Although Bach's music is very clear as to what notes has to be played he leaves the pianist with a freedom as how to play it. However this also can be applied to other music too, that we are open to interpretation. However Bach wrote pretty much on Clavichord, Harpsichord and Organ. Could he really imagine the modern piano of today? As exponents of the modern piano we have to make intelligent decisions as to how to musically express Bach.
Let me paraphrase 48 Prelude and Fugues (Tovey and Sameul)
"..One thing is certain, before anything "pianistic" is attempted the student should have thoroughly mastered Bach's exact part-writing as written, should be able to express its climaxes distinctly without adding or altering a note.
... our appreciation of Bach loses more than it gains from the occasional bursts of pianistic effectiveness accidentally possible in passages which may not be climaxes at all.
JS Bach is fond crowding all the harmony he could into both hands; not until we have learnt to achieve Bach's part-writing with our fingers can we venture to translate him into any pianoforte style which produces volume at the expense of part-writing.
... it may be taken as an axiom that when a phrasing or touch represents a "pianistic" mannerism that would sound ugly on the harpsichord, that phrasing will misconstrue Bach's language and tell us nothing interesting about the pianoforte. If players think it "natural" they are mistaken, however habitually they may do it. They are merely applying a small part of the pianoforte technique of 1806 to the clavichord and harpsichord music of 1730.
There are very simple ways of detecting what is unnatural in the interpretation of most of Bach's themes; and, if the test sometimes fails to answer directly, it certainly never misleads. It is summed up in two words, Sing it.
If the phrase proves singable at all, the attempt to sing it will almost certainly reveal natural types of expression easily perfectible on the pianoforte and incomparably better than any result of the natural behavior of the pianists hands. Even in matters that at first seem to be merely instrumental, the vocal test reveals much.
Organists who play fugues more often than most people, do not find it necessary, when the subject enters in the inner parts, to pick it out with the thumb or another manual. They and their listeners enjoy the polyphony because the inner parts can neither stick out nor fail to balance within the harmony, so long as the notes are played at all. On the pianoforte however constant care is needed to prevent failure of tone, and certainly the subject of a fugue should not be liable to such failure. But never should the counterpoints, indeed the less heard clearly (e.g: the clinching third countersubject of the F minor Fugues in Bk1) Most of Bach's counterpoint actually sounds best when the parts are evenly balanced. It is never a mere combinations of melodies, but always a mass of harmony stated in terms of a combination of melodies.
When Bach combines melodies, the combination forms full harmony as soon as two parts are present. (Even a solitary part will be a melody which is its own bass.) Each additional part adds new harmonic meaning, as well as its own melody and rhythm, and all are in transparent contrast with each other at every point. No part needs bringing out at the expense of others, but on the pianoforte care is most needed for that part which is most in danger of failure of tone.