Stretching the octaves

 

In Laura Turnbridge's Beethoven:  a Life in Nine Pieces:

The standard piano keyboard today consists of eighty-eight keys strething just over seven octaves. By comparison, in the late 1790s, Beethoven owned a fortepiano by Anton Walter whihc ranged a mere five octaves. Although Beethoven often hit the top of that range, all his piano music necessarily remained iwthin the five octaves until 1803, when he began to compose for five and a half octaves, as in the 'Waldstein' and "kreutzer' sonatas.  That year, he had received the Erard iano from Paris, which had a bigger keyboard, in keeping with newer instruments being built in Vienna.  By 1808, Beethoven was regularly exploring the lowest notes of the now six-octave span. But it was only with op. 101 that he began to use the bottom noes that were available on British keyboards.  [In the 'Hammerklavier' Sonata he pushed limits.] ... The ADagio repeately pushes into the higher register, touching notes the Broadwood did not possess. Towards the end of the fual finale, by contrast, there is a long fortissimo trill that rumbles on a bottom E flat which, when he composed it, only the Broadwood had.

Beethoven very rarely goes beyond the physical boundaries of the instrument available.