# Atonality: Creeping Redundancy?



## millionrainbows (Jun 23, 2012)

When Schoenberg began using ordered sets, he was creating atonality.

As to the "they all look alike," the cumulative effect of adding notes to an unordered set might be mistakenly seen as a creeping-in of "redundancy" and lack of variation, as this chart from Howard Hanson's Harmonic Materials of Modern Music shows:


> _p=perfect fifth (or fourth) _
> _m=major third (minor sixth)_
> _n=minor third (major sixth)_
> _s=major second (minor seventh)_
> ...


Which is all fine and well when dealing with scale-sets in harmonically-related ways, as unordered sets.

This statement is where Hanson falters: 
*
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> *"This is probably the greatest argument against the rigorous use of atonal theory in which all 12 notes are used in a single melodic or harmonic pattern. These constructs begin to lose contrast, and a monochromatic effect emerges." *



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There is a flaw in Hanson's statement about atonality, however. The chart above assumes that these additional added notes all refer to every other element of the set, like an unordered scale does: in scales, each pitch shares an interval with every other pitch in the scale.

But ordered tone rows relate only to each other (each preceding and succeeding note).

Ordered tone rows are used for their intervallic properties, as precise sequences of intervals. These intervals possess sonority, in terms of consonance/dissonance.

The row-sets, although usable melodically as "themes" or motives, are not referenced to a single tonic, as an unordered scale is, so the above chart of "creeping redundancy" is really only applicable to unordered sets, i.e. scales, as Hanson was using them.

This underscores the true primary significance of ordered sets: as conveyors of intervallic sonority due to their interval differences (not primarily as melodic entities). The most "variety" and unity comes from these intervallic sonorities, which Webern seemed to understand the best of the "Big 3." Schoenberg was still playing with "themes" and seemed to be more concerned with this aspect of the row.


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