I did try -18,644% percent and the tempo was quite beside it
I don't understand what you mean by "the tempo was quite beside it".
It looks like you're not noticing the difference between the two different ways of expressing the same thing. The same tempo and timestretch variation yield a different proportional amount.
Different audio applications use these different names for the same process. Of the two I mostly use, Audacity calls it tempo, Cool Edit Pro calls it timestretch. I just need to use the right method with the right percentage figure in each application.
Consider the example of 1 minute at 100BPM, being reduced to 90BPM. That's a tempo reduction of 10% (i.e -10.000%), after which 90 beats then occur in the 1 minute. The remaining 10 beats after the 1 minute point are each now longer in duration, like all the new beats, so take longer than the 6 seconds (10%) they used to take before. So the total time is stretched more than 10%, it will increase 10/9, so 11.111%
10% tempo (BPM) reduction doesn't equate to 10% timestretch (total 110%).
That's why in your example, a tempo reduction of 18.644% results in a timestretch of 122.917%
To do the calculation, one is the inverse of the other, so as per Chris's original observation, 96BPM is 81.36% of 118BPM, inverse is 100/81.36 = 1.229 = 122.9% (neglecting rounding errors), your timestretch result. They're the same thing.
Equally, changing different BPMs by the same number of BPM has to result in different percentages. 100BPM made 10 BPM slower is a 10% reduction in tempo, 50BPM made 10BPM slower is a 20% tempo reduction. There's no way around that, and it will affect pitch proportionally if you do a speed change. So if the BPM change you desire doesn't match the resultant pitch change, you need to do it in two separate steps.
Edit: Incidentally, as to why the different, potentially confusing, terminology for the same process? I suspect it depends on whether those functions of the audio application are developed from the point of view of beats (dance, DJ, MIDI...) or elapsed time (soundtracks, radio/videos...)
Edited by Platypus, 29 October 2017 - 09:09 PM.