Analog to Digital conversion for an old analog synth
It sounds like you're wanting to create a hybrid analog/digital synth.  For a pure digital synth the only part you really need from your old synth is the keyboard (and perhaps power supply).

The Arduino Uno doesn't make a very good choice for a digital synth because of the limited memory, limited processing power, and no DAC.  You can make a DAC from the Arduino's digital I/O outputs using a resistor ladder or use a couple outputs in PWM mode to drive an OpAmp (which I've found to be a very noisy solution).

The Arduino Due might be a better choice since it has much more memory and processing power.  Whichever flavor of Arduino you use though, you'll need a circuit to shape the input to the Arduino's ADC from the AC speaker or line level output of your synth to a DC (0-5v) analog input that the ADC expects.

If you go with a digital only design then you'll only need to read the keyboard keys and have the Arduino play an appropriate tone based on the key pressed.