sorry, the example of multiplication (above) is relevant to cross modulation, ring mod actually produces the sum and difference of the factors.
I have been stuggling with anti-aliasing a softsynth implementation of cross-mod recently that will not alias horribly - so my mind was fogged with it. Damn.
the frequency of the signal isn't 'in the signal' as such
Erm, yes it is.
in ring mod the amplitude modulates from -1 to +1 at the frequency of the wave product
(which for ring mod is the sum and difference
of the two waves with their harmonics).The frequency of the wave IS in the amplitude across time. Amplitude is not a static calculation of +1 or -1 , it has frequency when applied to a wave. Just look at an oscilloscope for a clear example
This could indeed be called merely a fast trem for ring mod ... but dont go discounting aliasing of ultra high frequencies in synthesis altogether!
Sampling is a classic case where aliasing occurs, where most waves in synths are samples these days - thats bad.
Analysis of aliasing of popluar soft-samplers
A nice example of aliasing as a Java Applet
this demonstrates the limitations of nyquist as you even aproach the nyquist freq. in this case 4khz. The red dots represent the 'samples'
I can't really think of any process where the calculations you describe would take place outside some heavy FFT and Max/MSP wankery
I do this all the time, on my MonoPoly it uses Cross modulation.
Cross modulation, when the pitch of one oscillator modulates the other in the way that I foolishly called ringmod above - it is also sometimes referred to as Frequency Modulation , or FM - although the DX rage of synths actualy used phase modulation, all of these produce aliasing. Operator advertises this as a feature.
http://www.ableton.com/index.php?main=o ... -usability
so although 'ring' mod won't be as extreme as what I said above (the sum is never going as high), many other synth processes can easilly produce aliasing. Distortion, waveshaping, sampling, etc.
you can't seriously be claiming to be able to hear, much less reproduce, frequencies like 75 kHz?
I can neither hear nor reproduce 75khz of course - but I can produce and hear the aliases of those frequencies with very basic synth techniques ... not anything weird and outlandish.
here's a link to a demo synth that will happily produce lots of aliases of x-mod harmonics up to 75khz .. in fact I have spent a few months trying hard to stop it.
>>DOWNLOAD ANGSTRO2 DEMO SYNTH
1.2 meg rar file, PC only
Try the preset 51, near the end of the list ..called "Aliased mess" .
Notice the master oscillator is at a high pitch, osc 2 is normal - yet all you hear from osc 2 is distorted artefacts.
Of course you dont hear the high pitches of 75khz, just the folded down rubbish from the multiplication (the xMod slider)
As you can guess, the same operation/patch performed on a mono-poly will not produce that audio result.