Structure and character
To create a sixth chord you have to add a major 6th to a major chord. Sixth chords do NOT contain a 7th!
A major 6th can be found a whole step (2 frets) above the 5th or a half step (1 fret) below the minor 7th.
You are allowed to omit the 5th when you play a 6th chord.
Sixth chords have a dark, melancholic character. They create less tension than seventh chords and therefore don't tend that much towards a next chord change.
Guitar chord shapes for sixth chords
Changing the basic C major chord shape into C6
Taking the "classic" C major chord shape we can raise the G by two frets (a whole step) to get a 6th. So we're giving up the 5th G for the 6th A here.
To change the C major chord into a C6 in that way, drag the slider below the chord shape to the right
If you look closely you will recognise that it looks like going for an Am chord, but playing a C as bass note instead of A.
C6 can be seen as Am (or Am7) chord with the minor 3rd as the lowest note.
Creating C6 with the parallel Am chord
Ok, let's create some more C6 chord shapes by taking an Am or Am7 somewhere on the upper four strings and then add a C in the bass on low E string or A string. Here are some examples:
Creating G6 with the parallel Em (Em7) chord
If we can see C6 as Am/C or Am7/C, we should be able to derive G6 from Em (Em7) chords!
G6 can be seen as Em (respectively Em7) chord with the minor 3rd G in the bass.
Looking at the last pair of Em7 and G6, it becomes evident that sometimes we don't even need to change the chord shape to play a different chord type. It just depends which chord tone is considered the root respectively which tone would be played by the bass player (no matter whether there is a bass player or not - it just works!).
Minor 6th chord (m6)
If we want to play a minor 6th chord, we can take a major 6th chord and change the major 3rd to a minor 3rd.
In the shown chord diagram you can see a C6 with a major 3rd E changing to a Cm6 with a minor 3rd Eb by using the slider below the chord shape.
Special appearances of 6ths in chords
Minor chord with minor 6th (mb6)
You'll practically stumble across mb6 chords, but they're normally written as slash chords. Cmb6 for example will be written as Ab/C.
A 6/9 chord is a 6th chord with an additional 9th. Its main field of application is the use as final chord of a song. If we would follow a consistent syntax where we write chord extensions in brackets, it would be more appropriate to write 6(9) instead of 6/9. However, the notation with a slash has established itself and has nothing to do with the so-called slash chords.
6th and 7th in one chord: 6 vs. 13
In case a chord contains a 7th and a 6th, in the chord symbol the 6th is notated with as 13 (instead of 6), because then the 6th is an extension of a 7th chord. No matter whether we count 6 or 13 scale tones up from a root note, we'll end up with an equally named note. The absolute pitch of the note is not important for the chord type - 6 and 13 both mean a 6th, but writing 13 tells the player that there is also a 7th in the chord → G13 e.g. is a G7 with an additional 6th. It can also be written G7(13).
In case a chord contains a 6th and a 7th (or maj7),
"13" is notated in the chord symbol instead of "6".
Chord progressions with 6th chords
Reduction of the harmonic movement
The two chords Imaj7 and IVmaj7 (here in G major) are often enough to provid the basis for a whole song. "Waiting In Vain" by Bob Marley is a well-known example.
Theoretically you can always add a 9 to a maj7 chord. If we do so and replace the Gmaj7 with a G6 chord, we end up moving the bass tone only. Sometimes it may be good to play that variation just from time to time.
Common chord tones and a melancholy mood are the purpose to modificate the standard chord progression of this example. The result may remind you of Lionel Richies "Hello".
Standard chord progression in A minor:
Modified chord progression:
Creating harmonic movement
Instead of playing just one chord (e.g. 7, maj7, m7, major, minor) for two or more bars, a corresponding sixth chord is often inserted to be played alternately with the original chord.
More movement with inserted 6th chords:
Reducing the bass movement
Two-five-one progression (IIm7 V7 Imaj7) extended by a VIm7 chord (very common):
The chord shapes are shown in the previous example.
The Dm6 chord can be seen as a G7(9) without the root. C6 has exactly the same tones as Am7.
Chord progression with bVII7 chord (here: G7 chord in A major).
Again the G7 is replaced by a Dm6 chord. It doesn't matter that Dm6 contains the tones of G7(9) instead of G7(13). You can normally switch between the chord extensions 9 and 13 in nearly every situation. So wherever a G7(13) is written, you can normally play a G7(9) instead.
A melody that is ascending or descending in half steps (chromatic line) is generated by changing the chord type.