D → Dmaj7
That's how a basic D major chord turns to a Dmaj7.
And here the circle is closing...
Moving the root of this Dmaj7 to A string and adding a 3rd on D string instead - that's practically the same grip as the Cmaj7 we created at the beginning of this lesson (just 2 frets higher).
We can move both of the shown Dmaj7 chord shapes two frets up to get an Emaj7 chord. This will sound better and is more handy to play than modifying the "classic" open E major chord. Let the low open E string ring out - that sounds fat!
Where can we play maj7 chords?
When we build up stacks of thirds over every note of a major scale (using only notes of the scale), we obtain the modal chords of the major scale. Depending on how much thirds we stack, we'll get triads or seventh chord (or even ninth chords, etc.).
Doing this, we get maj7 chords on the 1st and 4th scale degree. If you have a song (or a part of a song) in C major, you can play Cmaj7 and Fmaj7 instead of the plain C or F chord - at least in theory. Practically it always depends on the style of music.
Further chord shapes
There are quite a few different chord shapes for maj7 chords. The root does not always have to be the lowest note, for instance if you've got a second instrument (bass, piano,...) playing the bass note, or if you're packing more than one chord shape of the same chord into a bar to make your accompaniment more interesting.
This lesson is not intended to show all possibilities. The construction of maj7 chords should be clear by now. The chord finder shows more maj7 chord shapes - fiddling out others by yourself is of course strictly allowed!