Bach was a prodigious skill at the keyboard, well known throughout his lifetime for both his technical and improvisational capabilities. A lot of Bach’s keyboard works begun as improvisations. Bach composed commonly for the harpsichord, producing many creations, suites, fugues, partitas, overtures, as well as keyboard plans of concerto music by his contemporaries. The fortepiano is an instrument Bach would have encountered as soon as, by the end of his life when it was just recently developed, while visiting his son in Potsdam. The visit led to Das Musikalische Opfer, parts of which might have been planned for the new instrument.
Modern composers have actually continued to draw inspiration from Bach’s keyboard output. Dmitri Shostakovich, for instance, composed his own set of Starts and Fugues after the Bach model. Jazz artists and authors, in particular, have been drawn to the contrapuntal design, harmonic expansion and balanced expression of Bach’s compositions, particularly the works for keyboard.
After the composer’s death the majority of his keyboard structures, and lots of others, are, or were, typically carried out on the piano, played either directly from a rating for the instruments as the composer knew them, or from a rating that was a transcription for piano. The latter is often required even for harpsichord ratings while for instance a structure meant for a two-manual harpsichord (like the Goldberg Variations) can present difficulties for the crossing of hands when carried out on a single-keyboard instrument like the piano. A few of the transposers/arrangers of Bach’s work added their own inspiration, like Busoni in his arrangement and growth of Bach’s Chromatische Fantasie und Fuge, BWV 903. The fourth section of this list refers to such transcriptions and arrangements for the piano.