and semitones. The sequence looks like this:
C - D - E - F - G - A - B - C
W W S W W W S (W= whole tone, S-semi tone)

This is where music gets super math. Think of that as a basic formula for generating your major scale. Now remember that a major scale is what we use to generate all our chords - the fact that we have to adhere to this formula means that the sonority of a chord in each numerical position is consistent, regardless of the parent scale. Take F major, for example:

F - G - A - Bb - C - D - E
W W S W W W S

Notice that while the specific pitches in the top row are different, the interval pattern in the bottom row is the same. Meaning if you take the 4 in either of these scales and build a chord on it (F in the key of C, Bb in the case of F) you end up with a major third/minor third interval sequence in both cases. Hence, the 4 chord is always major. That's what's being referred to in that one sentence you asked about: "A third of an A minor is C because the 6 chord in a major key is always minor". Basically just talking about that pattern.


So then. If that all makes sense, you will end up with a universal pattern of chord sonorities in any major key:
1 - Major
2 - Major
3 - Minor
4 - Major
5 - Major
6 - Minor
7 - Diminished*

* in the diminished chord, the interval sequence is a minor 3rd followed by another minor 3rd.