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I have recently been trying to master this piece from Bartok's Mikrokosmos, and at first sight, it appeared daunting due to the fact that the right-hand part is in B major and the left-hand part is in C major. Before playing it, it looked likely to be incredibly dissonant, with 5 sharps for one hand and none for the other, but it is actually much more consonant than I expected.

My question is this:

How do you set about composing a piece such as this with different key signatures for the two hands?

As well as learning the piano, I am currently trying to learn the (very) basics of composition, and find this particular piece a real puzzle (but I really like it!).

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    I suggest making the title something Bitonal Composition - Mikrokosmos Book 3, no. 70 – Josiah Jun 22 '15 at 20:59
  • Thanks, but I think I will leave it for now. Don't want to scare readers away with words like "bitonal" :) – Old John Jun 22 '15 at 21:05
  • The concept is called dual modaliy and this question should help you out: music.stackexchange.com/questions/25123/…. I'll try and add a more direct answer later as I've actually written a few short peices using this concept. – Dom Jun 22 '15 at 22:31
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    I would definitely specify that your question is not directly about the piece, but more a general question about composition. – Jacob Swanson Jun 22 '15 at 22:33
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Look what the score is doing: you have an oscillation rising from F♯ in the initial RH part, moving up to C♯, but artfully dodging A♯. At the same time, you have an accompaniment that consists largely of the fifth D-A alternating with the auxiliary notes E-G. The entire section is acting like an elaboration of a D major chord in a kind of quasi-Lydian setting. The RH is working with F♯, G♯, B and C♯; the LH, with D, E, G and A.

From there, the RH holds a G♯ slightly overlapping the A which commences the melody in the LH. (Leading tone, anyone?) The LH melody oscillates around A using the same set of tones as the initial accompaniment while RH rocks between F♯-C♯ fifth and its auxiliaries, G♯-B, so you have an elaboration of F♯ minor, but with a stressed A. However, as the melody progresses, it starts to stress E and, later, D against the auxiliary chord (i.e., E7).

At m.17, both voices start a two-part counterpoint. These two bars are slightly ambiguous. There is a suggestion of F minor to E diminished to G major, but the real point seems to be oblique movement out from F to B, with a wedge motion in the LH through E to G - not so much a progression as a contrapuntal movement towards a goal. This is the first time that F♮ and A♯ make an appearance, and they are both acting as stressed upper and lower leading tones.

G leads to the D-A dyad, which leads to A held under an F♯-C♯ broken figuration, with the A "resolving" to the initial E-G third under C♯. (The A is held slightly under the C# before dropping into the third, i.e., there is a strong suggestion of A7.) From here, both sets of accompanying dyads - E-G and D-A in the LH, G♯-B and F♯-C♯ in the RH - settling into an alternation of D M7 and E split-third, finally touching on F♮-A♯ which leads into a wedge back through the E split-third to the final D M7 chord. This piece is very definitely in D.

The thing to note here is that the wedge to the final D M7 is possible due to the fact that the segments in each hand are related by inversion. F and A♯ give the missing semitone in each segment, which is why they get special handling.

So...

  • You have strong contrapuntal movement in a wedge to D M7 due to the inversional relationship between each hand's scale segments.
  • With F and A♯ being omitted until the crux of the piece, and the limitation of each hand to a range of a fifth, you have scale segments that essentially define a quasi-Lydian D.
  • The harmonies that are stressed tend to play up a quasi-Lydian D: D, F# minor, with E7, G, and A7 strongly suggested.
  • Wow, that is going to take a bit of understanding! I had noticed some of the things you say (like the first appearance of one new note in each hand in m.17), but some tings (like "wedge"?) might take me a bit longer. +1 for now ... will accept when I fully understand! – Old John Jun 23 '15 at 1:42
  • Wedge melodically at ms.17-18 in the LH, because the melody opens out F-E-G. I said the passage is a bit ambiguous because there is some suggestion of E minor as well as G. At the end of the piece, you can see the harmonic wedge movement quite clearly (from D M7 to the fourth on F and back) - it's a direct result of the mirroring between the hands. The music closes to the bare fourth and opens back up linearly to the final chord. – user16935 Jun 23 '15 at 1:51
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I have no idea what Bartok was thinking when he wrote this, but one way to create something similar would be: 1. Start with a "big idea". In this case, "hey, what happens if the left hand plays the white keys and the right hand the black keys". (OK, that's not quite accurate because the right hand plays the white key B, but you get the idea). 2. Figure out how to make some reasonable-sounding chords using that idea. In Bartok's case, D major and E minor. 3. Add some more notes around those basic chords (and don't get hung up about "rules" or "major and minor scales", just do whatever sounds interesting to you).

Then once you have a few bars (about 8, in Bartok's case) try using some general principles for writing counterpoint. The middle section is just a mirror image, top to bottom, of the first section. (J S Bach played that sort of game all the time - Bartok didn't invent that idea!)

The final section is (approximately) the first two sections superimposed on each other (Bach also did that at least once, in the "Well-Tempered Clavier"). That will make sense to the listener by reference to what has gone before it, even if he/she can't analyse exactly what is going on just by listening.

Of course if you try to make your own piece using those sorts of ideas, it probably won't sound as "good" as Bartok, the first (or even the hundred-and-first) time you try - but don't let that stop you from trying!

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