Ring Modulation

Probably best read Yesterday’s FM Post before you read this one.

So yesterday after I posted the FM synthesis piece I was asked by @RLM_UNIT1 on twitter if I could explain ring modulation. I have tried a number of times in the past to find out what ring modulation actually does and have been driven back by the horrible electrical engineering and advanced mathmatics type answers. Wikipedia’s entry is particularly useless in this regard. As a result I have never understood ring modulation, and I suspect that is true of many people… and possibly synth developers too as the manuals of synths that have ring modulation airily declare “The ring mod knob applies ring modulation to <insert source here>” and swiftly move on. You guys are not fooling anyone!

Last night I was determined to understand this mysterious thing, at least a little bit. I found a load of very technical sources and sites, and some horribly unwatchable videos until I came across a video by ohdratdigital  (linked below) that explained it all beautifully.

Ring modulation is a particular type of AM synthesis (bear with me a second here).

As you recall from the FM post I did  yesterday FM synthesis is where we modulate the frequency of a carrier signal with another signal – in other words we apply a vibrato effect to a signal but do it fast enough for the vibrato speed itself to be an audible wave, and once that speed is reached magic occurs and harmonics are spewed out all over the place (that is the technical explanation)
In AM synthesis we do the same thing but instead of modulating the Frequency (making the note go up and down) we modulate the Amplitude (make the note go louder and quieter). For anyone wanting a pithy soundbite then, FM is really fast vibrato and AM is really fast Tremolo (that is the technical term for tremolo, not the misnamed tremolo as in the ‘tremolo arm’ of a guitar, which actually provides vibrato)

Bingo – we are all now experts in AM and FM synthesis! All those electrical engineers screaming at me saying “it’s not quite that simple” and the mathematicians wincing at my lack of formulae are just wrong and I am right. So there.

Ring Modulation is a type of AM synthesis. The “ring” bit incidentally refers to the shape of the circuit you need to create to perform this modulation on real actual hardware. It is a singularly unhelpful description to anyone who isn’t an electrical engineer. In the world of synths it should be called “Dalek Modulation” because the voice of the Daleks is the most famous and instantly recognizable example of Ring Modulation – so Devs out there I inist you now rename the Ring Mod buttons on all of your synths with “Dalek Mod”, if you like you may add a translation in the manual for the purists.

knob

Maths stuff happens but the result is this, applying ring modulation to a frequency will create two frequencies, one with the frequency of the modulation signal ADDED to the original and one with the frequency of the modulation signal SUBTRACTED from the original frequency:

<addendum> I am not sure I expressed that right – the 2 figures are the sum and difference of the two waveforms, not that it matters much because I am dealing with positive numbers below so the difference should be the same as (signal – mod)

example 1: If I have an original signal of 400hz and I apply Ring Mod at 200hz I will get two output signals at (400+200)hz and (400-200)hz, (or for those of you more mathematically challenged that me 200 and 600 hz)

As 200 and 600 hz are closely related musically this will sound tuneful.
200hz is an octave below the original sound and 600 hz is in the related harmonic range, related to the 200hz, although not the original.

example 2:  If I have an original signal of 400hz and I apply Ring Mod at 400hz I will get one signal at 0hz (ie no signal at all) and one at 800hz – so the effect here will be to produce a single note an octave above the original.

So if you are dealing with really basic sine waves with really basic relationships the effects are not particularly interesting

But what if I have a more interesting sound with a number of harmonics from (for example) a saw wave

Say my original is 400hz with harmonics at 800, 1200, 1600hz and I apply a ring modulation at 200hz I will get the following out:

200, 1000, 1400, 600, 1400, 1800

While all of these harmonics are related to the new base note of 200hz the timbre of my sound is considerably changed (apart from having a fundamental an octave below the original signal) note I am getting 1400 twice now so this harmonic is going to be sounding pretty significant in the sound.

but what if I was to add a ring modulation at 150hz, now I would get

250, 650, 1050, 1450, 550, 950, 1350, 1750

The only harmonics here related to each other are 250 and 1750, this is going to sound pretty discordant.

So basic points then:

The more closely related the modulation frequency to the original frequency the more melodic the result (same as FM synthesis)
The more complex the incoming signal (more harmonics) the less harmonic the likely result as the same modulation frequency is being applied to ALL the harmonics too and the chances of those then all lining up to make a melodious note is smaller – in other words the more complex the input signal into your ring mod the more clangy and discordant your output will be.

Think “Dalek voice” – if you apply Dalek Voice to a sine wave the result is dull, but if you apply it to something complex, like a human voice, you are all “exterminate exterminate exterminate!”

See the tutorial vid here http://www.youtube.com/watch?v=NrYJKzr-TM4

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One Response to Ring Modulation

  1. David Wilson-Okamura says:

    Thank you, PoD. And I hope the next synth app has a Dalek knob.

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