John Higgins asks a question about playing arpeggios in the piece:
If you are in a situation like John, I recommend to practice playing the chords consisting out of these notes. Play them together, without starting on the lowest or the highest note. Aim for at least 3 correct repetitions in a row and do it extremely slowly.
Another technique which helps is transposition of these arpeggios. But don't start transposing to other keys right away. Instead, try to analyse the arpeggios mentally and understand what kind of chords they comprise. For example, in the above case, E-C-G-E-C-G-E-C is a C major root position chord and D-B-G-D-B-G-D-B is G major 1st inversion chord.
Even better, you can identify each note not only as belonging to a particular chord but being a certain scale degree in this key (G major). For example, these two arpeggios would consist of 6-4-1-6-4-1-6-4 and 5-3-1-5-3-1-5-3. Naturally these chords are the subdominant chord (C major) and tonic 6th chord (G major).
Since scale degrees really help "to translate" the music you are playing, I am pretty sure that playing them without looking at the fingers will become for you much easier as well.
Ausra's Harmony Exercise:
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Don't have an organ at home?
Download paper manuals and pedals, print them out, cut the white spaces, tape the sheets together and you'll be ready to practice anywhere where is a desk and floor. Make sure you have a higher chair.