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This Bachiana was dedicated to Villa-Lobos' superior, Minister of Education Gustavo Capanema. It is the one that comes closest to the exuberant contrapuntal density of the Choros series. At over 25 minutes, it is the longest Bachiana, and is often ranked as the best work of the series, though in popularity it probably is third, after the lovely Bachiana Brasileira No. 5 and Bachiana Brasileira No. 2, with its popular "Little Train of the Caipira" movement.

Each of the four movements has two titles in Portuguese, one drawn from musical forms used by Bach, and the other making a Brazilian reference.

It opens with "Prelúdio; Ponteio," the latter being a Brazilian song form. It is a flowing aria with one of the best melodies in this tuneful series, beginning in a flowing Adagio tempo which then speeds up a bit, but slows for the conclusion, in this case to Largo.

The second movement is called "Giga; Quadrilha Caipira." The tempo marking is Allegretto scherzando. Here Villa-Lobos happily mixes together several diverse musical influences, and piles them up into his trademark dense and exciting layers. His musical return to the "caipira" is every bit as rhythmically exciting as the train ride in Bachiana No. 2. ("Caipira," has been translated as "hillbilly," but "boondocks" seems an apt term.) In this movement Bach's gigue, which itself derives from the Celtic jig, meets a "boondocks quadrille" or square dance with Brazilian Indian and Afro-Brazilian elements also prominent.

The third movement, "Toccata; Desafío," has a strong flavor of festival days in the dry northeastern part of Brazil, in a rapid tempo.

The work ends in a magnificent "Fuga; Conversa." Villa-Lobos had in mind the "conversations" that chôros players have with each other while improvising, yet the fugue in this concluding section is formally correct and takes on the sound of Bach's organ fugues.