Using formulas to construct all chords

It is possible to harmonise in thirds beyond ‘7th‘ chords. These will create chords such as ‘9ths’, ‘11ths’ and ‘13ths’. These are called chord extensions.

Figure 16. The extended A major scale (Enlarge)

9th (11th & 13th)chords

Using the A major scale again, taking 1-3-5-7 creates the chord of A major 7 (Amaj7).

If the next third up the scale is added, this is the ninth note which is B. This creates the chord of A major 9th (Amaj9), (1-3-5-7-9).

Figure 17. Chord of A major 9th (Amaj9) (Enlarge)

Continuing beyond this, adding thirds, will incorporate the eleventh (11th) and then the thirteenth (13th). Note that only the ninth, or eleventh or thirteenth is added to the major 7th chord (e.g. Amaj13 = 1-3-5-7-13) at any one time.

Rules for creating chords

There are really only two rules that must be kept in mind when using formulas to create chords.

Minor chords have a flattened 3rd.
In a chord with a number in the title which is ‘7’ or higher, the 7th is ALWAYS flattened unless the word ‘major’ appears in the title (e.g. Amaj9).

As an example, we have taken the root of A and created a series of chords.

Note

Figure 18 can be extended to include 11th or 13th. Simply replace the 9th with either an 11th or 13th note. The rules for constructing the chords are exactly the same as for the 9th chords.

Figure 18. Deriving 9th chords from the (A) major scale) (Enlarge)

You can see that with 9ths you can have a minor chord with a 9th or a major 9th.

Playing the chords

When playing 9th, 11th or 13th chords, you will see that, if you play them as they are shown in the table, you will span more than an octave. So, different voicings of the chord are often used. The important thing is that all the notes are played. For example, on the keyboard, the chord of Am maj9 in the right hand might be played:

Notes:	E	G#	A	B	C
Fingers:	1	2	3	4	5

Notes:	C	E	G#	A	B
Fingers:	1	2	3	4	5

Next: Suspended chords