Robert Syrett briefly touched on the subject of Wavefolding in his recent Know your Nodes Audulus tutorial on Phase Modulation. He notes that even in the case of the carrier oscillator having a frequency (ratio) of zero, one can still obtain a result – the carrier can be used as a waveshaper.

Rob Hordijk takes a closer look at this fascinating topic in tutorial #18 of his series given at the NOVARS research centre. Using Robert Syrett’s Audulus Wavefolder as a starting point I set about recreating what I could glean from Hordijk’s tutorial video.

As usual, Hordijk takes care to think things through and combine elements in a way that takes it all to the next level. He cleverly adds a crossfader to the waveshaper so that one can easily adjust between the original signal and the folded one – something that can be especially effective when subjected to voltage control. The one side of the crossfader can furthermore be set to point to either the original signal, no signal at all, or the output of the VCA.

The VCA is, as far as I can gather, a bipolar VCA along the lines of the one in his Dual Fader. With an inverted signal equally present alongside the original the two signals cancel each other out – until one introduces some modulation. With modulation at audio rates the resulting ring modulation provides a nice counterpart to the harmonic content generated by the wavefolding.

The waveshaper also works nicely alongside the Harmonic Oscillator since the oscillator lacks the verticals of conventional sawtooth or square waves that don’t lend themselves well to wavefolding.¹ Conversely the shaper can add a little more definition to the more rounded shapes of the Harmonic Oscillator, at least in my Audulus version of it.

I’ve put a little demo on the Audulus forum.

As I mentioned yesterday I was intrigued by the placement of the sawtooth between the triangle and square waves in the new Ableton Wavetable synth, and I spent a little time today exploring the results of changing the order of the oscillator shapes in one of the Audulus µVCOs. In the case of crossfading between oscillators, that placement, along with shifting the phase of the sawtooth to match the edge of the square, results in the octave harmonic of the sawtooth appearing before the fundamental when shifting between the sawtooth and the square. With the Wavetable synth the interpolations don’t appear to be the same as would occur when fading between set waveforms and I guess this is what opened up the possibility of arranging them in that order. When simply crossfading between waveforms a (co)sine–triangle–square–sawtooth ordering with all the waves sharing the same phase provides the smoothest transitions.

While a change from sine to triangle is fairly subtle, the square and sawtooth waves are more tricky when attempting to morph smoothly between waveforms. It’s an issue that Jerobeam Fenderson touches on in the third of his Oscilloscope Music tutorials. He explains the discrepancy between perceived loudness and the actual amplitude of the waveform in terms of our not hearing positions, but rather changes in positions – referring to the explanation of DC-offset in his second tutorial. The discrepancy might also be explained in terms of the higher overtone content of the sawtooth and square waves and the increased sensitivity of our hearing in the ranges in which the overtones of mid to lower tones appear.

In its current state there’s no easy way to implement wavetables in Audulus, but taking a look at Brian Funk’s tutorial/walkthrough/exploration of the Wavetable synth that will be included in Ableton Live 10, I was struck by how much has been achieved in Audulus recently on the waveshaping front – a lot of it thanks to the interest and efforts of Robert Syrett. Making wavetable waveforms without using wavetables, as he puts it.

A detail that intrigued me with the Ableton Wavetable setup was the order of the basic oscillator waves as sine–triangle–sawtooth–square, with the phase of the sawtooth shifted 90 degrees to match the edge of the square instead of the peak of the triangle, as one might expect. In the Audulus morphing oscillator included in the µCollection the sawtooth comes last and shares the same phase as the other waves.¹

Something to take a closer look at and experiment with.