Make your own free website on

     Part 3:    N e w   O r d e r

The retreat from tonality has not resulted in completely disordered structures, but in the new order: dodecaphony with the tonal series, where the classical patterns the chords, are replaced by the new patterns: permutational twelve-tone series. Isometric transformations of tonal music are replaced by permutational symmetries, where the invariant remains the twelve-tone material (mod 12) (Fig. 6: A Schoenberg - Wind quintet, op.26, where the basic series and their retrograde and retrograde inversion are visible only after the vertical reduction mod 12).


Figure 6

This way, the static symmetry of the classical tonal system is replaced by the dynamic permutational symmetry of a serial system: the classical symmetry is replaced by its generalization - colored (permutational) symmetry (Fig. 7).


Figure 7