Recently I was asked a question about the left hand. An organist wanted to know if there was anything he could do about a left hand that just didn't seem to be able to keep up with his right.
There is nothing really new about this problem--most of us are right-handed (90%, I think). Most composers, therefore, have been right-handed. And most of the time the most difficult parts are written for the right hand.
At least, that's true of a lot of piano music.
The trouble is, that isn't always true of organ music, for the reason that it is frequently contrapuntal, in which every voice, and therefore both hand, are taking equal roles. That is also, of course, true if you are playing, let's say, Bach, on the piano. It is only after Bach, and maybe well into the 19th century, when you get music in which the right hand rollicks along and the left hand merely provides a little plunk plunk here and there.
And anyway, it is not good to try to make a career out of having a right hand that can play like the wind and a left hand that lumbers along like an octopus missing three arms (does that make it a pentapus?). So what to do about it?
Here's one extreme. Brahms reversed Schubert's Impromptu Op. 90 n. 2 in Eb so that the rapid passages were in the left hand, and the accompanying chords in the right. He did the same thing, if I remember right (or left), for Weber's Perpetuum Mobile and a Chopin Etude. Obviously the young Brahms thought that equality between the hands was important, and he couldn't find an existing piece that emphasized the left hand.
There are, however, some passages in the Chopin Etudes, and also the Moszkowski Etudes, that give the left hand all the hard work. They are rare; most of the time the right hand gets to do all the derring do, but occasionally even Czerny or Hanon will focus on the left hand as a tour de force. But Brahms's example is useful. If there aren't enough such passages, create your own. Play right hand parts with your left hand. Make it work, especially while the right hand takes it easy.
In fact, you could give your right hand the day off. Sometimes it is good to work the left hand by itself. Often we find it impossible to play the left hand independently; if trying to do so leads to that unpleasant discovery it is because your left hand is always dependent on the right for orientation, both in physical space and to find the rhythm. Making it play by itself often helps your mind concentrate on what you may have not thought was a very important part. Make it important--make it the focus of what you are doing. Coordinating it with the right hand is much easier when the two are on a more equal footing (handing?) and this won't happen unless you can imagine your left hand as an independent force. I'll bet you can play your right hand by itself. But your left?
Much of the literature I've suggested is for the piano. Maybe this is the product of my pianist training--and lack of it on the organ. But I find piano skills helpful in playing the organ. It seems to help with the precision of the fingers to have an instrument that fights back a little; and a modern organ usually doesn't. My pianistic background is probably why my organ playing is more rhythmic, articulate, and less sloppy that many organists I know.
There is one more pianistic angle I've thought of. When you are playing scales with both hands, learn to lead with your left hand. That is, concentrate on it, make it the one running the show, focus on it, and don't let the right hand go any faster than the left hand will go.
In time, the left hand will become more agile and able to hold its own with the right, though if that is your non-dominant hand, it will probably never be entirely equal. Sometimes you just need to play a passage very slowly and concentrate on the interplay between the hands, speeding it up a little each day, but never without being able to think of each note as you play it. Don't let your hands, either of them, run ahead of your mind. That's really your third hand, and it is the most important one; the physical inequity between the hands can largely be overcome through focus, and concentration.
The bias toward the right hand is built right into our language. In Latin the right hand is the mano dextra (the dexterous hand) and the left is the mano sinestra, which is where we get the word sinister, as in there must be something very wrong with left-handed people! Pianist Leon Fleischer used to pun on this etymological connection: before he commenced a concert of music entirely for the left hand alone (having sustained an injury to his right several decades ago), he would say to the audience: "And now for an evening of sinister music...."