"Would you know a piece of literature about what I'd call the theory of
arpeggios? Or more arpeggio sheet music for practice? I'd like to
compose my own organ music, and I'm desperately in love with arpeggios
(Bach, but also later composers), and I'd also like to dig a bit deeper
into what I think is the theory behind it. Arpeggios are based on
certain harmonic patterns, but a nice arpeggio is more than just a chord
split up into separate notes. Any theoretical text or music score
greatly appreciated (and doesn't have to be for organ ... there is a lot
of arpeggios music for piano, and others)."
After reading this request, I thought about how arpeggios can be constructed and it turns out that in any 4 note chord, there are 24 different permutations in the order of pitches:
Once you know this, you can do all kinds of interesting things with this information: you can create an entire variation based on one specific permutation only, you can mix them together in any order, you can play them in different major and minor keys, you can assign different meters and rhythmical figures to them etc.
If you want to find out the limits of your arpeggio playing skills, play these 3 Arpeggio Variations with optional pedal part I wrote yesterday. They are based on the harmony of the opening 8 measures of the famous Aria by J.S. Bach from his Goldberg Variations. There are total of 24 measures in this piece (actually 25, if you count the final chord) and each measure features one specific permutation of the four-note chord in the above order.
Don't feel compelled to practice them in a fast tempo as there are certain stretches for the hand that need to be played carefully and slowly at least at first. I hope you will find these variations useful.