Volume for Bram

>The main thing I'm
>still unclear on at the moment is how to compute volume, although at
the
>moment I suspect it's based on the integral of the square of the second
>derivative of f(x). Hopefully I'll know for sure after doing my
homework.

The usual quantity for measuring the volume of the signal is its RMS, or
the square root of the average value of the square of f(x). The average
value is the integral over a long enough time divided by the time. No
need to take derivatives of f(x).

P.S. Have you tried any listening experiments yet? I strongly suggest
that you do before you get too deeply involved in your project.