3

Ofcourse there is the notation 1 2 3 4 5 for each finger. But are there other (quasi-)standard symbols for indicating, for example, hand movements, stretching the hand, putting the thumb under, etc.? It would be possible to create my own notation system, but if there are existing coherent systems, that would be nice to know.

3

Not really, the fingers should be all you need. For example, to notate the cross on a scale, indicating "1 2 3 1 2 3 4 5" suffices to indicate a thumb-under-3 cross. And since you can pretty safely assume that each finger in order is going to play each note, you can leave out everything except the crosses. For an ascending C major scale in the right hand, "1 - - 1 - - - -" (where the '-' just means nothing indicated) would suffice, and descending "5 - - - - 3 - -" would indicate the cross to 3.

The only other thing is indicating which hand to use, in cases of hand crossing or cross staffing. The standard abbreviations can be seen here, and I would suggest simply using the English "LH" / "RH".

Anything beyond this is pretty much unnecessary. If there's something really unusual that you need to notate, I would recommend simply writing out whatever it is that you want in the margin.

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    There's still 'sopra' or 'sotto', indicating how to position your hands relative to each other when they interfere with each other. Rarely necessary, but can be a bit of an eye-opener when used judiciously. – Kilian Foth Nov 18 '14 at 8:32

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