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Hi Rui,
I took your formula and built an Python script comparing the velocity data against Qtractors normalizer and my alternative normalizer.

What is quickly obvious is Qtractor does not compress the data range, just re-scales velocity data.

My alternative normalizer does compress and normalizes in on step. This in my opinion is more musically desirable.
When you find a spare minute, have a play with the attached python script. Please check my maths :-)

PS I had to change the script to a .txt to upload it :-)

Thanks for your time.
I have used Rosegarden and Muse. Qtractor is my favourite :-)

Regards Dave M.