Thanks for your respons jrcramer!
The first part of the piece is based on a 12 tone melody which I took from one of my try-out pieces which led to this one. (C E G A Eb Ab B F# Bb D F C#) Then I had to think of a way to make harmony under the melody. I just took the harmony out of the melody (chord 1: C E G A chord 2: Eb Ab B chord 3: F# Bb D chord 4 (overlapping 3): D F C#). To make it more interesting I used inversions and I started on another note (Eb ).
The middle part is not really based on anything. Especially the pizzicato is randomly played at the beginning and later it uses the inversion of the main melody (expect for the melody that returns in the first violin in the beginning). The viola and cello both play a melody I made up to have the feeling of a tonality but then trying not to stay in the same tonality.
The last part is obviously based on the first part (minor 3rd lower).
I hope this will help you with your compositions. I myself am also very interested in the use of tonality in an atonal setting.
About the notation, I still have to "clean up" the score, so things like unnecessary tied eights will be replaced.