Alright I have done some more research.
I can forget about using the eeprom storage because it's not possible to communicate that fast for fetching the samples. And it will even be more impossible to communicate to my external eeprom memory. ATtiny > ext eeprom > back to ATtiny > music.
But that's okey, I could use my ext eeprom for other projects.
I also ordered this https://www.sparkfun.com/products/301
a flash memory.
Do you guys think It's possible to store some samples on that and then connect it to my attiny and let the attiny fetch the samples from that flash memory? It shouldn't be any different then fetching from an sd card (I think).