The simple answer to this question is a huge amount. I might even go so far as to say that use of the piano developed more in the 20th century than in any other period of musical history.
The great period of technological development was the late 1700s into the mid 1800s when the invention and refinement of the mechanism that allows the piano to play both loudly and quietly took place. Musically, composers certainly explored these new opportunities – look at the expressive range of Beethoven’s piano music in comparison to Mozart’s and the difference is obvious.
The difference in the demands made on the instrument by composers at the end of the 19th century were not massively different to those at the beginning of the century from a technical perspective. A slightly wider range was used and the dynamic range was slightly extended (though goodness knows, Beethoven puts the instrument through its paces). The developments happened more in musical language than in the use of the instrument itself.
The 20th century, however, saw an extraordinary variety of imaginative ways to use the piano. Perhaps most famous are the pieces for prepared piano by John Cage. He had performers place objects inside the instrument – pegs, bits of metal, wood – to change its sound. Another idea explored by a number of composers is the use of the sustain pedal not only connected to the piano itself playing but also to other instruments playing into the piano. This can have the effect of creating not just an echo of a sound but also setting up sympathetic vibrations. These can be used to generate quite beautiful chords.
As well as putting objects on the strings of the piano, objects other than the hammer of the piano’s action were used to strike the strings. Different metals, wood, rubber – all change the kind of sound created.
As early as the 1920s, composers started experimenting with different ways of tuning the piano. Charles Ives in his imaginatively titled ‘3 Quarter Tone Pieces’ has two pianos tuned a quarter tone apart.
In the late 1800s a new kind of self-playing piano was invented (the player piano). By the 1900s composers were exploiting this instrument to write music that was unplayable by humans. The most famous of these was Conlon Nancarrow who wrote a whole set of studies for player piano beginning in 1948 with some astonishing polyphony and metric modulations.
I think we have also to bring into the mix electronic equipment – not just electric pianos but synthesizers and all manner of other piano-related keyboard instruments that enabled almost the entire gamut of musical sounds to be available to the pianist.
The 20th century was also the time in which the technical capabilities of the instrument allowed for absolutely stunning artistry on the part of performers. The level of dynamic contrast, variety of articulation, subtlety of touch, and clarity of texture possible on the best pianos now matches the great string instruments. Pianists like Martha Argerich, Maria Joao Pires, Oscar Peterson, Duke Ellington have been able to perform to sublime levels thanks to the technical brilliance of their instruments.
The repertoire for piano embraces just about every conceivable style in music. There is barely a part of music in which it is not used in some way from art music through jazz and gospel to pop, rock, hiphop, and beyond.
The 20th century was really the time when the piano and its cousins came of age. If you were going to spend time exploring one era of piano music, then that is the one to pick!