As each timp. only has a range of about a fifth, I would interpret C to C# or C ➝ C# as meaning change to the nearest C# within that range rather than to one in a different octave. While eliminating any uncertainty, a sloping arrow could be considered unnecessary as there would realistically be only one possibility given the physical limitations of the instrument.
But what about this scenario? (and I know I need at least 3 to 4 seconds per timpano for retuning).
Say I have two timpani, one 32" kettle drum (d2 to a2) set to g2 and one 23" kettle drum (d3 to a3) set to g3, and I want to retune the higher one (23") to f#3? Without being very specific how would the timpanist know which one to retune?
My initial tuning for five timpani (yes, I know this is unusal), would be: A,C#,D,E,G
32" (d2 to a2)
28" (f2 to c3)
25" (bb2 to f3)
23" (d3 to a3)
20" (f3 to c4)
After the first playing of the timpani, I’m retuning as follows: G to F# (in this case no octave delineation is necessary obviously), so now: A,C#,D,E,F#
After the second playing: retune C# down to C (no octave delineation necessary) and F# up to G (again, no octave delineation necessary), so now: A,C,D,E,G
Never mind, I think I got a little overambitious on what I was trying to do and realized there’s not enough time to do three retunings in the number of rest measures I’m looking at. Lol
If text, such as high G to high F#, is not an option, one way of indicating it would be to have a small section of ossia staff (with playback suppressed) showing the actual notes involved. Because music notation is a visual medium, words can sometimes be less efficient. I am reminded of an English teacher who once asked our class to describe a spiral without using our hands.
Ok, I will look into using an ossia staff… Thanks again! Btw, when I was working this out just now, I realized with insufficient time to retune it wasn’t feasible anyway to do what I was trying to do; however on the next playing, there were enough measures to retune my ‘a2’ to ‘g2’, but like you said it would only make sense for the lowest drum for this to happen.