Looking around at other people's solutions - I found they'd return a large value on the first tap if left alone for a while, so I made this little tap tempo with a timeout that resets it.
TapTempo_timeout.pd
I like its immediacy so haven't added averaging or anything, open to improvements!

@ddw_music Amazing, thanks so much - I'll try building in SuperCollider

@jameslo Thanks for replying after such a long time, it seems I wasn't asking the right question in the first place.

@ddw_music Thank you for taking the time to write such a detailed response, I think I finally understand.

So what I actually mean is I want to minimise the error in a BPM change of two semitones, and find the start and end values where it's lowest, even if they're both fractions. I think?

@jameslo Two years later but hey - ratio was probably the wrong word to use, sorry. I updated the patch so it starts with whole numbers, hopefully making it easier to understand:

bpmcalculator2.pd

So good ones would be:
69 BPM gives 61.472
59 BPM gives 52.563

A bad one would be:
77 BPM gives 68.5992

It's for a studio project where I have to pitch and slow everything down 2 semitones. The starting point isn't so important, but the nearer to a whole number it is the better precision there is with keeping everything on the grid.
So, starting with the smallest number of decimal places and ending with the smallest number of decimal places is preferable, does that make sense?

@jameslo Am I right in thinking you put the dll, lib or vst3 (renamed?) in the folder with the patch (text file and so on) for Windows? ...and then add the folder to your plugins directory?
Rather than editing a renamed package's contents and relocating it as on Mac?

It's implied in the wiki but it seems to just stop at stage 6 for Windows/Linux when the Mac instructions continue, which I guess could confuse people.

Yes please!

This is immense! Thanks a lot

Have you had a look at the patch I posted? I think that’s what I did!

I suppose I’m looking for the most ‘harmonic’ ratios. Would be useful going forward too I suppose when working with anharmonic spectral stuff.

Thanks - but the maths help I need is how to find ratios between the bpm changes.

BPMcalculator.pd

Messing about with this simple patch to calculate BPM change when something is slowed down two semitones and I wondered - how would I find the most whole numbered/least amount of decimal places change/ratio?

I think this is probably a basic maths question, but I have no clue how to approach it. Thanks!