Major 9th Chords derive from Major 7ths by adding the 9 note to the Major 7th. So it contains 1; 3; 5; 7&9 notes.
Just as in the Dom9th chords the root note is implied because the 9 note 'hides' the root note.
Let's look at some forms of this Chord:
CM9 = CM7 9 (D) C#M9 = C#M7 9 (D#) on 3string DM9 = DM7 9 (E) on C string
Although the shapes first seem to be quite different, only the root note rises up 1 whole tone (or 2 frets)......
In these examples the same formula holds true, but in these cases the resultant chord shape is inverted to a more
comfortable position on the fretboard.
Yet one other 'chameleon' effect is uncovered in this series of chords. It is this. The final Major 9th chord is
the exact shape and position as the Minor 7th found 4 frets or two whole tones higher up the neck of the Ukulele !
So, the CM9 = Em7; C#M9 = Fm7 and so on. As an exercise, name each of the Min7s relative to the M9s I have
shown in the above examples and then add to your chord library by discovering more M9s/m7s.