Your knowledge in this piano piece?

I know this piece very well and think you should do your own homework.

Hint:: read the title

Edit:

Dear sir, I think you are arrogant. I get annoyed at people like you who ask questions either for their homework assignment, OR who already know the answer and just want to prove something. that's not really the point of this website.

Of course there is more than the title, but it's a good starting point. did you know that there is also a folk melody in there. I suggest listening for it, In Peter Laki's analysis it's a third type use of folk, such that the feeling of folk is innately buried in there, but not a literal transcription .

I also suggest revising your use of [0167] the tritone is not a particularly important interval in the way your mention of it suggests. It is important but not as a harmonic unit, instead it is a unit of progression, that is where it finds importance. harmonically as part of [0167] it just isn't important ask yourself how often it comes up. Also you may ask yourself how many chords are there of more than 2 notes?

Answer: almost none.

how many chords of two notes?

Answer: almost all.

The tritone has some melodic interest, but more as means of melodic and harmonic pivoting, also as part of a melodic flourish as a non-chord tone.

Also [0167] is too simplistic. there is much going in with register. [0167] analytically assumes octave equivalency. this gets back to the title: [01] is both a minor second and a major seventh. but that is point, the piece is playing a game with the similarities and differences of these intervals. The second is used at the beginning of phrases and seventh usually more cadentially at the end of phrases. if you have an analysis with octave equivalency you completely miss this fundamental aspect of the piece.

Also about the golden mean. way too many theorists and analysts have been obsessed with this in the past 30 or so years. First, if you search hard enough you can find the golden mean in almost any piece of music, who cares unless it adds up to something else. Second, I seriously doubt Bartok used the golden mean on purpose. I'm not aware of anything Bartok said, or any of his writings that suggests he had an overt interest in using it.

The whole point of theory is to be able to make projections and predictions that help us understand what's going on and better ways of listening to and playing music. In this regard the golden mean is usually a distraction. It is definitely a distraction in this piece.

Edit #2:

You are quite right about Bartok being in absolute control of all the contrapuntal relationships in his music, the inversions, canons, strettos and so on. It seems for both of us it's one of the qualities that draws us to his music so much. In this respect I think only Bach, Webern and Palestrina could rival Bartok.

Why would you want to study Bartok? He makes me vomit. Do Shostakovich instead.