DCO/VCO Fine clock output?

Hey there,
I'm trying to figure out how to output a clock frequency depending on
the position of a potentiometer slider.

I need the clock frequency to range from 39KHz to 49KHz and the
mid-point to be 44.1KHz. I've been informed a DCO would be the best
option but I'm not sure if their output range can be that finely tuned?
All the DCO's I have found go up to around 20MHz and do not seem suited
to a lower frequency task like this.

Does anyone have any advice as to how to finely tune an output
frequency of one of these devices?

My original thoughts were to use an ADC to sample in the position of
the slider and then use a DCO. Are VCO's not stable enough? I need the
clock to be accurate and precise...

Any help greatly appreciated! Many thanks, Alex.

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