Having made a start on recreating Rob Hordijk’s fluctuation waveform I’ve now been trying to clarify for myself the sync aspect of this type of modulation – the way the modulated signal syncs with the modulating signal.

Hard sync is fairly easy to understand but soft sync, which is what is at play in Hordijk’s fluctuation can have many different forms. The Hordijk info site explains the fluctuation soft sync as follows:

The “fluctuation” modulation is a combination of AM and FM which soft syncs to the harmonics of the modulating signal.

Hordijk himself provides a little more detail in his Waveshaping & Fluctuation masterclass:

…when you come to the extreme points then it sort of forces it to zero again, but only if it is within a certain distance and that means that it basically tries to sync on harmonics, but traditional soft sync in an oscillator actually syncs on higher harmonics, but this actually syncs, soft syncs on subharmonics, so the modulating oscillator needs to be higher than the fluctuated modulator, oscillator, which with normal soft sync would be the other way around, so it’s not really soft sync, so I cannot call it soft sync, so I had to give it another name and I thought well maybe Fluctuation is a nice name, and so I call it Fluctuation…

Hordijk’s explanation brings up something else that I’ve had to clarify for myself – what exactly it is he means by subharmonics. The possible definition of subharmonics as “integral submultiples of the fundamental (driving) frequency” offered by the Wikipedia article seems to help here. I simply take it to mean that since the modulating oscillator is higher than the one it is causing to fluctuate, the modulated oscillator syncs at subdivisions of the modulating frequency, rather than multiples.

Now how does one do that in Audulus?

I came across the Rob Hordijk’s Rungler in the Audulus forum a while ago and that particular module, as well as his system and approach in general, is something that I find myself repeatedly returning to.

The Rungler also forms the core of his Benjolin and Blippoo cicuits, and one element of it that I’ve found particularly fascinating is his Fluctuation modulation – a kind of combined FM/AM modulation that seems to have grown organically out of a double integrator algorithm used to round off the edges of a triangle wave. I haven’t quite figured out how to implement that algorithm directly in Audulus, but I did figure out that the edges could be rounded off a triangle wave in Audulus using the tanh (hyperbolic tangent) expression with similar results, and with that as a basis simply coupled regular AM and (linear) FM modulation to imitate Hordijk’s fluctuation – the only trick being to invert the AM signal so that the highest points of the FM correspond to the lowest points of the AM. Looking at the resulting waveform in a scope seems to come close to what Rob shows in this video around 16m10s.

Fluctuation is also used in Hordijk’s Triple LF-VCO and the result is an “extremely natural sounding vibrato, much gentler than with a normal LFO”, as explained on the Rob Hordijk information site.

I posted my first, somewhat rough, tryout in the Audulus forum a while ago and I’ve since been trying to refine the patch and experiment a little with what it sounds like at different frequencies. Robert Syrett has already put together something approaching a Benjolin (and a Rungler), and as the next steps in my own learning process I’m looking forward to figuring out my own implementation of a little more of the Rungler cicuit.