Arnold Schönberg
Inversions and (superfluous) devices
Twelve tone dice
Undated

Even when not working on a concrete piece, Schönberg engrossed himself in abstract tasks. Such problem-solving often prepared the ground for later ideas. A whole series of self-made, small booklets is labeled with “Umkehrungen“ [Inversions] on the cover. Schönberg notated only chromatic scales in these, first ascending and then descending – that is, inverted, in relation to the sequence of notes notated in each case on the first staff line. He also highlighted individual pitches in both staff lines: either in places where octaves occur in the same position, or where tritones or perfect fifths occur. The significance of these small books is, to date, as little understood as is the purpose of two red-colored dice made from wood or papier mâché. Thinking about the dice might lead to the unfortunate speculation that Schönberg composed his twelve-tone rows by chance procedures; but such a conjecture can be dismissed with certainty. If one writes out the pitches found on the sides of the dice, two six-tone series result, each of which is a whole-tone scale that can be combined with the other to form a twelve-tone row.