How to play 3 against 4

[MCE2]

I am a recreational player trying to learn first movement of the Beethoven sonata no. 10 opus 14, and I am struggling with playing the triplets with one hand while playing 16th notes with the other.  

What is the best way to learn this section?  Should I practice hands separately?  Should I try to practice it slowly?  Any help would be appreciated!

Mason

[janice]

I just looked at my Beethoven Sonatas.  Are you talking about Op. 2 No.1?  I didn't see any 3 against 4.  I only saw a couple of measures of 2 against 3.  There's a huge difference between the two.  3 against 4 is far more difficult.  But I was only able to glance at it so maybe I overlooked it.  The only 3 against 4 that i've done is in Chopin's Fantasy Impromptu.  I'm sure that most of us have played that.  Now I'm only speaking for myself here, but I didn't find it all that difficult.  It took me a couple of weeks to tackle it.  The reason I learned it quickly is because the left hand has the repetitive part, the 3's.  So I let me left hand go on "automatic pilot", and I just thought about my right hand only (the 4's).  Maybe I "cheated" but it worked!!  But I'm willing to bet that that was the case with most of us!!  And that's only natural to go on auto in Fantasy Impromptu, because it's a LONG section (2 of them).  Once you tackle it, it will stay with you forever, kind of like riding a bike!  I don't have any profound words of wisdom here, but just write back because I must've overlooked it.  I just want to make sure we're on the same Sonata here  Alot of you here are very advanced and/or teach advanced students, so maybe you would give a better answer than I did.  My only "solution" is to tackle the hand that has the 3's at first.  Then do the other hand (the 4's) by itself.  Learn the hand that has the 3's SO WELL that it can go on "automatic pilot" when you put them together.  Write back!

[janice]

I'm sorry!  I wasn't looking at the right Sonata!  DUH!!!  Let me look at the CORRECT one now!  I feel stupid!

[MCE2]

You do not feel as stupid as I do for not being able to play it!  Placing the one hand on autopilot is an excellent idea.  I will try it.  Thanks for your help.

Mason

[ludwig]

hey, are you talking about Beethoven sonata opus 14 nr 2? I don't think there's a nr 10 is there? if you are you mean around bar 81? anyways, its always good to play it really slowly and figure out where the notes fit... draw them in if you have to, and just practice getting gradually faster. also you can sub divide note values even more for a more accurate playing.

[MCE2]

Yes, the sonata I am referring to is opus 14, no. 2.  I will try to practice slowly and get the timing right.  Thank you for your help.

[martin_s]

Heinrich Neuhaus has got a couple of very good things to say about 3 against 4 and similar matters, in his book 'The Art of Pianoplaying' (that, in my humble opinion, should be no.1 in every serious pianist's library!!). According to my own experience, the only situation where the quasi-mathematical process of finding out exactly where things actually happen helps you, is when you have to play these kind of rhythms in a very slow tempo. (first page of Amen du Desir, from Messiaens Vision de l'Amen, is one example)
But try Neuhaus first, he was a wise man.

[MzrtMusic]

This may be slightly... um... childish, but it really helped me get the three agains four down! I take the cleff that has the three rythm in it, and draw a line to show where it will hit with the four rythms. That will give you a concept of what pattern you are working with. That way, it will help you with all the other pieces you have to play, because you have the basic rythm down.

Love,

Sarah

[Binko_Binobo]

Well, tackle Brahms' 51 Exercises, and you'll have 3 against 4 in both hands engrained. And wait 'til you get to 4 against 5 and the more ridiculous ones.  

But really, I took both approaches. The mathematical and the natural, "autopilot" approach. In the end it really was a mixture of the two before I got it down.

So let's start with the mathematical. Get your grammar school math out and what's the lowest common multiple of 3 and 4? 12. So subdivide the beat into 12 sections. You have the triplets playing on 1,5 and 9. The 16ths are playing on 1,4,7, and 10. Draw it out, and you'll see how the beats fit together.  Now try drumming it at a slow pace on your knees. You should discover that drumming the rhythm isn't too difficult.

Now, try doing the same with your fingers and a simple pattern. I like playing c-d-e-f over and over with my left hand, and c-d-e with the right. Start slowly to see how the beats should feel together.

Unfortunately, this approach doesn't work very well once you speed the tempos up. However, it seems to help with the muscular memory of how the two parts should fit together. What I did afterwards was to put left hand on "autopilot" and play the four notes over and over and over, and trying to fit those triplets cleanly over the 16ths. Initially, you probably will be able to fit the 3s over the 4, but with a tendency to shave different parts of the 3s, thereby not getting true triplets. I had the tendency when learning 3 over 2, to play the 3 as dotted eighth, dotted eight, eight, rather than a true triplet. I find the same thing happening with 4 over 3.

So then just practice the pattern over and over again, try to keep those triplets clean. Eventually, you should be able to speed up the tempo and once you get it, it is like riding a bike. You get it!

[88keys]

Are we talking about Beethoven's Op. 14/2, measures 81-96?

If I am not mistaken, this is 2 against 3, rather than 3 against 4: There are 3 triplet notes on the right hand for every 2 16th's on the left.

What's the difference between the two?

Well, let's just say that I can fluently play Betthoven's Sonata Op. 14/2, yet 3 against 4 is totally beyond my ability... As Janice said, 3 against 4 is much trickier than 2 against 3.

So how does one master playing 2 against 3?

I agree with Martin_S on this one:

The mathematical approach of analysing the rythem is nearly useless at the tempo required for this piece. You simply don't have enough time to think about the math when playing in real time.

Therefore, you must teach your hands (rather than your mind) how to play the rythimic pattern naturally. I think Binko_Binobo's "autopilot" approach will work well in this respect.

Also it is recommended, if you can, to listen to a recording of yourself playing. This is the only way you can be sure that you got the rythem exactly right.

[Ktari]

Weeeee this is SOO belated! Randomly clicking on year old links... oh yeah!! I always felt like the autopilot thing made me uncomfortable -like, where's the control? I prefer the mathematical approach -it doesn't really hold when you speed up the tempo, but if you practice it slow enough, and then slowly speed up, it'll be ingrained.  Also, (I did Jeux d'Eau recently) in that one section that's 3 against 4, and.. yeah, just listen to the song, instead of watching every single note and making sure it was on beat, I found it easier to watch every quarter beat -fit in four of those and 3 of those in every quarter beat -so with less micromanaging, it just kind of turned out (although the math helped). Finally, when you get into the REALLY ridiculous stuff, like 7 against 11... um, just go for it and fit it all in before the next beat, really noone can tell... ...