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Slashes can be used to abbreviate repetitions...
...but, are there any marks or standard instructions to repeat and sequence up or down by step or half step?
I figure that I can always notate the figures and then just write in English "repeat by ascending step through an octave" or something like that.
I'm wondering is there is some commonly accepted way to do this?
You could write the first few repetitions of the pattern then 'sim.'. But it would have to be VERY obvious how the pattern continued.
I'd certainly only advise it in an etude or exercise, not in a piece to be sight-read and performed.
I have seen notation like this only in instructional materials. For instance, here are two examples from Jerry Coker's "Patterns for Jazz":
In the first example, he writes a few repetitions with "etc." written at the end of the line.
In the second example, he writes one measure of the pattern then uses slash notation to indicate where the pattern should move to.
As Laurence has stated, this type of notation should be reserved for instructional material. If you are composing a piece for someone to perform, you should notate out everything explicitly.
