# Welcome to Music Theory for the Songwriter!!

## Theory Lesson 4: Chord Formation

Chords are made up of intervals. You can figure them out either by:
1 - counting the Halfsteps,
OR
2 - by applying the interval formula.

#### 1. Counting the Halfsteps

(H = Halfsteps)

```Major chords are made up of:        4H + 3H
minor chords are made up of:        3H + 4H
diminished chords are made up of:   3H + 3H
Augmented chords are made up of:    4H + 4H
```

For example:
The notes for the C Major chord are C, E, and G. From C to E is 4 Half steps. From E to G is 3 Halfsteps. If you didn't know what the notes were, you would start at C and count 4 Halfsteps which would take you to E. Then from E you would count 3 Halfsteps which would take you to G.

You can do this to figure out any Major chord.
The degree numbers for each note in the C Major chord are:

the C is the 1st degree
the E is the 3rd degree
the G is the 5th degree

Figure out other Major chords (like F Maj or G Maj) & then see what degree numbers they are. Once you know how to figure out the Major chord...from there it's easy to find out what the minor, diminished or Augmented chords are.

If you lower the 3rd degree (deg) of a C Major chord by a half step, you get C Eb G...a C minor chord. Count the halfsteps between the intervals to see that it is 3H + 4H.
If you lower the 3rd and the 5th degrees by a half step each you get C Eb Gb...a C diminished chord. Count the halfsteps between the intervals to see that it is 3H + 3H.
If you raise the 5th degree of a C Major chord by a half step, you get C E G# ... a C Augmented chord. Count the halfsteps between the intervals to see that it is 4H + 4H.

Examples other than C Major. Let's say you want to know what a Ddim chord is. First figure out what the DMaj chord is:

Begin with D, count 4 H to F#, then count 3 more H, taking you up to A.
So DMaj then is: D, F#, A.

To make this diminished, lower both the 3rd and the 5th (lower the F# and the A). That will make it D, F, Ab.
So Ddim is D, F, Ab.

That was the easy way. My special trick...it's how I first learned to play chords on the keyboard. The following is the way to understand why that works...it's more the theory part of it.

#### 2. Applying the Interval Formula

If you take a closer look at the intervals between the notes in the C Maj chord, you'll see:

the interval between the C and the E is a Major 3rd (M3)...
the interval between the E and the G is a minor 3rd (m3)...
the interval between the C and the G is a Perfect 5th (P5).

Here is the interval formula for each interval quality.
M = Major m = minor d = diminished A = Augmented

```Major chord:      M3 + m3 ... the 5th is Perfect  (C to G)
minor chord:      m3 + M3 ... the 5th is Perfect  (C to G)
diminished chord: m3 + m3 ... the 5th is diminished (C to Gb)
Augmented chord:  M3 + M3 ... the 5th is Augmented  (C to G#)

Let's look at the different C chords and break them down so you can see
this.

Chord             Lower 3rd        Upper 3rd            5th

CM is C E  G      C to E  is M3    E  to G  is m3      C to G is a P5
Cm is C Eb G      C to Eb is m3    Eb to G  is M3      C to G is a P5
Cd is C Eb Gb     C to Eb is m3    Eb to Gb is m3      C to Gb is d5
CA is C E  G#     C to E  is M3    E  to G# is M3      C to G# is A5

(M= Major;  m= minor;  d= diminished;  A= Augmented)

Knowing and understanding this formula then enables you to work out any
chord without having to look it up.

To figure out minor, diminished or Augmented chords you could either figure
out the Major chord and then make the changes to the 3rd and/or 5th degrees
as was just explained, OR, you could simply apply the proper formula. Which
method you prefer will depend on your individuality. Some may find the
formula method easier while others may prefer not to memorize more than the
Major chord formula and simply make the necessary changes to the Major form
of the chord.

To figure out any minor chord, you could either apply the minor chord
formula (m3 + M3) which would be memorized in addition to the Major chord
formula (M3 + m3), Or you could use the Major chord formula and then lower
the 3rd degree one half step to make it a minor chord.

Below is an example of both methods for finding a minor chord.

Gm:
minor formula: m3 + M3 = G Bb D
Major formula: M3 + m3 = G B  D.....lower the 3rd deg = G Bb D

Theory Lessons

Theory Lesson 1: Scales

Theory Lesson 2: Key Signatures

Theory Lesson 3: Intervals

Theory Lesson 5: Modes