The break of tonality: appearance of atonality
by leaving of mono-centric classical tonality,
historically coincide with the similar process
in painting – the appearance of cubism.
There, the Renaissance mono-centric perspective
is replaced by cubist polycentrism - a chance
to see simultaneously an object from several
viewpoints in space (Fig. 4). Every point in space
has an equal chance. The same holds for the
tones in dodecaphony: all the tones have the
Together with the break of tonality,
appeared the question: are we perceptively able
to accept the music without tonal center and
without the standardized patterns - the chords
and their isometric
transformations. In the given example of the retrograde motion
(Fig. 5), the melodies of the first and second voice are mutually exchanged by the
retrograde motion (moto retrogrado, the glide reflection in the y-axis).
In the x-axis
(the time axis) we may follow the rhytmical structure, where the time unit is
1/8, and the y-axis is the peach axis.