Originally posted by Sal_:
But that still isn't 3 notes over two beats combined with 4 notes over two beats... I think I've broken it down into 12 subdivisions over X beats, which is divisible both by 3 and 4.
1 2 3 4 5 6 7 8 9 0 1 2|1 2....
Mathematically there is no other solution but to find the common denominator, and it is 12.
The number of "beats" doesn't really enter into the solution.
There is another solution which is intutive, and here is an example.
Suppose you are working on something like Chopin's Fantasy Impromptu. Begin with a logical approximation. Play the first LH note with the first RH note, which is correct. Play the second in the middle of the second and third notes in the RH. Play the last note of the LH with the last note of the four.
This is the best solution with a common denomitator of 6, and the LH is most definitely wrong, but it will be close.
For each set of four 16ths in the RH, the left hand will be doing this:
Dotted 16th (3 32nds), another dotted 16th (3 32nds) and finally a 16th. This short-changes the final LH note, and there will be a noticeable limp to the LH. The last note will also conincide with the RH, which is wrong.
However, once you have gotten this feel, you may be able to move the other notes, by instinct and ear, to the correct mathematical location.
If you reverse the patterns, and you can do this with any set of four notes in one hand against three in the other, the RH will have the triplet, and it will limp. This time you just concentrate on keeping the LH going evenly, while adjusting the RH slightly so that it stops limping.
For me 3 against 4 ends up being a "feel", and all the mathematical tweaking in the world is not what I actually do when I try to get it to sound right.
For a feeling of what it works out to be, try this…
RH C E G C G E, repeat over and over
LH C E G Bb C Bb G E, repeat over and over
This keeps both hands within an octave. Try getting both hands together, then try recording. If you finally get them even enough so that you can listen to either hand, on playback, and neither one is noticeably limping or stuttering, you have it.
For me this is the acid test:
Chopin Trois Nouvelle Etude No.1 in F minor
If you can play this right, you will probably never play anything with three against four that will not work.