Dizzy’s World comes alive under the leadership of Gillespie protege John Faddis. The band includes James Moody or Don Braden on reeds, Slide Hampton on trombone, Mulgrew Miller on piano, Chuck Loeb on guitar, John Lee on bass, and Ignacio Berroa, Duduka Da Fonseca, and Duke on percussion. Chris White makes a vocal cameo on his own “Barbados Carnival,” a spirited detour from the path of music associated with Gillespie. The repertoire avoids most of the obvious choices, and includes arrangements of three of the five movements of Lalo Schifrin’s Gillespiana Suite. Faddis is superb, his homage less a matter here of technique and more of style.