Musical Iterative Ring Modulation

Plugins & Modules
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One of the things my Venom Recurse module can do is Ring Modulation. This happened out of a desire to amplify a signal by 32 or more to support deep wave folding (I’ll post a video about this soon). I didn’t want the built in scale attenuverter to exceed x 10, and the easiest way to achieve the high amplification was to multiply the scale CV input by the attenuverter value. Oh, that 's cool, I thought - the module will then do ring modulation. But I never really had worked with ring mod, and didn’t know how it could be used.

I don’t see it in many patches, and all the literature I could find mostly talked about the inharmonic frequency shifting it does, so it seems it is mostly used for weird effects. But after doing some ring mod experiments with Recurse, I think ring mod is seriously under valued. Just like with FM, if you keep the ratio of modulator frequency / carrier frequency to integral values, then it is easy to get harmonious musical results, especially if the modulator is a sine wave.

What I was really surprised to find is that you can iteratively apply ring mod using the same carrier, and each pass yields a different, yet still musical sound. It is well known that ring modulation does not preserve the original frequencies of the carrier or modulator. But I was pleasantly surprised to learn that an even number of ring mod passes restores the original carrier frequencies, though at different amplitudes.

I prepared a patch and video to demonstrate the musical application of ring modulation. I use the Venom Harmonic Quantizer module (HQ) to easily compute the carrier frequency at various integral ratios. And since I never do more than 8 iterative ring mod passes, the 16 polyphonic channels allow a single Recurse module to perform all the ring modulation for two independent voices.

The ring modulation is performed by patching the carrier to the Recurse input, and the modulator to the Scale CV. I use +/- 5V signals, and as long as I set the Recurse scale factor to 0.2, then the output remains 10V peak to peak no matter how many iterations I perform.

I slightly detune the carrier VCO so that the modulator / carrier frequency is not quite integral. This adds some really pleasant undulating shifts in harmonic content when using a harmonically rich carrier. I also add a bit of DC offset, which I find gives the bass tones a bit more emphasis, so technically I am introducing a bit of amplitude modulation to go along with the ring mod.

There are many brilliant minds that have worked with electronic music over many decades, and I have only been doing this for about two years. I can’t possibly have discovered something new. But I haven’t been able to find anything written about the technique I am using. I would be very grateful if someone could point me to some content about musical usage of iterative ring modulation, preferably on the web. I would like to read more about the technique, and see where it can be taken.

Also, feel free to post your own ring mod patches, using whatever ring modulator you prefer. I think there is expansive territory to explore.

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Cool possibilities there. You’re probably familiar with Stockhausen’s use of RM, historically it was one of the few truly musical devices available to the earliest electronic studios. Alas, I don’t know of any published explications of how those pioneers specifically used it in their works (i.e. what settings they used, the device specs and so forth). Could be an interesting research paper.

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Frequency shifting is a close cousin of RM, btw. Don’t know if the recursive thing would be cool with that or not…

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I found this paper about the RM setup for Mantra

It sounds as though the RM is manually tuned one octave down from each central note of the piece. So each central note is consonant with the RM, and the RM applied to the other surrounding notes creates varying degrees of dissonance.

I’m wondering if back in the day ring modulators were too expensive and finicky to even dream of applying them in series. Maybe RM got an undeserved “bad rep” for “traditional” sounding music, such that no one tried running them iteratively once digital versions became readily and cheaply available.

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As I understand it, frequency shifting is generally only done in one direction, whereas a ring modulator shifts equally both up and down. With the frequency shifting, successive application will push the frequency further and further away, and probably sound “worse and worse”. But the symmetry of the RM has all the even iterations returning the inner bands back to their original frequency, so it is able to remain harmonious (assuming the use of integral ratios)

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That might well have been the case. Peter Manning’s book emphasizes the scarcity of musically-oriented electronic gear - much of what they used was not designed for musical application - and all of it was expensive. I tried a quick search for a price in 1970 but got no joy. The RM for Mantra was custom-built, so clearly Stockhausen had some decent funding by then.

Interesting too that Bode had designed a synth that used it in 1947 (!).

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Yes, sounds right.

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The Bode/Moog frequency shifter cost $1100 when it came out!

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So about US$6700 today. Yikes.

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Classic ring modulator was four diodes in “a ring” and a transformer. Shouldn’t have been super expensive. I made mine in the 70’s from an analog multiplier chip.

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My PAIA synth in 1973 had a ring modulator module. By today’s standards, it was cheap. At the time as an undergraduate university student, everything was expensive. But, I lived at home with my parents.

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The little section in the lower left that says “mod” is a ring modulator. I originally build it in a cardboard box, but it was happier in here. The “road cases” are from PAIA!

rm
rm960×720 126 KB

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Nice tones Dave. Energy and Dark Energy are built around this and you can get similar tones.

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Multiplying 2 signals yields the sum and difference frequencies of all frequencies contained in boths signals. Unlike FM/PM, negative frequencies are NOT reflected back into the spectrum (though at inverse phase). They simply disappear into the infrasonic domain. As with FM/PM, for AM ratios are important, if you want to maintain harmonic series spectral content.

It so happens that I do regulary play around with AM. Generally more or less from an additive synthesis perspective. Creating and modulating “quasi additive” spectra, not by adding/modulating individual harmonics (which is quite tedious work), but using (summing and multiplying) AM generated/based spectra.

Recently I have been fiddling a lot with feedback circuits as well. In the AM context for example feeding back AM output(s) back into input(s). Including chaining AM operations and feedback.

Anyway…

AM (just like FM/PM) is indeed mostly “known” for the inharmonics. But sticking to integer ratios and sines (or at least sparse spectral signals) will generally yield harmonic spectra. Add noise (just attacks or hiss or rumble) to taste.

Very useful module for AM experiments:

Martin Lueder’s OctaTimes

Remember…AM (in audio synthesis) is just modulating the amplitude of some signal using some other signal at audiorate. So generally, any module with an ‘audio amplitude level’ modulation input could be used (e.g. most VCA’s and Mixers). As long as they actaully evaluate the amplitude of the incoming modulation signal at audiorate (some modules save CPU by lowering the modulation/parameter/input evaluation samplerate).

EDIT: if unchecked, multiplying frequencies could soon reach and ‘cross’ the Nyquist frequency and introduce digital aliasing (reflecting back into the audible spectrum at some integer division of the offending frequencies, causing inharmonics).

BTW. AM is not dead as a main concept for audio synthesis. Recently (somewhere in very recent years), there was even a new beast of a (hardware) synthesizer (mainly) based on AM. For some reason I can’t remember (or even find) it’s brand and name right now…

EDIT: I meant the innovative NONLINEAR LABS C15, mainly exploiting the what you can achieve, starting of with the humble sine.

A bit of a tangent on the use of AM…

You can also use AM to remove the sharp wave transients, e.g. of oscillator sync, since when multiplying by some bipolar signal, you will periodically multiply by 0, a perfect transition point. Check out the concept as explained by deep diving synthesis wizard Jakub Ciupinski.

Silky smooth sync

Even more of a tangent…

Come to think of it, I guess AM could possibly be used to do or emulate sort-of VOSIM like stuff.

Multiplying a sine by itself, and mutilplying the resulting “bumps” at some integer ratio with a saw. Multiplying by an offset pulse of varying width can introduce the silence bit at the end. Anyway…plenty to experiment with.

VOSIM, Werner Kaegi et al.

Mutable/Audible Instruments Macro Oscillator 2/Rings offers a VOSIM model.

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Adding to the above…

@DaveVenom, I am very happy with your HQ module. I use it a lot to generate harmonics (or harmonic ratios).

Venom HQ - Harmonic Quantizer

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Thanks Lars. I had seen that both Energy and Dark Energy were based on ring mod, but I was not comfortable with the concept, and so didn’t use use them, or remember they used ring mod. For some reason I am often reluctant to use a module until I feel I have a decent understanding of how it works.

Now that I have experimented with ring mod, those two modules make a lot more sense, and I am more comfortable with them.

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