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

[Magnus Danielson]

> >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 fully agree. And for the "more triangle than sine" this is totally untrue.
There is no difference between them except the amplitude. The "steepness" of
the waveform depends on the amplitude and frequency. However, just cause you
raise the amplitude you will _not_ get a different waveFORM!

However, a stronger (have more amplitude or really, more power) sinus (or any
other signal) can be perceived a little different by the ear, but 
mathematically
there is no difference. For instance is our pitch judgement dependent on the
strength of the tone... just to confuse things :)

> >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.

It will most probably distort since many mixers use standard +/- 15V or +/- 18V
system. I know of only one mixer that would be close to run 40 Vrms, but then
it was custom built.

Note also that 40 peak to peak is only and amplitude of 20 V! Peak-to-peak
measures are rearly used in these perspectives so we better drop their use...
And those 20 V of amplitude is just 14.1 Vrms (if assuming a sine waveform).

Unless we really speak of the waveform amplitude we'd better stick to the RMS
values cause they tend to be much more usefull in discussions. They are more
easilly compatable to DC calculations among others... they have the effective
value!

> 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.

Yeap.

> 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.).

Yeap.

Cheers,
Magnus