The subject of the first Contrapunctus is stated simply in the alto voice and given a tonal answer in the soprano. The ten statements of the fugue's subject may refer to the ten commandments which represent, allegorically, the contrapuntal "laws" which Bach intends to observe in this great cycle.
This fugue contains the first two of many subject transformations. The first of these (hereafter called "t1") involves the incorporation of a dotted rhythm in the subject's tail. The second (t2) involves syncopation which becomes the object of further transformation in the next fugue. The fourteen statements of the fugue's subject may have stood for the composer (B+A+C+H = 14). The only appearance of the t2 syncopation is in statement 13, a number which, in the cosmogony of Bach's day, represented betrayal. Dotted rhythms counterpointing each entry of the subject hint of a countersubject, but the intervals are not consistent.
The third fugue transforms the subject by means of melodic inversion. The first inversion (t3) consists of the original answer (see Contrapunctus I) with pitches moving in the opposite direction. So, what had been the answer now becomes the subject, and the subject becomes the answer. The fugue's exposition is comprised of four such statements. The second transformation (t4) combines the t2 syncopation with a rhythmic expansion of t1 (dotted value written in tied notes), moving the whole in contrary motion. The first developmental episode contains three of these. The third transformation (t5) consists of t4 bumped forward one beat, removing syncopation from the subject's head. Bach counteracts this removal by adding a new syncopation near the tail. The second episode contains two of these.
In Contrapunctus III Bach employs the first countersubject of the cycle. This motive runs counter to eight of the twelve statements of the subject (or answer). Not as discernable as the subject, the countersubject is a significant figure in that it lends this fugue its distinctly chromatic sound. The harmonic complexity generated by this countersubject is a precursor of things to come.
This first quartet of fugues concludes in tonal opposition to how it began (see Contrapunctus I). Whereas the subject of that fugue began with the ascending fifth do-sol, this subject begins with the opposite: sol-do. Tonal functions of the answer are also reversed. The sixteen entries of this subject now dance as if the prior transformations have released it from the prison of studied counterpoint to become pure music.
Canon alla Ottava The "canon at the octave" comes after the simple fugues and before the stretto fugues. Here Bach continues the contrary motion of the preceding two fugues but with lower neighbor decorations (t6). Toward the middle of the canon Bach reinverts the subject creating a decorated transformation (t7) of the Art of Fugue's original subject. For a complete analysis of this canon refer to the Canons of the Art of Fugue study.