Major 7 Chord Construction
Jazz harmony is (traditionally) founded on chords constructed in thirds.
Let's take a C major seventh chord. It is made up of C, E, G and B.
You can notice that the interval between the first two notes is a major third.
The interval between the second (E) and third note (G) is a minor third.
To finish, the interval between G and B is a major third. This is how a major seventh chord is built.

The other way to build major 7 chords is to take the first (1), the third (3), the perfect fifth (5) and the major seventh (7) of the major scale.
For example, the major scale formula is: root (1), second (2), major third (3), fourth (4), fifth (5), sixth (6) and seventh (7).
You just have to take the first, the third, the fifth and the seventh of any major scale and you will get a major seventh chord.
As it is shown below you can see that the C major 7 chord has an additional note (the seventh) in comparison with the basic major chord.
| C major scale |
C |
D |
E |
F |
G |
A |
B |
| Formula |
1 |
2 (9) |
3 |
4 (11) |
5 |
6 (13) |
7 |
| C major chord |
C |
X |
E |
X |
G |
X |
X |
| C major seventh chord |
C |
X |
E |
X |
G |
X |
B |
Abbreviated Chord Symbols
There are several different ways of writing the same chord or scale sound. It is often complicated for a jazz student to become familiar with all the nomenclatures for writing chords.
The most used symbols for major seventh chords (example in C) are CM7, C? and maj7.