Waveguide synthesis. Sounds like something from a 70s sci fi movie, doesn’t it? It’s actually a form of physical modelling, and in some ways a form of rudimentary wavetable synthesis, in which a delay, or delay line, is used to model a physical object.

The Beginning

The most common, well-known, and easiest to perform method of waveguide synthesis is Karplus-Strong synthesis. It simply uses a single delay with feedback set to audio rate (above 20hz) and employs a lowpass filter in the feedback loop (which most delays have anyway). This 1-dimensional waveguide is generally best for recreating the sound of a plucked string, albeit alone in space rather than tied to any particular instrument.

Typically, waveguides such as this are excited, or plucked/struck, with a short white noise burst, generally less than 10ms. This gives the delay sufficient spectral data to work with, while allowing the lowpass to have a noticeable effect on the sound. The phase cancellations within the delay and filter quickly narrow down the noise to a resonant sound, which deadens as time goes on thanks to the lowpass being increasingly steeper each delay/recursion.

However, it is much more interesting from a sound design perspective to feed non-noise sounds into the delay. A sine wave, for example, will create a very mellow plucked string, such as if you were to pluck a cello string or fretless bass. Varying the frequency of the sine will create interesting additive-like additions and subtractions as the frequency goes towards and away from intervals of the delay frequency. A saw wave will create a very interesting, almost distorted highpass-like sound. Constant signals fed into the delay will also create interesting sounds depending on spectral content and modulations.

A Little More

2-dimensional waveguides are best for synthesizing membranes like drum heads. They work similarly to 1-dimensional waveguides but employ multiple delay units in a sort of grid such that they feed each other. When similarly excited, instead of plucked strings, you get beaten stretched membranes, again not tied to any particular instrument.

However, it is worth noting that using a comb filter rather than a delay network can yield similar results with a much simpler design. A comb filter is very similar to a Karplus-Strong delay unit, except it includes a mix control to allow some dry sound through (and is technically a phase shifter instead of a delay). Comb filters have a variety of uses I’ve covered in another article, but in this case the dry and delayed wet signal combined and fed back through the delay make for a very interesting membrane synthesizer – or other sounds, depending on how you use it. Experiment!

The Last Piece

1- and 2-dimensional waveguides are cool, I guess, if you like boring things with little control. You’re probably expecting me to introduce 3-dimensional waveguides, which are really more into reverb algorithms than waveguide synthesis – also cool, just not in the scope of this article. No, what I’m going to tell you about now is a tool I’ve been using for years and seems to have gone somewhat unnoticed compared to the above types of waveguide synthesis: Banded Waveguides.

Banded waveguides follow the same principle of delays with feedback and filters in said feedback loop, but are infinitely more powerful due to their ability not only to accurately recreate all the above forms of waveguide synthesis, but also entirely new things – namely, solid bodies. Banded refers to using filters to only use a certain band of the spectrum – or, more accurately, multiple bands. The first implementations were fairly rudimentary and best for synthesizing things like idiophones, but the concept has since expanded vastly to utilise banks of macro-adjusted bandpass filters in the feedback loop, or multiple feedback loops with multiple delay lines. More commonly, banded waveguides are referred to as modal synthesizers, modal resonators, or, in the case of the filterbank by itself, modal filterbanks – useful devices in their own right, for sure.

The settings of the modal resonator can be adjusted to macro-adjust the filterbank and delay. This refers to one control modulating multiple things, in this case filter frequency, quality (also known as Q, peak, or resonance), amplitude, delay time, and feedback amount. Usually multiple controls affect some or all of these in different ways to get a wide range of various sounds. Again using a short white noise burst as an exciter, we can observe sounds from plucked strings, struck metals, membranes, woodblocks, and a wide variety of other sounds. Using alternate exciters, from various colours of noise to tonal sounds like oscillator waveforms and even more complex sounds, and varying the length of time they excite the resonator, we can achieve an even greater range of sounds.

Interestingly, when using complex exciters in a similar way to impulse responses, one can use modal synthesizers for something called commuted synthesis. This is a yet further expanded version of waveguide synthesis that includes the pluck/strike/bow exciter with an exciter for the body of the object being struck. Effectively, one complex exciter with one modal resonator can accurately synthesize a whole object, be it a concert bass drum, solid body guitar, pebbles or glass, wood boxes and boards, metal cans, and so forth.

One of the tools I use for waveguide synthesis, Mutable Instruments’ Elements, is designed specifically for the mixing and modification of a wide array of exciters under 3 main categories. It’s freely available to use within VCV Rack, and can be difficult to master, but once you have it’s a very powerful tool to have, even if you use no other modular equipment (in VCV this is a moot point given you can have infinite instances of Elements as well as custom exciters and modulators). However, despite Elements’ power, I find myself using MI Rings more, which I have covered in another article. It offers more flexibility in terms of voicing of the filterbank and offers multiple other modes of operation which are all just different ways to use a modal resonator.

Conclusion

I hope this article has opened your eyes to a somewhat lesser known and understood synthesis technique. I use waveguides all the time in my work, and is part of how I can work just as efficiently as my library-hugging colleagues while still having absolute control over every sound from scratch. I hope you’ll explore not only MI’s offerings in this field, but also explore other synthesizers that offer it (such as U-GO’s string and M theory synthesizers, Vital, Surge, and Helm) as well as modular environments such as Bitwig’s Grid (despite having a rudimentary banded waveguide resonator as a stock plug-in), PureData, M4L, and Reaktor to build and better understand such devices, and in doing so create wild custom synthesizers. I also encourage you to abuse your effects and existing synthesizers to play with this technique, as I often do with my Yamaha SY77 and recently-acquired Roland System-8.

Go forth and synthesize weird and realistic sounds!