There is one almost forgotten chapter in the music history: Quarter-tone music: https://en.wikipedia.org/wiki/Quarter_tone
There has been pianos constructed to play this kind of music - I have seen one on display in Prague. It has three keyboards, one of them shifted (by a quarter-tone) and inside two full scale piano frames with strings. Quite a monster, though. There were some composers composing this kind of music (czech Alois Haba, for example) and one can find even recordings of this kind of instruments.
There is a picture on czech wiki: https://commons.wikimedia.org/wiki/File:%C4%8Ctvrtt%C3%B3nov%C3%BD_klav%C3%ADr_3.jpg
VitVit, CC BY-SA 4.0 https://creativecommons.org/licenses/by-sa/4.0, via Wikimedia Commons
The August Forster website contains additional information. The first of his/their quarter-tone pianos was a grand built in 1923 for Alois Haba. It contained two actions tuned a quarter-tone apart. In 1928 another version of the instrument was built for Ivan Wyschnegradsky.
Here is an image from the patent (SOURCE).