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

[Mark Pulver]

>Bert Schiettecatte wrote:
>> > eg... You have two sines, one at say 400hz and another at 800hz. He
>> > doesn't wanna hear the two waves "mixed" together (thus you hearing
>> > two tones an octave apart), but what he wants is to hear the result of
>> > the voltage values of the waves being added together at various points
>> > in the time domain.
>> 
>> finally. somebody understands what I mean :)
>
>I still don't understand.  If you add the instantaneous voltages of
>two signals, you're mixing them, right?  or what distinction am I
>missing?

No. This can't be true, and it *JUST* dawned on me as to why...

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.

Lemme do the numbers again (and I'll do 'em right this time <g>):

	sine #1   -3 -2 -1 0 +1 +2 +3 +2 +1 0 -1 -2 -3 -2
	sine #2   -3 -2 -1 0 +1 +2 +3 +2 +1 0 -1 -2 -3 -2
	sum	   -6 -4 -2 0 +2 +4 +6 +4 +2 0 -2 -4 -6 -4

The frequency of this waveform will be the same (the zero crossings will
occur at the same place in time), but the peaks are twice the value, hence
twice the "volume", and since the voltages are changing faster and covering
more "distance" to reach the same point in time, then the slope must be
greater. No more sine wave.

If you accept this for an example of two sines at the same frequency, then
the same must be true for two sines of different frequencies, and any
number of complex waveforms at any number of frequencies.

Here's my other example, but sdone correctly:

	wave #1   -3 -3 -2 -2 -1 -1  0  0 +1 +1 +2 +2 +3 +3
	wave #2   -3 -2 -1  0 +1 +2 +3 +2 +1  0 -1 -2 -3 -2
	sum	   -6 -5 -3 -2  0 +1 +3 +2 +2 +1 +1  0  0 +1

>From the looks of this.... It's gonna be awhile befor the final waveform
ever gets back below the zero crossing. This could be quite cool...


If you then go back to what Bert originally was looking at... I think that
we'd *ALL* want a module like this...

Think about *really* dividing waveforms... wow.

This sounds like it'd be right up Serge's alley... Anyone wanna run this by
Rex and see what he has to say?
---------------------------------------------------------------------------
 Mark Pulver - http://shoga.wwa.com/~mpulver    The "Son of The MIDI Wall"
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