specific curve for a digital potentiometer

Hello,

I would like to replace an old mecanical potentiometer (pitch) by a digital one on a turntable. Actually, the mechanical potentiometer is a linear 5,23k, this is what I measured after desoldered it. Then, I would also like to have a very specific curve (neither log, nor antilog or whatever), not linear like the normal pot, and it is not possible to obtain this curve without a digital potentiometer. So my idea is to have a linear potentiometer (voltage divider) on the input of the Arduino, then connect the Arduino to a digital potentiometer.
Then, I need a quite good resolution, at least 512 steps. However, there are only 256 steps potentiometers in 5k (that's what I found). I suppose I juste have to connect 2 x 10k 512 steps in parallel for example (A with A, B with B, and W with W) with the same instructions, and I'll have a linear 5k 512 steps potentiometer.
Well, this is where I need help: I begin to learn how does an Arduino work, and also how could I connect it to a digital potentiometer... And I am quite lost!
First, there are many different kinds of potentiometers; I mean, I have seen there are many ways to control them (SPI, I2C, etc), and I don't really understand the differences, as well as the ways to connect them.
Then, I will need to know how can I put the curve inside the program.
I hope you will understand my request! Don't hesitate to ask me if you need information, but what I just know is that I want to control a digital potentiometer with a normal potentiometer, applying a specific curve inside the program (the wipper of the digital pot is a specific function of the wipper of the normal pot)