Commonly accepted flooring underlayments are either red rosin paper or builder's felt. These materials help to mitigate squeaking between the bottom of the hardwood and the top of the subfloor. They do nothing to absorb sound and they do not make the surface softer to walk on.
So how to manage the noise? First off, realize that 3/4" solid hardwood itself does a remarkably good job of absorbing sound. Of all the types of flooring you can install, it's probably the best in that respect.
You can put down a solid (vs. foam) underlayment that is specially designed for absorbing sound. SoundEater, made by Impacta, is described as a "free floating underlayment designed for nail down hardwood flooring." A floating floor is one that does not need to be nailed down. So, in this case, the underlayment does not need to be nailed to the subfloor, though the hardwood will be nailed down to the underlayment.
Keep in mind, too, that area rugs and runners will go a long ways toward eliminating the sounds of footsteps.