What is tonality?

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This is less a scholarly paper and more a series of observations and ponderings..

Several years ago I wrote a set of Piano Preludes. Rather than having each one in a single key as say Bach or Chopin did, I opted to put each hand in a separate key. The first few are fine, but when they get to the 3rd prelude dealing with three sharps and three flats most pianists tend to balk at looking at the music with key signatures. They'd rather have it written with no key signatures and lots of accidentals.

Add to this every indigenous culture has some form of a pentatonic scale with natural relationships between the tonic, 4th and 5th of the diatonic scale. So, do we naturally hear harmonies and tonics in music?

If this is the case, is moving to an "atonal" system which seems to eliminate a tonal center going against the way our ears naturally hear? Although it should be pointed out Schoenberg didn't like the term "atonal" as he felt that suggests music without tone --the 12-tone system certainly has tone, just not necessarily a specific tonal center.

In a discussion on LinkedIn this has been broadly argued pondering if poly-tonality can even exist, or if we can even escape tonality. While some pieces are non-tonal (i.e., Penderecki's Threnody) these are more non-pitched pieces (as per Paul Henry Smith).

What is Tonality?

When we talk about tonality are we speaking of the tonal center of a piece, or the functional harmony? In Mozart's Symphony No. 40 in G minor the piece begins in G minor, but the second movement is in E flat major, the third's trio is in G major and the final movement has a chromatic passage that plays every note except G. The overall work is centered around G minor, but is that the functional harmony of any given section? No... but it is for the overall work.

Moving into the 20th century, what is the functional harmony for John Adam's Phrygian Gates which shifts between modes rather than keys?

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