Perhaps the least known of the six, the A minor Partita, (first printed along with its C minor companion piece in 1727), exists (like no. 6 in E minor) in an earlier version in the Anna Magdalena Book of 1725. The opening movement of no. 3, originally called Prélude, was re-named Fantasia for the printed publication; curiously, the same term that Bach had used originally for the three-part Sinfonias of 1723 in the Clavierbüchlein vor Wilhelm Friedemann. In any case, the opening movement is a serious and even rather austere two-part invention, uncompromising in its use of inversion of some of the material and occasionally awkward in its contrapuntal working out and corresponding technical demands. Like a two-part invention, it opens with a subject and bass accompaniment and then employs imitation at the octave. Despite its close resemblance to them, it is of more substantial length than the fifteen works composed for Wilhelm Friedemann and finally assembled into a set in 1723.
The allemande is unusual in its use of a subdivided quarter-note upbeat, varied and elaborate figuration; and progressive in its galant use of appoggiaturas at the cadences. It exhibits a similarity of mood and style with the (even more elaborate) allemande of Partita no. 6, coincidentally (or by design) its companion work in the 1725 Notebook for Anna Magdalena. Clearly, Bach thought of both works as bearing a special relationship to one another and, indeed, they share a kinship that is unique among the Partitas, where diversity is the keyword. In some ways, no. 3 seems like a direct precursor of the final work of the set. The Italian corrente is unusually bold and exciting, with its relentlessly confident instrumental character, its lean two-voice texture and lively dotted figures juxtaposed with an urgent torrential flow of sequential sixteenth-notes. Part of its special character is due to the unusually wide keyboard range it commands, and the deliberate pitting of very high notes against some of the lowest on the keyboard.
The dance that follows is scarcely recognizable as a conventional sarabande, with the three-eighth-note upbeats that begin each section, flowing melodic invention and transparent texture. Nothing in the Partitas is more galant in style than this movement. Following this extraordinary re-interpretation of one of the core dances of the suite, Bach re-defines the originally-named Menuet of 1725 by calling it Burlesca, a designation that recalls certain works of Bach’s friend Georg Philipp Telemann (the Don Quichotte Suite, for example), and probably implies a more ironic, perhaps earthy manner of performance than the more courtly menuet would require. This sturdy, almost rustic dance in triple time is then succeeded by a quicker, duple-time scherzo(a non-dance movement that is not present in the 1725 version). In performance this short piece seems to grow out of the basic compositional idea of the burlesca, serving as an appendage to it, in part due to its opening upbeat, which disguises the change of prevailing rhythm from a triple to a duple time signature. The final, angularly contrapuntal gigue most closely resembles the corresponding final dance from the third English Suite, and seems to hearken back to an earlier time, as though Bach is showing his public that he can look back as well as forward, doing equal justice to both styles. Like most of the gigues throughout the English Suites (nos. 3, 4, 5 & 6), the counterpoint is uncompromising, the dissonances prominent, and the theme inverted in the second half.