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Watch the C Major 6 Chord Inversions online guitar lesson by Frank Vignola from Inversion Excursion

Now that you have a good grasp on the triads and major 7th chords let's move on to playing major 6 and major 6/9 chords and the various inversions. We start with adding the major 6th to the triad to make a C major 6th chord. Remember: a triad is a three note chord consisting of the 1st, 3rd and 5th step of the applicable scale. In this case C, E and G spell the C major triad. Adding an extension to the triad creates a 4 note chord. In this case we are adding the 6th step of the scale to the C major triad. The 6th step of the C scale is A or the major 6th. So the spelling of a C major 6th chord is: C-E-G-A or 1-3-5-6. You may notice that these are the same notes as the A minor 7th chord. A C major 6th chord inverted with the A in the lowest voice is also an A minor 7th.
Next we will add the 9th to the major 6th chord making C 6/9 chords. Now that we are adding 2 extensions to the triad, they are essentially 5 note chords. The spelling of a C major 6/9 chord is C-E-G-A-D. The 1st, 3rd, 5th, 6th and 9th of the C major scale. Since we are using 4 note chords, we will be leaving one of the 5 notes out of the chord creating even more inversions on our excursion through inversions. For each inversion, look at the chord and pick out each of the chord tones naming the notes.
Let's start inverting. In this case, when playing the A in the bass this is considered the 3rd inversion. Root position has root in the bass, 1st inversion has the 3rd in the bass, 2nd inversion has the 5th in the bass and the 3rd inversion has the extension or in this case the 6th in the bass. When we play the 9th or D in the bass this is considered the 4th inversion.