Spin Semiconductor

The FV-1 uses the IC2 format to communicate with the EEPROM.

Now, there's dedicated SDA and SCK pins on the Arduino Nano, so could I somehow store programs (patches? effects? I'm new to all this DSP terminology) in the Arduino's memory?

OMG this would make me happy.

This seems a quite clever idea! So you could store more FV-1 programs externally plus parameter descriptions etc. This means the Arduino would act as an emulated EEPROM. A short googling for "arduino i2c eeprom emulator" brought several results; I thing it's worth investigating them!

Yes, you have to emulate an eeprom with the arduino.