Watch the Major Arpeggios online guitar lesson by John Stowell from Modern Jazz Improv

When playing dominant 11th or suspended chords, very often I'll use the major 3rd in the chord as well, sometimes in the same octave as the 4th (11th). If an 11th chord is called for in a tune, the major 3rd (and occasionally some tensions, especially the b9) can and should be used in your improvised lines. Use Herbie Hancock's "Maiden Voyage" and the great solos that he, George Coleman and Freddie Hubbard take on that tune as references for ideas to play over suspended chords. Note that the b2 and b5 major arpeggios, which generate various tensions over the dominant chord, are also used to outline the Phrygian and Locrian modes, respectively.