I’m curious as to what this really means when referring to the theremin and ondes martenot. Is this possible to do in Max msp and if so how would one go about it?
Both of those instruments used vacuum tube oscillators that produced extremely high–yet, relatively close–frequencies. One oscillator was fixed and the other was variable. Their two outputs were multiplied together which produced sidebands at the sum and difference of the two oscillators. The sum was way too high to be audible, but the difference frequency fell within the audible range. It’s essentially ring modulation where only the lower sideband is audible.
You can multiply the outputs of two cycle~ objects and do something similar, but since you’re dealing with digital audio and things like the Nyquist frequency, you’ll probably get aliasing as the upper sideband gets folded down.
how would you control the resulting frequency? and what sort of high frequencies should be multiplied? upwards of 20khz?
It’s pretty simple, the resulting frequency is the mathematical difference between the two oscillators (f1-f2). Look at the MSP tutorials on amplitude modulation and ring modulation. They will explain how all this works.
so the result of multiplaying two high frequency cycle~ objects appears to sound exactly the same as a one cycle~ at a much lower frequency.
Not really much point in heterodyning then?
theres a lot of point to it (radio for instance) but maybe not for what you want to do ;). Things like AM also have very different effects when using non Sine waves because of the harmonics produced by other waves. Also when you use two low signals both the sidebands may be audible.
I don’t think that there’s much point to it with a traditional sampled system, when the frequencies are above Nyquist.