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I have various audio loops that need to change pitch when I change the tempo. The relationship is not linear, so it must be exponential, but I don't know what the equation would be.

There is an online calculator that does individual changes, but I need to have it automatically change the pitch when I change the Beats Per Minute.

For instance:

If I gradually go from 123 beats per minute (tempo) down to 112 BPM, the overall pitch change is -1.62.

From 85 BPM to 111 BPM, the pitch change is 4.62

And from 176 BPM TO 137 BPM, the pitch change is -4.34

From these examples, is it possible to find exponent?