The violinist Hilary Hahn posted a video asking people to submit “tone rows” for some as yet unrevealed purpose related to her Encores Contest, ending June 15. I am using her announcement to experiment with embedding a video on this blog.

I wonder if she will want an all-interval twelve-tone row. I wrote my Princeton thesis in 1988 on some attempts to classify those. Wikipedia says “There are 3,856 distinct all-interval twelve-tone rows.” (A row is not distinct if it is just a transposition up or down of another row, so for each of these there are actually 11 others.) In fact, if you remove the inversions, you get 1,928, a finding of Stefan Bauer-Mengelberg and Malvin Ferentz from 1965. In my thesis I described several further operations that allowed me to reduce the number of distinct all-interval twelve-tone row generators to just 286. The total number of all-interval 12-tone rows is 46,272 and the total number of twelve-tone rows of any type is 12! or 479,001,600.