If you reduce the tempo of the audio file by say 20% does Reaper still maintain the correct bar numbering automatically?
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Yes and no, depending on how you configure Reaper in "Project Setting", which allows the bars to be set by Beat or by Time. I generally use "time".
Now that I better understand what you are doing, here are the details about how this is handled in Reaper. Ya, it can be complicated. But it does work well.
https://www.youtube.com/watch?v=A4M4BoYcwPcThis issue goes beyound just setting the starting bar to what ever bar number you like. It has to do with how the project adjusts the "item" during tempo changes.
Or have I just sent us down a rabbit hole??
Hey Dan, no rabbit hole my friend and I do think you're getting it now. I could only watch about half of that video untill my eyes and brain glazed over. I'm not a Reaper user but I gathered that this sort of thing is no slam dunk for us meer mortals

That guy (in lightening fashion) flew thru 2 different menus and made at least 3 setting changes in about as many seconds.
And I think you are spot on. This is more than just setting where Bar 1 should be. Maybe that's why I couldn't easily find a similar video dealing with Studio One. All of this gets into how the particular DAW "thinks" about the audio file that it's being asked to operate on. Clearly I'm no S1 expert and I just recently upgraded to ver 6. But there are several configuration settings in any DAW that will force it to think/interpret things in certain ways.
Bottom line for me, is that I figured out how do get the bar numbering to synchronize and because I don't want to re-invent this wheel again I captured the steps based on the default/factory S1 configuration settings. It wasn't easy to arrive at a solution useful to me which is why I'm offering it to whoever wants it.