Choosing correct fingering: a science or an art?

Is fingering more of a science or an art? Are there special rules you must adhere to or is it just what feels comfortable?

This question is a very complex one. I think you can treat it like it is both a science and an art. There are definitely rules and traditions that help to decide and also since everyone's hands are somewhat different, you can look at it quite creatively at times.

What can I recommend for an organist who is stuck in choosing the right fingering? Imagine that you have no teacher to help you, no treatises to consult with, no experience with the scales and arpeggios. Is it hopeless? Do you need a coach to do it for you? Or perhaps there could be some secret trick that would save your day?

If you want to do it on your own, you have to prepare yourself that this process will be much slower than if someone guided you. Here are some general guidelines that might be helpful:

1. Avoid placing the thumb on the sharp keys (especially in the right hand).
2. Use finger substitution only when necessary to play legato more than one voice in one hand.
3. If the passage is wider than a perfect fifth, figure out the place you can change position.
4. Change position by placing the thumb under.
5. If the passage starts with an accidental, begin with 2 or 3.
6. Play the thirds with 1-3, 2-4, or 3-5.
7. Play the fourths with 1-4 or 2-5.
8. Use 1-5 for wider intervals.
9. For the middle note in three-note chords use 2 and 3. It depends on the interval of the fourth - play it with 2-5.
10. For the third note in four-note chords use 3 and 4. It depends on the interval of the third - play it with 4-5.
11. For root position chords in the left hand with accidentals use 3-5.
12. Use 3-5 when the third is major in chords.
13. Use 4-5 when the third is minor in chords.
14. Use 4-5 when the third is major in chords with natural keys.

Probably the most important thing to remember about fingering is that it's best not to take it for granted and figure it out, especially the tricky places. There is no use in playing the same passages with accidental fingerings repeatedly. Your fingers might become confused. However, sometimes you need to give it more thought and practice before writing it out with pencil.

Whatever the case, playing scales, arpeggios, chords, scales in double thirds and double sixths in different major and minor keys will teach you to choose the correct fingering for music composed after 1800's.

For early music, there is much more variety about the strong and weak fingers in each hand. But the rule of course is to avoid finger substitution and placing the thumb on the accidentals whenever possible. I find it very useful to play the same intervals with the same fingers in early music. This helps me to create ideal articulate legato touch without thinking about it.

By the way, if you want to be good at choosing fingering, become a skilled sight-reader.