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The exact science is 6% per semitone. To show an example, A4 is 440.00Hz, and going up +6% to Bb4 (or A#4) gives you 466.16Hz.
There's no magic calculation for pitch-to-BPM changes, as 6% at 80BPM is 84.8BPM but at 130BPM, that same 6% increase will make the track play at 137.8BPM; 3BPM faster for the same pitch.
The pitch is not linked to tempo, Master Tempo is a keylock to keep the same audible pitch while the tempo changes (so really, it's named backwards; Master Tempo is really Master Key!)