My [very] rough count says there are about 1500 unique word-roots in the Psalter - about 19,551 words barring arguments from textual critics. There are 6,982 distinct words. So the average word is used about 3 times and the average root about 4 times.
Which words / roots are unique? Lots - about 360 roots [+/- 1 30% - the algorithm has many boundary failures] and about 4600 words are used only once [reasonably accurate - a pure count].
I am finding that short of writing a whole book on the story in the psalter, its structure is elusive - there are signs of structure but they are so manifold, the engine of their being is not easily summarized in a single image.
If I did one unique root a day, it would take a year. Does this seem like a project worth the effort? [Can I find them all accurately?]
Any project in the Scriptures is worth the effort - even the scoffer can enter the world of the saints.