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Harmony.

Harmony is the bare minimum of two notes played together. Pairing two notes together from the chromatic scale gives 66 possible outcomes, groups of three will give us even more possibilities. While that is a lot of options, not all of them will sound that good. If that is what you are going for, great, but if you are looking for harmonious sound, you need to follow some guidelines.

Stacking 3rds.

I have previously written about constructing a sale that is guarantied to have notes that sound good when played in a sequence.

From each note in the scale, we can pick other notes from the same scale and build up a harmony. There are seven notes in the scale, so there are also seven harmonies that can be constructed.

The harmony can be a group of 3, 4, 5... notes. The more notes that are in the harmony, the more color is has. The smallest block used in popular music (or almost all western music) is a group of three, called a triad.

The formula is simple: Pick every other note until you have a group of three notes.

It makes most sense to start on the far left and pick note 1, 3 and 5. Note 1 will become the root, the 3 will become the 3rd and the 5 will be the 5th. Then move onto the second note and pick 2, 4 and 6. The 2 will now become the root, the 4 will become 3rd and the 6 will be the 5th.

As this is done for all the notes in the scale, the intervals between the notes will vary. This gives each harmony its own characteristic and the name of the chord will be derived from it.

7th.

But let's not stop there. Let's create a group of four notes by adding the 7th.

A reminder, jumping one box to the left is a ½ steps (half step), jumping two boxes to the left is a 1 step (whole step).

• 1 ⇒ 3 : 2 whole steps
• 3 ⇒ 5 : 1 and ½ steps
• 5 ⇒ 7 : 2 whole steps

This internal configuration, 2 whole steps over 1 and ½ steps is called major. Major chords get a capital letter in the Roman numeral system, and since this is the first chord in the scale it will be labeled as I. This configuration also tells up this there is a perfect 5th in the chord as well as a major 7th. The full name of the chord is therefor maj7. If this was, let's say, the C scale, this could be the C major seventh chord and would be notated as Cmaj7.

• 1 ⇒ 3 : 1 and ½ steps
• 3 ⇒ 5 : 2 whole steps
• 5 ⇒ 7 : 1 and ½ steps

This internal configuration, 1 and ½ steps over 2 whole steps is called minor. Minor chords get a lowercase letter in the Roman numeral system, and since this is the second chord in the scale it will be labeled as ii. The chord has a perfect 5th and a minor 7th. If this was, again, the C scale, this could be the D minor seventh chord and would be notated as Dm7.

• 1 ⇒ 3 : 1 and ½ steps
• 3 ⇒ 5 : 2 whole steps
• 5 ⇒ 7 : 1 and ½ steps

This is the same internal configuration as before, so a minor chord, labeled as iii, In the C scale, this would be Em7.

• 1 ⇒ 3 : 2 whole steps
• 3 ⇒ 5 : 1 and ½ steps
• 5 ⇒ 7 : 2 whole steps

This one has the same configuration as the I chord, so a major. It is the fourth chord, it will gets the Roman numeral of IV and in the C scale, it would be Fmaj7.

• 1 ⇒ 3 : 2 whole steps
• 3 ⇒ 5 : 1 and ½ steps
• 5 ⇒ 7 : 1 and ½ steps

This configuration is the same as the I chord between 1 ⇒ 3 and 3, ⇒ 5 making it a major chord. But it differ in the 5 ⇒ 7 interval, making it a minor seventh. It still gets a capital V but no maj, just the 7. IN the scale of C, this would be G7.

• 1 ⇒ 3 : 1 and ½ steps
• 3 ⇒ 5 : 2 whole steps
• 5 ⇒ 7 : 1 and ½ steps

Another minor chord. This time the vi chord. In the C scale, it would be an Am or A minor.

• 1 ⇒ 3 : 1 and ½ steps
• 3 ⇒ 5 : 1 and ½ steps
• 5 ⇒ 7 : 2 whole steps

We haven't seen this 1 and ½ steps over 1 and ½ steps before. This configuration has the same 1 ⇒ 3 interval as the minor chords, so this is a minor chord and in the Roman numeral system it will still get a lowercase label. It has a minor 7th, but is has a flat 5. The full name would then be m7♭5 and in the key of C, it is the Bm7♭5.

To get a better overview, we can have a look at it in a table

In popular music, the 7 is sometimes used, often called the Dominant 7, specially in blues. One will sometimes see the m7 in acoustic rock music. Neil Young uses it quite a bit in his early songs. Probable to get that acoustic mellow-guitar sound. The maj7 is almost never used and if it is, it is used as a novelty. A good example is Something by The Beatles. The m7♭5 is almost never used

You might have noticed that even though there are seven chords in the diatonic scale, there are only four types of chords: major, minor, dominant (which is a major chord with a flat 7) and diminished. On the guitar they could look something like this.

Movable, root six string.

Aligning the roots.

If this all is still a little bit of a blur, There is another way of looking at it. Shifting the boxes so that the root or the 1st note always lends on the far left, it becomes clear how the internals differ between the chord types. Compare this table to how the open guitar chords (A shape) are constructed. One can see how the 3rds 5ths and 7ths shift up or down by one depending on the chord type.

Open chords, A shape.

9th and beyond, the extensions.

The 7th has been stack onto the harmony, but why stop there, how about the 9th? Hold on... aren't there only seven notes in the diatonic scale, how could there possible be a 9th? That easy, we just go round in a loop ending up at the 2nd stop, or the 9th spot depending on how you are reading it.

Likewise there also the 11th and the 13th. By that time we have completed all the notes in the scale.

Anything beyond the 7th is considered an extension. It is available for coloring of the chord progression but not required for the progression. Often Jazz songs will be written out with only the 7th noted, then it is up to the musician to add more (or less) extensions depending on the mood of the song (or the instrument player).