The museum has the Bartok Archives section and also shows Hungarian folk instruments and you get to try playing a few of them. It also features Haydn (because he worked for a Hungarian aristocrat family) and Liszt (I think he is the most famous Hungarian composer) and other lesser known composers.
In the first room folk instruments are exhibited and there is a computer which plays the sound and performance of these instruments. You can also listen to them on their website.
It looks like it is a combination of a violin, keyboard and maybe a barrel organ. According to the museum, this instrument was originally played by two people (naturally... it's too complicated!) back in the 12th century.