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Strict rules wasn't what "atonality" started out at. It was an idea of liberation from certain boundaries and hierarchies. That later different rules were invented to assist with this kind of composing is irrelevant, as it was merely a tool.
The definition of tonality as "having tonal centres" also is very common, but very ambiguous. How long does a tonal centre have to dominate for the music to become "tonal"? Is a tonal centre that happened "by chance" without intention of the composer enough to create "tonality"? Is every kind of weighting or hierarchy between notes the same as "tonal centres"? Can there be more than one "tonal centre"? Is music only "tonal" if the tonal centres are actually perceived by the listener (and thus subjective)?
It is also incredibly easy to compose music without tonal centres of any kind, which is stylistically completely different from what is usually called "atonal music". You can easily achieve that by use of pentatonic or wholetone scales, for example.
There's so much music that has nothing to do with serialism or even the general sound of the New Vienna School, but which still clearly doesn't strive towards one single gravity tone.
Without a clear definition of what "tonal centres" actually are, we won't get very far.
One further "statistical" explanation: Assume a music where every pitch is randomly chosen by a computer. You have to accept this as the average case. There's a tiny chance something like a Beethoven symphony will be produced and a tiny chance a serial piece will be produced. But if we look at the average output of such a machine and determine whether it sounds tonal or atonal to us, we can easily judge which is the more basic, or natural case. And I assure you, most people (as we're making a statistical example here) certainly wouldn't classify this music as tonal. There won't be tonal centres over the whole piece. Something that resembles a tonal centre may pop up now and then, but it will soon vanish again.
The statistical average of "mindlessly produced music" is not tonal, so any musical creation that is tonal must be a conscious limitation of the possible material.
It is true that many "atonal composers" of the 20th century sought to avoid any hint of tonal centres. But it is a wrong assumption that their music would have become tonal if they hadn't avoided major chords by all costs. But a large part of the listeners are so trained to hear in traditional tonality, that they hear tonality -everywhere-, even where it doesn't exist, unless you try your best to work against it. Schönberg had to write all these fourth-tritone chords because they were the type of chords the audience could hear best outside of a tonal context. If he had used major-seventh chords, a large part of the audience would have heard his music in a context that Schönberg didn't like.
Again: The reason why "tonal sounds" were avoided so much wasn't because otherwise the music would have become tonal, but because the "tonally trained listener" would have heard it as such. (And also, because Schönberg and his fellows were -also- tonally trained and would have easily "slipped" into tonality, if they hadn't tried so much to avoid it (with the exception of Berg, who willingly let it happen).)
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