The order of the movements is, in any case, of debatable importance.Bach did not conceive the work for a complete, cyclical performance; Bradley Brookshire, in the notes to his forthcoming recording, states: “The reordering of the later version seems to reflect Bach’s concern for lending an agreeable rationalism to the appearance of his planned publication, but does not necessarily speak to performance at all”. This view, if accepted, arguably leaves performers free to re-shuffle the pieces to accomplish the most varied and interesting performance sequence, without fearing authorial censure. On a CD, the question becomes even less important: individual listeners can re-programme the pieces to form the sequence that they find, at that particular moment, the most satisfactory.

This is not to say that the order of the movements is arbitrary or unimportant. In each version, the movements are arranged to form a more-or-less steady progression from simple to complex – an arrangement that certainly makes pedagogical sense, and arguably also contributes to an effective performance sequence. The early version focuses attention on the transformation of thematic materials; the later version groups the fugues according to their sub-genres.

The list below is based on the assumption that the order of the first 11 pieces in the 1751 edition reflects Bach’s intentions (as argued by Christoph Wolff and Richard Jones, among others). The classification of fugues into sub-genres matches the categories proposed by the eighteenth-century theorist Mattheson, as applied to The Art of Fugue in Laurence Dreyfus’s “Matters of Kind” (the fifth chapter of his book Bach and the Patterns of Invention). All the fugues are in four parts, unless otherwise indicated. The numbering corresponds to Richard Jones’s edition; other editions and performances might employ different numbering, especially for Contrapuncti 12-14 and the canons.

Contrapuncti 1-4: Simple fugues

The designation “simple fugue” means that each fugue is based on only one subject, which appears without notable alterations. Contrapunctus 1 presents the subject in its simple version:

In Contrapunctus 2, the subject is rhythmically altered; in Contrapuncti 3 and 4, it is inverted.

Contrapuncti 5-7: Counter-fugues

In these fugues, different variants of the subject appear simultaneously, playing against one another. These fugues are also referred to as “stretto fugues”, since the voices enter in quick succession – whereas in the simple fugues, each voice makes its initial entry only after the preceding voice stated the entire subject.

In Contrapunctus 5, the subject and its inversion are juxtaposed. In Contrapunctus 6, the subject appears in inversion and diminution; Contrapunctus 7 is titled “per Augemntationem et Diminutionem”, but features inversion as well.

Contrapuncti 8-11: Double and Triple fugues

In these fugues, the subject – or one of its variants – is joined by one or two additional subjects in invertible counterpoint (that is, lower and upper parts are exchanged without contravening the rules of harmony).

Contrapunctus 8 is a triple fugue in three parts; Contrapuncti 9 and 10 are double fugues. Contrapunctus 9 is “alla Duodecima”: that is, one of the two subjects “is moved above or below the other by transposing it up or down a 12th” (Richard Jones). This means that the interval relationship between the two subjects changes: in some entries, they begin an octave apart, while in others they begin a fifth apart. Contrapunctus 10 is “alla Decima” – here, the subject is transposed up or down a 10th. “This species of double counterpoint allows either or both subjects to be doubled in 3rds, 6ths or 10ths” (Jones) – that is, while one voice plays one of the fugue’s subjects, two other parts present the other subject simultaneously in two different pitches.