How can I turn this into an (Ableton) controller? I found this lovely decade box in a demolished house recently and want to turn it into an Ableton controller. As you see, there are 18 knobs, each with 12 individual states. 

I'd like to have a program which can access the states of all the knobs at any time, and I have an arduino which I can use. Is this possible to do without a shield?

My first thought is that, since many of the leads on the back already have resistors on them, I could use a sort of total-resistance-across-the-connection approach which would suit itself to the analog inputs. But I'm not sure that's the way to go, especially if I want very low latency.

How can I wire up a board that has digital access to all the pins here? How does a multiplexer play into this? How many inputs would I need? I am super new to this kind of stuff, so I imagine this must be a pretty simple answer.

Thanks for your help.
The hard part here is that you essentially have 216 inputs you need to read.

You could multiplex the analog pins using two 74HC4051. Analogread takes around 0.1ms, so around 2ms for all 18 knobs. Debouncing would however be pretty hard.

I'd probably go with input shift registers, and remove all the resistors. You would however need 27 8-bit shift register (3 registers per 2 knobs). 

To reduce this you could encode the rotary position into 4-bit using a diode network. That way you can use only 1 shift register per 2 knobs. So 9 in total.