Hauer's discoveries: the trope and the twelve-note piece

During his creative period Hauer conceived two different methods for constructing dodecaphonic pieces: the technique of tropes (1921) and the twelve-note piece (1940).

The trope
The basic idea of the trope is to divide the twelve notes into two groups of sixes within which there is no further system. There are only 44 tropes which can include all the 479.001.600 possible twelve-note series.
Within one trope those notes that are chromatically close are always placed next to each other, therefore do not occur simultaneously. This avoids the most glaring dissonances (minor second and major seventh).

The twelve-note piece
In the twelve-note piece the chromatic scale is divided into four voices. A twelve-note row decides the progression of the individual voices. This results in four-note chords which change with the notes of the twelve-note row. More open dissonances develop according to the chosen twelve-note row.

Josef (Matthias) Hauer 

Further information:
Trope
Zwölftonspiel
Zwölftonreihe