You see, for all of us who are right-handed, playing with the left hand precisely is much more difficult than with the right hand. This is because not only we do everything with our right hand much more often but also because in the music you can find many more places when the melody is in the right hand.
That's why we like to practice the right hand first and more often that the other hand. It is like a closed circle: we have a weak left hand, practice more the right hand, and consequently, our right hand develops faster but the left hand not. To break this circle you need to work on the left hand more. That's why you realize that playing with your weak hand is more difficult and you may have to practice this part more times in your organ pieces.
Obviously, if you do like every good organ instructor would teach (practicing parts alone, combinations of 2 voices, combinations of 3 voices, and finally, all parts together) all of this will come naturally to you. You will start developing your left hand technique the same way as the right hand.
Another great help in overcoming this problem is to practice piano exercises either on the piano or on the organ. Good piano exercises will develop both of your hands equally well.
In addition to exercises, you can practice scales, chords, and arpeggios in various keys. Especially valuable are scales in double thirds and double sixths. This type of practice is of course a little more advanced so it is best to master simple scales in parallel and contrary motion first.
If you don't like the dry nature of exercises and scales, you can practice piano etudes on the organ. Great piano composers like Czerny, Berens, Lemoine, many others have left invaluable collections of etudes you can use for your daily practice. If you are an advanced player, try etudes by Chopin and Liszt.
Whatever you choose, play slowly, practice repeatedly, and don't worry about the concert tempo. You will reach this tempo when you are ready. Remember that this kind of playing will help you develop your left hand technique at the same level as the right hand.
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