Here, in brief, is the history of Western music.
In the beginning was Gregorian chant, the beginning of our musical tradition. At first consisting of simple recitation formulae, the chant tradition became increasingly elaborate, with longer melismas and more adventurous melodic lines. The anonymous composers of chant found monophonic music too limiting, and so they experimented with adding additional voices. At first, the new voices simply doubled the existing voice in parallel fifths and fourths, but the independence of the new voices gradually increased until the polyphonic style was born. Through the medieval and Renaissance periods, polyphony became more and more complex until the vertical sonorities created by the superimposed melodic lines became almost as important as the melodies themselves. When this happened, we were in the Baroque, and it was good. Composers had a system for writing melodies, a second system - polyphony - for combining several melodies, and a third system - tonality - for controlling the succession of vertical sonorities that the melodies created.
This was the beginning of "modern music" in the truest sense, and the history of music since then consists of the attempt to grapple with the ramifications of the tonal system, and to push its boundaries - just as the medieval composers sought to push the boundaries of monophonic chant by adding additional voices. And so through to the end of the nineteenth century, composers worked within the tonal system, adhering to the basic concept of a "tonal centre" around which music should be organized. But to make their music more original, to overcome these limitations, they edged farther and farther from the tonal centre. Sometimes they'd wander so far from the centre that you could hardly tell whether it was there at all; but the system demanded that they return to it eventually, so they always did.
Then there arrived a man, and his name was Schoenberg, and he saw the Truth, and the Truth was that tonality is merely a human construct. Why have a tonal centre at all, he asked; couldn't music get along with the old rules of melody and polyphony but without the newer rules about producing certain successions of chords? And so he created music which had no tonal centre, and which followed no harmonic rules, and when this happened, he had created Atonality, and it was good. And the people rejoiced in their freedom from the shackles of harmonic oppression, and hosted dance parties to Schoenberg's Moses und Aron.
Except we all know this never happened. Atonality wasn't the be-all and end-all of music, and no-one really believes it ever was. The history I just presented is totally old-fashioned. Here, now, is what really happened to Western music:
In the beginning there was the Harmonic Series, and from the Series sprouted music as we know it. Because of the physical fact of the Harmonic Series, tonality is ingrained into the mind of every human being. So when Catholic monks began to compose the earliest examples of polyphony, it was natural for them to use parallel fifths as their building blocks - since fifths are the purest intervals in the harmonic series. When John Dunstable began composing with major thirds in the fourteenth century, he was merely taking the next logical step by using the next consonant interval in the series as a building block. And so our harmonic system, based on thirds and fifths, is founded on physical fact; there is no other basis for pitch organization than the major triad. As music progressed to the end of the nineteenth century, its relationship to tonality became more and more distant. Finally, a man named Schoenberg decided to try to do without tonality, starting a strange historical aberration called the "atonal school". His disciples set out to indoctrinate a generation of musicians to their indefensible viewpoints, and succeeded in imposing nothing less than a musical Dark Age. Composers who believed in tonality had their careers destroyed, while talentless, mathematically-inclined poseurs filled the composition departments of universities everywhere. Now that Schoenberg's disciples are finally dying off, we can finally repudiate this horrific period to the past. The few musical works worth playing from the last century are those by composers who stood up against the atonal cabal. Thankfully, we have now reached a new golden age of enlightenment, when we realize that all musics - Western music, world music, popular music, and every other kind of music that isn't atonal - are equal!
As you may have gathered, I don't find this viewpoint particularly convincing either. The first one was orthodoxy at most universities in the 1960s, while the second one seems to have become orthodoxy now, but they both strike me as equally foolish. But, on the other hand, I've never come up with a narrative of my own to replace these two ideas, and usually end up advocating whichever one seems like the lesser of two evils at the time.
Well, no more! I'm going to take a crack at developing my own historiography of Western music, with the specific goal of explaining what happened to atonality. This is obviously too broad for one post, but I'm going to start by putting down two axioms:
1) Pitches separated by an octave are equivalent.
2) There is no such thing as atonality.