Why is the intended instrumentation of The Art of Fugue uncertain?

The intended instrumentation of The Art of Fugue remains uncertain because Johann Sebastian Bach did not provide any performance instructions or specify which instruments should be used for the work.1

Because the score lacks explicit instrumentation, musicologists and performers have long debated the composer's original intent. Experts generally surmise that Bach may have envisioned the work for a keyboard instrument, such as the organ or harpsichord, or potentially for a small string or chamber orchestra.1

The ambiguity is further complicated by the question of whether the collection was intended for public performance or if it served a primarily pedagogical purpose, similar to his The Well-Tempered Clavier. Due to this lack of direction, the work has been interpreted through a wide variety of arrangements, ranging from solo piano to string quartets and chamber ensembles.1