I spent a few minutes playing today -- not really a string quilt because I used some 1½" strips I had bagged -- lights and reds -- they were just handy. Strip pieced them and then placed a 4½" square ruler with the diagonal line on one of the strip seamlines and cut them out -- it works great without foundations and I think working with different width strips would be okay, too. But, actually, I kind of like what I ended up with and will sew a bunch more strips together whenever I have a free moment. There's quite a bit of waste, but I think you could also cut 2½" squares from the leftovers -- maybe use them in the borders of a quilt or in another quilt sometime.
The square that is separated on the right was cut with the diagonal line of the ruler through the center of the red strip instead of on a seamline -- just playing again! I think there's lots of possibilities to play with here, too.