Jan Adam Reincken (1643-1722) was a church organist in Hamburg, renowned as a master of organ art during Bach's time. An anecdote relates that when Bach sought employment in Hamburg in 1720, Reincken heard his audition performance and highly praised Bach's mastery in freely handling traditional techniques.

The Fugue BWV 954 was composed slightly earlier, during Bach's period of studying past musical works in Weimar. The original piece is the second number from Reincken's instrumental ensemble collection Hortus musicus (1687, Hamburg). Originally conceived for four parts: two violins, viola da gamba, and harpsichord, it consists of 30 pieces, each set comprising a sonata and a dance suite. The dance movements are the four basic dances: allemande, courante, sarabande, and gigue, while the sonata is divided into a slow introductory section, a fugue, and a free development section. Bach used the fugue subject from this sonata, which was originally played by the violin. Bach altered the repeated notes in the latter half of the subject to a turn (measures 3-4). This represents a transformation from violin idiom to keyboard idiom. The entire piece is spun from this subject material.

It is inaccurate to frequently refer to this piece as an "arrangement" in articles. Bach composed a new and original fugue based on the master's subject. In it, Bach's unique style, characterized by flexibility and clarity, is already emerging. The lowest voice not only presents the subject and sustains bass notes but also participates in the counterpoint by stringing together intricate figures. Monotonous sequential progressions and suspensions, often found in improvisatory styles, are largely excluded. The concluding section is neatly brought to a close after the subject's presentation in the lowest voice, without abrupt interruptions or arpeggiated figurations.

Among the clavier fugues from the Weimar period, there are works that clearly show a departure from his early style, and this piece is one of them.