Extensions are simply Major, minor, or Dominant 7th chords with one or more scale steps added to the formulas.
To make an extended chord from the major chord, we take all the notes from the major chord, specifically the root, 3rd, and 5th scale step, and add more notes based off of the same scale. In Example 1 below we see the C Major scale. Below the scale, the steps of the scale are numbered. While there are only 7 notes in the Major scale, there are 15 steps in this diagram. This is the major scale in two octaves. The notes in parethesis are the root note (C).
Remember that a major chord is composed of the root, 3rd, and 5th scale step (in parethesis):
To build an extended chord we simply add more scale steps. In Example 3 you see all the scale steps commonly included in extensions.
Most extensions are named for the last scale step included. For example a Major 9th chord is constructed using the root, 3rd, 5th, 7th, and 9th scale step. A Major 11th chord is constructed using the root, 3rd, 5th, 7th, 9th, and 11th scale step.
Minor Chord extensions work in the same way major chord are extended, except we extend from the minor triad consisting of the root, flat 3rd, and 5th scale step.
Dominant 7th chords are extended just the same as major chord extensions, except they always have a lowered 7th step (flat 7).
Take a look at chord formulas to see different chord extensions and the formulas that make them.
Not all the scale steps in the chord formula are necessarily needed in the actual chord played. A 13th chord has 7 notes in it and a guitar has only six strings! That’s okay, because some notes of the chord can be ommitted. They’re not all needed to create the desired tonal color. For example, the 5th step is often not used as it is common with Major, minor, and Dominat 7th chords. Whereas the 3rd is usually included because it establishes if the chord is major or minor.