Setting action for semi-sympathetic strings

[Liam McGillivray]

I want to make an instrument with doubled courses. But I want to have one string at a higher action than the other, so that the string below is a semi-sympathetic string. By "semi-sympathetic" I mean that it resonates with the other string instead of being struck directly (like a sympathetic string), but it is fretted with the other string. Here is a picture:

What geometry do I need to know when I make the bridge so that I can have strings at these two different heights, but they will be in-tune with each other at every part of the fretboard?

[Brian Evans]

Presuming the two strings are the same gauge, I would say your picture is correct for differential compensation. Compensation is mostly needed due to the added string tension from fretting the string (different string stiffness/core wire gauge react differently to the added tension). Higher action requires more compensation all else being equal.

[Mark Swanson]

That is going to be quite problematic if you ask me. It won't work because fretting the string will interrupt what you want a sympathetic string to do. In order for you not to pick or pluck it, the difference between the two strings would have to be large, and that would mean really high action...I just can't see it.

[Chris Richards]

Are you saying it has a 12-string like geometry with one set of strings at a lower action...just to get it straight in my mind?