OK, I misunderstood. It’s closed at the CCW end, opens up by about “3”, and doesn’t change much above “3”.
So yes, changing to a log pot would make something like “6” be the old “3”. But, again, the overall cutoff range wouldn’t be affected. If the circuit is like the above Schmitz circuit, the range is very large, 24 octaves. It might be better to reduce that range. In the Barton 055 Sallen-Key filter, for example, the cutoff knob is wired like this:
With the fixed resistors added to the pot the voltage range is reduced from ±12 V to about -5 to +8 V, or about 13 octaves.
But what’s significant is not just the range but also the minimum cutoff value. If your pot is wired straight to ±12 V (of course I don’t know that, maybe it’s 0 to +12 V?) then your position “3” would be about -5 V. So using Barton’s version would move your “3” right down to “0”! Definitely not what you want. It would reduce the range but also raise the minimum cutoff frequency. Assuming a 100k pot it would be better to add say 100k on the CW end and no fixed resistor on the CCW end. Then you’d have a 12 octave range with -5 V at about “6” on the knob.
(But if your pot currently is wired to 0 to +12 V then “3” is about 3.6 V, which would be toward the upper end of the -5 to +8 range, so in that case Barton’s configuration might be exactly what you want.)
The minimum cutoff also is affected by the caps used in the filter. Both Barton and Schmitz use 1 nF caps. If one used for instance 10 nF then the minimum cutoff frequency would be 10x lower, or about 3.3 octaves.
So if the problem is that the range is too large, you can reduce it by adding fixed resistors to the cutoff pot, and if the problem is that the minimum cutoff value is too low you can raise it by reducing the filter capacitors or by using a smaller fixed resistor at the CW end and/or larger at the CCW end.
Another thing to check is whether the CV response really is 1 V/oct. If not, that would affect the range too. Easiest way to do that is if you can put the filter into self oscillation at high resonance, then you can see if the pitch it produces goes up 1 octave when you change the (un-attenuated) CV by 1 volt. But it should be close to 1 V/oct if the 1.8k resistor is correct.