Can somebody explain how the harmony works in Bartók's Mikrokosmos, BB 105, Vol. 1: No. 17 Contrary Motion (1)?:
It seems that the right hand plays on C key and the left hand alternates between G and D.
Why, when played in opposite direction do the intervals sound consonant?
Try to think of this piece less in terms of harmony and more in terms of counterpoint. In other words, try to think of this piece more in terms of the horizontal musical lines that are written instead of the vertical harmonies that are the byproducts.
You'll notice that the "keys" of each hand are related by fifth. The right hand at the start is "in C," but the left hand, on account of the F♯, is "in G," a key a fifth higher than the right hand's C. In my opinion, the right hand in m. 5 is now "in G" (even though there's no F♯) because it's an exact transposition up a perfect fifth of the first four measures; now, the left hand is "in D."
And notice that the intervals aren't always consonant. The first two beats of m. 2, for instance, are a dissonant seventh and dissonant ninth!
Maybe 'sound consonant' is the wrong description. If you linger on many of the intervals in this piece - the 4th, 5th and 6th notes, and their equivalents in the next phrase for instance, they are demonstrably dissonant. But Bartok is demonstrating that strong melodic lines can make dissonances acceptable - or, rather, irrelevant. He's not abandoned tonality, there are definite tonal centres of C, G then C again. But he's exploring structures not based on tonal harmony.
Bartok (and Stravinsky) avoided complete atonality and demonstrated that music could enter the 20th century without discarding EVERYTHING that had gone before. For which I admire and salute them.
Can somebody explain how the harmony works in this piece?
There's is nothing to explain. The harmony is the result of the counterpoint of 2 contrary parts. This is a teaching example:
The goal of this interval study is to demonstrate - or to find out by the pupils themselves - which intervals we will become by starting of a certain pitch and two parts are playing in contrary movement. (As they are notated in octavas you can play them as well close together). And then notate the results you get:
start: unisono
1) one tone up and one down: 3rd
2) two tones up and two tones down: 5th . . .
etc. you can complete the liste and also consider the specific intervals:
It seems that the right hand plays on C key and the left hand alternates between G and D.
I don't agree with this point and with other answers. Both hands are playing in C, while the 2nd phrase (i.e. the middle part measure 5-12) is in G.
Why when played in opposite direction do the intervals sound consonant?
