well you can make a circuit that operates bells. you may have amazing quality and fairly simple circuit. question is how many bells you want. simple tunes can be done with only 3 or 4 bells. if you want bell orchestra that plays rachmaninov, that will be a bit more complicated (you will need more memory).
basic idea is to produce some sort of ROM (could be clock, one set/reset flip-flop and a button, counter/decoder, series of dip switches, transistor array driving coils that trigger bells).
if you have MCU skill, you could put everything into a lookup table and this is what these melody chips all do. only they produce sound by synthesis while in proposed plain solution bells are real just operated by clock based circuit.
heck, you won't even need circuit, we can make this old school, just use mechanical clock mechanism or weight with pulley to run drum with columns of nails, each colum triggering one bell...