Part 2:    d I s O R d E r

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 equal role.


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Figure 4

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.


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Figure 5: The retrograde motion: glide reflection gy.

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