Add, subtract, multiply, divide, logic operations ...

[Christopher_List at Sonymusic.Com]

  > Take the first wave, and center it on 0v
  > so that you have a + and a - swing (ie, no bias). Set a sample
  frequency,
  > say one value for as fast as I can type it, and then you
  > may end up with sample points like this:
  >
   > -3 -3 -2 -2 -1 -1  0  0 +1 +1 +2 +2 +3 +3
   >
  > Now, the second wave may end up looking like this over the same amount
  of time:
  >
   > -3 -2 -1  0 +1 +2 +3 +2 +1  0 -1 -2 -3 -2
   >
  > And, if you *add* these points together you'd get:
  >
    > 0 -1 -1 -2  0 +1 +3 +2 +2 +1 +1 0 0 +1
    >
  > Which is not the same as hearing two tones an octave apart.
  > I think this is what he's looking for...
  >
  > Mark
  This must be that new math. In my book (-3) + (-3) = -6, not 0. What're you
  trying to pull here, Pulver?  :)
  Seriously, though - looks to me like you're just subtracting the values - not
  adding them.

  As far as I'm concerned, a summing circuit, adds together the voltages at any
  point in time.
  Period.
  If you mathmatically add a sine wave to a sinewave an octave above it, you
  hear two sinewaves an octave apart.
  Period.
  Mixers add voltages - they therefore add sounds. Mathmatically, acousticly,
  however you wanna slice it.

  When you mix (a.k.a. "add") the voice of, say, William Burroughs with the
  sound of, say, a hip hop beat, the fact that you
  can still recognize each sound in the mix doesn't mean that the sounds haven't
   been modified by adding
  them together - they've been modified quite a bit. In fact I would challenge
  you to ever get back either of the
  original sounds. The sounds have been added together - period.

  Although, the mixer circuit in the Autoconfabulator mkII did realtime
  frequency inversion before adding the
  incoming waveforms - but that was driven by a microprocessor...

  - CList