I can't tell you what the angles are because I chose them by eye. As I went along, I made a series of story sticks for the dimensions and angles rather than measuring anything.
You may be wondering how I drilled the holes for the pins. I drilled vertical holes through the seat and sawed the tops of the legs at the compound angle I chose for the leg using two bevel squares for reference. Then I put the seat in my vise and positioned the leg at the proper orientation for drilling. This was the wrong way to do it. As you will see, I could have completed the base then set the seat on top of it to drill the holes. Much easier and more accurate.
This spare, long-legged look appeals to me, and I didn't want to add anything more to it than I absolutely had to. You want at least one stretcher because most people need something to put their feet on when sitting on a 26" high stool. So, I decided I would have lower stretchers on the fronts. I chose to have them 19" below the seat for a comfortable position to rest your feet. The pins joining the seat to the legs are close to the edge of the seat, so I am concerned about breaking out the round mortise as a result of racking sideways. This stretcher will share the load and I wanted to make it as strong as possible, so I oriented it vertically and attached it with a rabbeted dovetail. Here's what they look like:
A wedged through-tenon would have been another good choice, but I thought having the stretcher on the front of the legs would be most comfortable because it would minimize the angle of your legs when resting your feet on it.
I wanted the absolute minimum I could get away with for a stretcher between the legs in the other direction, so I settled on a small one rabbeted just 1/4" into the insides of the legs up high in an effort to preserve the long line of the legs.
So, this is my experimental prototype and I am pleased with it, enough that I decided to put some finish on it. Next time, I'll show you my prototype and critique it.