Yes, it's self-striping. It's called "Poems" by Wisdom. 100% wool, single ply. Soft, but not merino soft. It will pill, too, as most single ply yarns do.
I bought the yarn from an LYS close-out sale, so I bought her entire stock on hand in 3 colors, 10 skeins each. My girlfriend bought all the skeins on the other color. Sadly, the LYS was going out of business after being open less than a year. This little one-horse town we were visiting for the day had no other shops or stores that sold yarn, not even a Walmart or Target.