A few things I wanted to clarify and I hope I get this right. Please correct me if I am wrong.
First, ring modulation is related to amplitude modulation. In amplitude modulation, a sin wave is used to change the amplitude of the carrier signal which is the equivalent mathematically of multiplying the signals. the process itself if known as heterdyning and produces two “sidebands”, one at a lower frequency and the other at a higher frequency at equal distance, equal to the bandwith (inverse of frequency) of the modulating sin wave.
FM does something similar but produces multiple side bands which are related to the amplitude of the modulator. More volume, more sidebands which is exactly what happens with natural musical instruments. For example, a trumpet played at low volume is darker but when louder it has a brighter sounds. With tonguing, one can get a lot of expression by chaning the transient. FM synths mmic this which is why the Yamaha FM7 was so sucessful and even its later soft synth equivalents.
Ring modulation is related. It gets its name from the circut that produces it which is a circut with a diode on each side of a sqare which forms the ring.
Now what is interesting in either Frequency modulation or ring modulation is that the ratio of the two fundamental frequencies and their overtones combines to create a complex spectrum. I they are of the same frquency and waveform then the spectrum is doubled (or raised an octave to simplify).
Now with other frequencies, the frequencies of the side bands become the sum and diference of the frequencies but usually with the original signal removed which gives it its unique character.
Ratios of the fequencies which are whole numbers create more harmonics tones reminiscent of musical instruments but with fractional ratios, the tones sound more and more bell like and inharmonic. Some of your more “spacey” sounds can be created this way especially with a bit of reverb added.
A true master of ring modulation is Karlheintz Stockhausen especially his renown Kontakt found here of no doubt for which the Native Instruments sampler owes its name:
http://www.youtube.com/watch?v=aNt6a5xFOnE
or his later work “licht” (German for light), for which I believe the work of the series has been completed.
Another master at this is Morton Subontick. Subotnick used something called a “ghost box” which consisted of a pitch and envelope follower, a VCA and a voltage controlled ring modulator and frequency shifter.
What is interesting is that the pitch follower, I presume, was analogue so it would be nice to have a pitch follower in a fooger along with a frequency shifter or even a multiple frequency shifter like an EH POG. Of course the EH POG does not have CV control.
Clearly, the history in electronic music and even jazz (Miles Davis and Chic Corea on a Rhoades) has made significant use of ring modulation which is why I find it interested that the best use people find for these is running a drum machine through them.