Variable resistance value scaling

[ExpAnonColin]

Hello everyone.

I have always wondered about using a large pot value (100k, 1Meg) in place of a smaller pot value (10k, 1k).  The clear application for this is for expression pedals-if you want to use the same expression pedal for all of your potentiometers, they must all be the same value, which isn't always immediately possible, depending on the circuit (for example, certain oscillators or chip-required potentiometers might have a necessary value to get a reasonable response), although in many cases such as op amps you can vary other resistances (for the most part) to get a value you want.  There are other clear applications too, such as using photocells, voltage control, etc...

In many cases it is easy to use a larger value pot for a smaller value one using the equations on the emh:
http://diystompboxes.com/analogalchemy/emh/emh.html
However, there is no really clean way if you are just using to lugs of the potentiometer-that is, the pot being used as a variable resitor.  If you put a resistor in parallel with that, you end up with a very poorly tapered pot because of the behavior of the parallel equation.  For example, if you had a 100k variable resistance and you wanted a 10k variable resistance, it would be fairly obvious to pick a resistor value of about 11k... giving you a max resistance of about 10k.  However, the taper of the pot will not be the same.  More on this at
http://www.geofex.com/Article_Folders/potsecrets/potscret.htm

So, there is a problem when working with simple circuits using the pot as a variable resistor.  There are active ways to solve this problem.  I have used H11F3's with great success-often a voltage divider using the pot value of choice, being fed into an op amp follower so there is very little output resistance, being fed into one or the other pins of the H11F3.  For the most part, I can come up with a circuit that gets extremely close to matching the value and taper of the smaller value pot.  You can see an implementation of this method (using two pot values, one as a "coarse" control and one as a fine-tuning control...) here:
http://experimentalistsanonymous.com/board/download.php?id=71
Note that you are just using pots as voltage dividers-making a CV input a very easy possibility in this circuit.  The output resistance here is about 5k.

But using an extra op amp and an H11F3, and usually a trimmer or two, is not very economical or practical.  So, I guess my question for you all is, what other methods do you use to scale down a resistance like this?  I realize that expression control is a topic not normally discussed in the DIY stompbox community, so normally people don't care about this value or that or this taper or that... but if I'm not mistaken, Moog uses the same pot value for all of their pots in all of their pedals (the expression pedal is unviersally useable), so there must be a way to do it!  (I doubt anyone has any moogerfooger schem's, so I doubt that would be worthwhile).

-Colin