How to play maj7 chords
The maj7 chord is defined by its major 7th. A major 7th is a half step(1 fret) up from a regular 7. Maj7 chords can be played both in open position and as moveable shapes. Let's first take a look at the most common open position maj7 chords:
Open position maj7 chords
These four chords are very useable. They sound great and are easy to play.
Emaj7 and Gmaj7 are a little bit trickier to play in open position and the Emaj7 chord doesn't always sound very good, cause it can get very dark and blurry, especially if you use thick strings.
Movable maj7 chords
The following chord shapes can be moved anywhere on the neck. For example if you move the Bmaj7 chord shape down 2 frets it becomes an Amaj7. If you move it up a half fret it becomes a Cmaj7 and so on.
Most of these movable chords are simply versions of the common open position chords. Instead of the nut you use your index finger, that is the only difference. For example the second Bmaj7 chord below is the same as the open Amaj7 chord, but 2 frets up, with your index finger holding a barre grip. The two chord shapes below are the most common maj7 shapes and if you only learn two maj7 chord shapes, these are the ones to learn. They work great in all keys, all over the neck.
The next two movable maj7 shapes use only the 4 thinnest strings(D, G, B and E). This makes the sound a bit lighter. Notice that the first shape comes from the open Fmaj7 chord and the second shape from the open Dmaj7 chord.
As I mentioned earlier, the major 7th is a half step(1 fret) up from a regular 7th. Another way to look at it is that the major 7th is a half step down from the root or the "8th". Understanding the theory is important if you want to get into more advanced chord playing. But learning the theory also helps you to memorize these patterns. A good exercise is to try to find out where the major 7th is in each of these chord shapes. I can help you to get started. On the Cmaj7, the major 7th is on the open B-string. On the Fmaj7 the major 7th is on the E string. Now see if you can figure out the rest of them.