I am reading though Dariusz Terefenko's Jazz theory book, and in the chapter on Improvisation (chapter 10) he lists a few typical 1-, 2- and 4-bars blues riffs, all on a Bb blues scale. Several of these riffs have an F flat, as in the example below:
Is there a particular reason why the 3rd, 4th, and 5th notes of the fragment are notated as F/Fb/E (with the b implied by the key signature), instead of F/E-natural/E ?