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).
![]() ![]()
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).
![]() |