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

[Tim Walters]

>If I had two sines, both at 400hz, and *mixed* them, then I would hear a
>single pitched tone, possibly SLIGHTLY louder.
>
>But... If I ADD them together I will *THEN* get a single pitched tone, but
>it will have twice the voltage at the peaks and the SLOPE of the viewed
>waveform will be twice as steep. It will be much more triangle than sine.

No.  Sin(x) + sin(x) = 2*sin(x) = another sine wave.

Mixing is addition.  There is absolutely no difference, in the analog or
digital domain.

Gain is multiplication.

>I run 40ish channels of audio at home... Now, if I split a 1v signal into
>40 channels, and all inputs and the mixer masters are at unity gain, then I
>gotta say, that I will *NOT* be getting out *ANYWHERE NEAR* a 40v signal at
>the mains. In fact, I would bet money that I won't get anywhere near a 2v
>signal at the mains!

If the signals were identical sine waves *in phase*, your mixer would in
fact attempt to put out 40 volts (p-p).  Of course, it might distort
instead.

Typically, when you mix 40 signals, they are neither constant-voltage nor
phase-correlated, and thus don't add their peak-to-peak values.  Momentary
voltage is what gets added.

With regard to one sound/many sounds:  To a mixer, there's no difference
between mixing a sine wave with one an octave higher and mixing Merzbow
with the Carpenters.  Your brain, however, fuses the first pair but not the
second (actually, whether it fuses the sine waves depends on many
psychoacoustic factors, including frequency, relative level, etc.).


-----------------------------
"This is digitally conceived New-Pagan vomit.  And I've never tasted vomit
this good." --yet another review of my CD, this time in _Sonar Map_

Tim Walters  --  walters at digidesign.com  --  http://www.slip.net/~coredump