Marco M asked elsewhere:
I am still wondering if this piece is originally written for 4 hands. I can see in the bass clef almost the same melody than in the treble clef, just a little bit delayed: And a little bit shortened, it is not a canon in the end. Members in the forum explained me about "voices", and I now see this. Anyway, my "4 hand" question is still not answered. Actually, having voices, and each of them is even individually a nice one, would point even more towards a 4-hand idea, or? Each player stays with a similar melodie!
Ah, many pieces have me wishing I had four hands, or more, to play them with! Unfortunately, composers all seem to be brilliant pianists and expect me to play their pieces with just my two hands.
Have you ever seen four-part choral music written out? Perhaps in a hymn book, on a treble and bass clef so the piano can play it easily? The soprano and alto lines are typically in the treble clef. The tenor and bass lines are typically in the bass clef. A quartet could sing the hymn, each line being sung by one person. When the hymn is sung this way, you can clearly hear the four voices, because of the difference in vocal quality of each of the singers.
When a pianist plays the hymn, she is using two hands to play all four voices at once. Composers often use this idea, or related ideas, as they compose. There might be a melody, which usually is the highest notes: like the soprano line, or voice. There is typically some kind of low notes forming a foundation for the accompaniment. This is usually the lowest notes: like the bass line, or voice. Then there might be notes in between the highest and lowest notes, filling in the harmony and creating a pleasing effect. These are like the alto and tenor lines, or voices.
Since the composer isn't limited to a quartet of four people singing at the piano, she doesn't have to stick with just four notes at a time. She can have just a few voices at a time, with rests in the other voices, or she can multiply the voices by filling out the chords with more notes. We see this kind of effect in Schumann's Trämerei.
The music is often written in a way that is similar to how a hymn would be written. In a hymn written in 4-part harmony on two staves, the soprano notes are written with stems up; the alto notes with stems down; the tenor notes with stems up; and the bass notes with stems down. If you look at Träumerei and pay attention to which notes on the treble clef have stems up, you can see the melody -- the "soprano" voice. On the bass clef, the notes with stems down give the underpinning of the harmony -- the "bass" voice. The other notes (stems down on the treble clef, stems up on the bass clef) fill in the middle parts of the harmony -- "alto" and "tenor" voices.
One reason why this is done is to help the player see the structure of the music. For example, in a piece which is basically melody plus accompaniment, which notes should be brought out (usually the melody)? Which notes form the framework of the harmony (usually the bass)? Which notes are middle voices and usually played softer? It might seem obvious on a piece which notes are melody and which are accompaniment, but part of what makes it obvious is the engraver's choice of stems up and stems down.
So I don't think this piece was literally originally written to be played by two pianists/four hands. But Schumann's conception of it may well have been of the separate voices each having their own identity and integrity, which needs to be brought out even when playing it with just two hands.