The idea was that in order to completely destabilize tonality, they would use all of the twelve tones in music equally. Notice that it is fairly impossible to find "do" in all of these examples. They use a tone row, its inversions and retrogrades, and even its inverted retrogrades, to compose the piece of music. You can generate your own matrix here: http://classic.musictheory.net/98
This will give you a pretty good understanding of how this music is frequently organized. The most helpful thing is if the composer includes a key with his piece, otherwise it is incredibly difficult to analyze and figure out what the tone row is. The chords and everything in this type of music are frequently analyzed on a clock face with every tone being represented by a number from 0 to 11 (because when you get back to 12, you are at the same pitch class again).
To get the prime form of a chord, you find the smallest 3 integers that will represent it. A minor or major triad, for instance, is 0,3,7 which is a right triangle. Pythagorea's theorem of a right triangle states that the smallest whole number integers which fit the formula are 3,4,5, and if you check the prime form 0,3,7 on the clock face, the distance from 0 to 3 is 3; the distance from 3 to 7 is 4; the distance from 7 back to 0 (base 12) is 5. There is also an idea of inversional (and retrograde) equivalence. This means that in 12-tone theory, the major and minor triad are essentially the same.
I hope that this answers a lot of your questions but I also know that it will leave you with many more, so my suggestion is to study music theory and 12-tone theory to answer whatever other questions you have about it, because me telling you is not as helpful to you as you learning about and intellectually experiencing it and applying it for yourself. :) happy studies
