For me if a rhythm is difficult sometimes I'm not hearing it correctly.In that case typing it into a notation program and having the computer play it back perfectly will get the rhythm into my brain. Once though with some piece, think it might have been a Clementi, I pointed out the difference between the way the rhythm was actually written vs the way it was usually played to my teacher. She decided it was probably intended to be played wrong.
I've heard that happen in Baroque music in the case of a dotted eighth and a sixteenth against triplet eighths, where the intent of the composer, according to Baroque practice, was for the sixteenth to line up with the third triplet.
I wish I could do what klavieronin suggests - I've known people who could do that and make it look easy, but I've never managed. Something that worked for me was to break the 6 against 5 into 3 against 3 plus 3 against 2 or 3 against 2 plus 3 against 3. Even if you just play it that way, at tempo it's hard to hear the difference, but I find once I've got that solution practiced it becomes easier to just relax a bit and the hands will sort of find a real 6 against 5 on their own.
Would it be correct to play a 3 in the right hand against 2 in the left hand and then play at the same time the remaining 3 notes in each hand?
Well, it would not be strictly correct, but breaking the 6 against 5 into 3 against 2 followed by 3 against 3, or vice versa, can be a useful step on the way to getting a real 6 against 5. And even if you get stuck with the simpler version, at tempo it will be hard for a listener to notice unless they've played the piece themselves.
Exactly, this is not the correct way to play the polyrhythm. My teacher years ago told me to play it that way and while it is not strictly correct it is unnoticeable to an audience. Do you play the polyrhythm strictly correct?
This is important to understand. In modern practice, the dot means "increase the note length by half of it's own length" (i e dotted half note is the length of three quarter notes instead of two). In Baroque practice, the dot just means "increase the length of this note" and that length is determined by the context.
Well, the notes do not coincide, except for the first of each group (5 or 6), but whether they are strictly correct, I mean whether I hit each note on the correct 30th subdividision of a pulse, I'm not sure, and I don't think that's really what Chopin had in mind for most of his polyrhythms in any case. I'm sure someone has learned those measures strictly mathematically, by breaking up the pulse into 30 subdivisions, calculating where each note in each hand occurs, tapping out that rhythm slowly, increasing the speed, and then finally getting it to feel like a real even six in one hand and an even five in the other, but it does not seem very efficient. The people I know who are naturals at polyrhythms do it the way klavieronin suggested, practice hands separate and then just throw them together. Not everyone can do that, though. I think the main thing is to try for the feeling of freedom and looseness that comes from the notes not lining up strictly. Thorn's suggestion of just alternating the notes after down beat is also good.
So Chopinīs intention was not to play the polyrhythm strictly?
How do you play the 6 against 5 polyrhythm in Chopin op 25 1 etude Aeolian Harp?
I think as a general rule Chopin did not intend his polyrhythms to be played strictly; I doubt he wrote a 22 against 6 fioratura wanting the pianist to break it into two 11 versus 3 groups, mathematically calculate which of the 33 subdivisions of the pulse each note landed on, and then play it mathematically correctly. Now you could argue that the case you are talking about in the Aeolian Harp Etude is different because it is an accompaniment figure rather than a fioritura, bit I still think (1) Chopin was aiming for a sense of freedom and relaxation rather than mathematical precision and (2) at performance tempo it's unlikely that you'll actually play it strictly correctly or that anyone with be able to perceive the difference.