Although originally it is notated in an open score notation on four staves, musicologists believe it is a keyboard work. Bach apparently chose the vocal score model with 3 different types of C clefs because this way all the parts are clearly visible and understandable.
The reasoning behind this theory is this:
1) It was a custom at that time to write polyphonically complex keyboard works in an open score notation (compare, for example, Frescobaldi's "Fiori Musicali" which Bach owned). Organists at that time, especially in Italy had to display a skill in reading open score, called Spartitura.
2) Most of the fugues and canons are playable by 2 hands only. In fact, in many cases, the texture falls quite comfortably within the hands. If one adds a pedals for the bass parts (not in all fugues, though), then the writing is very organistic, indeed very similar to that of other Bach's fugues for organ.
3) The range of the voices go far beyond the limits of any solo instrument. The traditional melodic instruments of the Baroque period, such as violin, flute, oboe, bassoon and others have their fixed range. If we assign a certain voice to a certain instrument throughout the cycle, then it is impossible to perform it without some compromises.
4) There are some additional voices at the end of some fugues which is quite customary for the keyboard practice. For example, ad the end of such fugue the texture might increase to as many, as 7 voices (1- in the pedals, and 3 in each hand). Such texture would not be possible to play on any single melodic instrument.
I have prepared a practice score of Contrapunctus I from the Art of the Fugue, arranged for the organ with pedals with complete fingering and pedaling written in for easy practice and ideal articulation.
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