What's the best method for learning how to play triplets over quavers?

Question

I've always struggled to play pieces where one part is in quavers (or any multiple thereof) and another is in triplets (or any odd number).

I'm going to have to finally conquer it, as I am attempting the Finale from Louis Vierne's Organ Symphony #1, which contains an example - albeit trivial - of triplets in the right & left hands vs. quavers in the feet, when the pedal theme returns (pages 50-51 in this score)

I can tap out the 'combined' rhythm, but using one hand (or foot, in my case) for only the quavers and the other exclusively for the triplets makes my brain switch to counting in either 2s or 3s, but never both! As a result the rhythm in one part gets squashed or extended to match my counting.

Any hints, tips, tricks or methods for learning how to separate them properly and not just fudge the rhythm?!

EDIT: A recording can be found here:

Answer 1

Take for example the end of the second bar on page 51 -- the eighth triplet over the two eighth notes. The notes of the triplet last 2/3 as long as the regular eighths. That means this is functionally equivalent to three quarter notes over two dotted quarter notes, since a quarter lasts 2/3 as long as a dotted quarter.

Noticing this makes it easier to see the pattern. Using a made-up notation for this -- b for both, r for right hand, l for left hand:

b---r-l-r---

Try just tapping this with your fingers, slowly. "BOTH two three four RIGHT two LEFT two RIGHT two three four."

Then speed it up. Get to the point where you can tap this pattern as quickly as you need to play the bar.

The move on to the actual notes. You'll probably need to slow it down. Just play those notes, don't try to play the whole bar or a section. Get comfortable with that. Then extend to the whole bar:

b---r---r---r---r---r---r---r---b---r-l-r---

Then keep extending. If this pattern is a habit for your fingers, you don't need to worry about counting twos or threes. Just play by habit. Of course, you'll need to practice to ensure you still put emphasis on the proper beats. If you find that difficult, just revert to slow tapping and emphasize the right taps, and proceed from there.

Answer 2

It depends on the piece of music you're playing. In your particular example, the triplets are quite important for the overall timing and sound, but they are not really part of the perceived rhythm. It is not really necessary, and perhaps not even desirable, to force your brain to count them. What you might rather do is train your hands to play these triplets correctly without thinking. This is easiest done at high speeds: start playing so fast that your mind is busy with the chords and cannot even care for the actually arpeggios. Just try playing as smooth as possible. This way, you should get something triplet-like automatically.
What you then need to do is slow down more and more, and – just for practice – play ever more staccato (it may also be useful to try percussion stops, or practice it on harpsichord e.g.). While doing this,

• Keep the phrasing smooth; equal note lengths
• Make sure you really have 3 points of attack, rather than 4. You can first leave out the double stops, this should make it easier.

Be careful not to fool yourself: one easily falls out of such a stable phrasing and starts playing the notes at completely random times when concentrating on the pedals. That's why it is a good idea to practice it on harpsichord or piano staccato, just tapping the pedal part on the ground: this way you immediately hear it when the hands get of of timing.

More important than the exact timing, anyway, is to play the overall passage fluently in the fast tempo and with rhythmic focus on the bass melody. This is very difficult to achieve by practicing the exact time relations between the triplets and quavers, because this way you literally tie your hands and feet together: that's not a good idea when you will need to run fast! It's easy to stumble, which would completely ruin this passage. But when your hands and feet can both act independently and merely need to be synchronized, it is quite doable and safe.

Answer 3

Tap out this rhythm so as to fit into a crotchet beat:

   1 2 & 3 (equiv: quaver, 2 semiquavers, quaver)

Now using two notes on the keyboard (one in each hand)play the above pattern like this: -Tap 1 with both hands -Tap 2 with the right hand -Tap the & with the left hand -Tap the 3 with the right hand. Repeat several times until the pattern flows with more fluidity. This gives you a fairly close 2 against 3 with the triplets in the RH Try swapping the 2, & and 3 over to give the triplets in the LH.

This is how I learnt to teach it while a music student at the RAM in the 60s!

Answer 4

One trick which can be helpful when trying to superimpose duple and triple meters is to consider the rhythm of the song "Chim chim cheree" from Mary Poppins. The first two measures each contain four syllables: "CHIM CHIM-i-NEE" whose durations are quarter, eighth, eighth, quarter. With the word stresses as indicated (how the song would usually be sung), the stresses fall on quarter-note beats in 3/4 time. If one were to keep the tempo and rhythm the same, but change the word stress to "CHIM chim-I-nee" the stresses would correspond to dotted-quarter beats in 6/8 time.

Three-against-two rhythms often generate this pattern of a beat which is shared between both meters, then a group of three where the first and last beats of the group are only in the triple meter and the middle one is from the duple. Recognizing that pattern, and recognizing where to apply stresses for triple or duple meter can make it easier to see how parts fit together.

Answer 5

(Agreeing with several of the answers). The good news is that our human brains can easily imitate rhythm patterns in language, so the idea is to find language phrases that match up to the desired musical rhythms.

3 against 2: Jump John-ny Jump (repeat)

Or try saying "Jump John Jump" as a triplet, and then just add the "ny" -- both ways gives this rhythm quite naturally. Try (slowly) using one hand for the triplet and the other for the duplet while saying the phrase.

Jump          John   ny    Jump         
_      _      _      _     _     _       
R      _      R      _     R     _    
L                    L

4 against 3: Jump John-ny Jump To Me

Jump                John  ny            Jump        To   Me
_      _      _     _     _     _       _     _     _     _     _     _
R                   R                   R                 R
L                         L                         L