I'm looking at putting a steel fork on one of my bikes. It's between two forks. One is double butted and the other is triple butted chromo.

I'm guessing the triple butted would provide a more compliant ride?

I'm looking at putting a steel fork on one of my bikes. It's between two forks. One is double butted and the other is triple butted chromo.

I'm guessing the triple butted would provide a more compliant ride?

Not necessarily. Most of the flex in a fork is in the crown and steerer, and less in the blades. Besides, which, I'm not so sure that the terms "double butted" and "triple butted" have real meaning for forks.

For constant diameter tubes (like the main frame tubes) these terms mean:

Double butted - the tube has two different wall thicknesses; the ends of the tube has thicker walls, and the center of the tube has thinner walls.

Triple butted - the tube has three different wall thicknesses; like a double butted tube, the ends of the tube have thicker walls than the center section, but the two ends have two different wall thicknesses.

There are also single butted tubes, in which only one end has a thicker walls, and the rest of the tube has thinner walls.

Most steel fork blades are are tapered. Usually they are made by starting with a single butted tube, and then the tube is tapered by "squeezing" down (swaging) the non-butted end. The squeezing down results in the wall thickness increasing at the narrowest part of the taper. Some might describe this as "butting" the end of the taper, and you might even go as far as saying the fork blade is "triple butted", since it is likely that fork tip will have a different wall thickness than the other end.

But long story short - just because the words "double butted" or "triple butted" are assigned to a fork doesn't make it more or less compliant - there are too many other variables involved. In particular, the diameters, wall thicknesses, design of the crown, and the thickness (and/or tapering) of the steerer tube all play a role.

I've never heard of a "good quality" fork being advertised as double or triple butted. As you said, the correct term is taper wall.