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Modular Diary

I’ve packed the modified uLope sub-stages into a module that more closely resembles the ADBDR envelope in Hordijk’s Dual Envelope generator.

One of the innovations in his design lies in replacing the sustain section with second decay stage that can slowly taper off, thus allowing for more ‘natural’ sounding contours. With the decay knob turned all the way up, a conventional flat sustain can be achieved. The second decay is also preceded by a break setting that adjusts how far the first decay falls. The resulting shapes are perhaps most easily understood by taking a look at the diagrams in Hordijk’s schematic.

Each stage also has a modulation input that adds to the values set by the knobs. Since modulation is most effective when the pitch of the modulating waveform is lower than the one being modulated, a sample & hold has been included. Hordijk provides a nice explanation of this technique in one of his NOVARS tutorial videos.

The patch can be found on the Audulus forum.

Modular Diary

I’ve made a further modification to Stephen Schoen’s uLope so that sustain modules can also be added to the envelope chain with the trigger mode activated.

Before I pack it into a module that more closely resembles Hordijk’s design, it’s fun to have all the controls available to experiment with. For example, by setting the first sustain module in the chain to a lower level than the one that follows, it’s possible to achieve a secondary attack-like phase with a resulting ‘reverse’ effect. It’s also interesting to play with the degree to which the curves are logarithmic or exponential, finding the sweet spots for what sounds ‘natural’ – at least in relation to what we know from acoustic instruments.

I’ve uploaded some patches to the Audulus forum.

Modular Diary

I’ve made a small start on putting together an Audulus version of the Hordijk Dual Envelope generator.

Hordijk mentions in one of his videos that designing an envelope generator is perhaps the most difficult of all the modules in that there are so many possibilities to consider, and that certainly rings true as I’ve begun to explore it.

In this first small patch I’ve adapted some of Stephen Schoen’s uLope modules to include a trigger mode – i.e. the attack time of the envelope is independent of the gate time. This means that a short trigger can result in a long attack swell, or a short attack can be triggered with a broad gate. It’s a simple feature that opens up a number of possibilities. With the attack time set to longer than the clock rate the envelope generator can suddenly starts to function as a kind of clock divider, as Hordijk points out in his NOVARS tutorial video. With in-between settings, e.g. with the gate setting in before the release stage has completed, interesting rhythmic effects can arise.

I’ve uploaded the patch to the Audulus forum.

Modular Diary

Further details on the frequency shifter all-pass filter network:

If one was only dealing with two (sine) frequencies it would be possible to use a single all-pass filter and adjust the cutoff point accordingly. However given that ring modulation typically produces multiple frequencies (especially when applied to a complex input signal) a network of filters is needed to cover the entire audible frequency range.

My first searches on the web brought me across Hordijk’s Frequency Shifting patch for the Nord G2 Modular, as well as Jürgen Haible’s descriptions and schematic drawings which filled in a little more detail on the Hilbert transform filter network. Fortunately I also came across an article on Analog Wide Band Audio Phase Shift Networks with a diagram (see fig. 4) and a table of frequencies that I could use as a point of departure.

Via Don Tillman’s collection of Moog Patents I could download a PDF of the Bode Frequency Shifter that Moog produced in the early 70s. That helped fill in the final pieces of the puzzle, showing how the sine/cosine oscillator (which I’d already encountered in Hordijk’s Harmonic Oscillator) connects up with the Hilbert filter network (or ‘Dome Filter’ in Moog parlance) to enable the ring modulation and phase cancellations.

I’ve uploaded a few demos to the Audulus Forum.

Modular Diary

Here’s my first take at putting together a Frequency Shifter in Audulus. Once again, one of Rob Hordijk’s NOVARS tutorials has provided the inspiration and point of departure.

Hordijk describes the frequency shifter as kind of luxury ring modulator – with the added feature that it’s possible to split the upper and lower sidebands and achieve some special transformations through that. In essence it’s a ring modulator and an all-pass filter network, with the filters making it possible to remove one of the sidebands through phase cancellations.

The all-pass filter is something that Hordijk covers succinctly in his video on the Physics of Sound, and I’d already made one on the basis of his description while putting together an Audulus version of his Dual Phaser. While Hordijk provides a good explanation of the principles behind the frequency shifter and a thorough demonstration of his own module, I needed to do a little detective work before I could figure out what was going on with the filter network.

Modular Diary

I’ve been fascinated by the Rob Hordijk’s description (in the Sines and Squares masterclass video) of how one might think about sound in three dimensions (rather than the two we are used to on our screens) and how sine and cosine waves can be used to describe the phase and amplitude of a resulting wave, defining its waveshape over time.

He describes it as a corkscrew waveform, also occurring in nature, with the phase describing its rotation, and the amplitude, distance. When viewed on an XY oscilloscope with a slow sine modulating the amplitude of the sine and cosine, it looks like a circle approaching from the distance and receding again. With very low frequencies one can view it as rotating points and get an even better idea of the ‘corkscrew’ effect.

This helps fill out some background on Hordijk’s thinking of sound in terms of depth – for example with his fluctuation waveform, in which amplitude and frequency modulation are combined to provide a special kind of vibrato. Based on a rounded triangle ’parabol’ waveform, the larger the wave is, the lower the frequency – i.e the lower part of the frequency fluctuation corresponds to the higher part of the amplitude modulation. In his 2015 masterclass on Waveshaping & Fluctuation Hordijk describes this waveform (when modulated) as advancing and receding – giving a perspective effect.

I’ve uploaded a little demo patch (used to create the gif above) to the Audulus forum.

Modular Diary

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.


  1. See the end (from around 20m46s) of the above-mentioned Hordijk tutorial 

Modular Diary

After taking a look at the NOVARS Rob Hordijk tutorials on the Physics of Sound and his Dual Phaser, I was keen to try out some of the ideas in Audulus myself.

The Physics of Sound video takes a look at phase shifting and All Pass Filters, and as a tryout I used the 1 Pole LPF in the Audulus library as a starting point for an APF with nice resonant qualities, and then used that as a point of departure for putting together a phaser along the lines of Hordijk’s Dual Phaser. He adds some nice touches such as a switch that flips the direction of half of the modulation input, or keeps half of it static while the other half moves, as well as a fader between the LP and Phaser modes.

I find the nicest thing is being able to push up resonance and then trigger the phaser with sub-audio pulses for some nice percussive sounds.

I posted some demos on the Audulus Forum:

Modular Diary

Despite Hordijk’s warnings on the difficulties of implementing his Harmonic Oscillator algorithm digitally, I was keen to try out some of the ideas in Audulus. One of the aspects of the feedback loop involves using a cosine waveform to avoid the DC offset that would occur when feeding the sine back on itself. In the Hordijk’s diagrams he indicates a crossfade between the sine and cosine signals as part of the feedback loop, but I kept on running into the pitch drop problem that he explains is a result of the DC offset.1 I eventually gave up on the linear FM route and decided to try implementing it with phase modulation instead – with some success.

The morph from sine to saw has a different character than making a crossfade between the two waveforms since the saw edge gradually tilts rather than appearing as an abrupt vertical,2 and the sawtooth and square waves also have a rounder edge than the characteristic forms of these waves. I haven’t been able to achieve quite the same sharpness in the shapes that Hordijk does with his analogue implementation (compare the waveforms at the beginning of the second video) since the phase modulation begins to distort, but the somewhat more mellow quality that results also has a charm of its own. 3

I’ve put it together as a simplified µModule, with the addition of a control that adjusts the level of both the odd and all spectra simultaneously in relation to the sine.


  1. There’s more from Hordijk on FM synthesis on the old Clavia Nord Modular website, fortunately still available via the Wayback Machine.  

  2. I’m also curious as to why the inverted form of the waveform appears to be slightly lower in pitch. (In the case of this oscillator shifting the “All” knob in the positive direction results in what is commonly know as a reverse (or inverse) sawtooth. This is the default result of the pitch being fed back on itself.)  

  3. It is possible to increase the definition of the square wave a little more than I have, but that results in distortion when combining the square and sawtooth spectra.  

Modular Diary

My next stop while working my way though the treasure trove that is the NOVARS collection of Hordijk tutorials, has been his Harmonic Oscillator – a module I’ve been keen to take a closer look at for quite some time.

In the first of two videos he provides a general introduction to the basic idea of the oscillator – one in which the three classic parameters of sound synthesis: pitch, timbre, and amplitude, are all present, and all available for voltage control.

In the second video he takes a closer look at the algorithm that defines the oscillator: a sine/cosine oscillator that feeds back on itself via linear FM, creating a spectrum that contains all harmonics. A second spectrum containing only odd harmonics is created with a Chebyshev polynomial feeding back the pitch an octave higher. The combination of the two spectra creates pulse-width timbres.