17/ The Sound of Cybernetics: Roland Kayn And the Voice of Electricity
17/ The Sound of Cybernetics: Roland Kayn And the Voice of Electricity
12/ Freeform / Modular / DAW-less
10/ Eliane Radigue: IMA Portrait Documentary
7/ Inside: Erica Synths
2/ Meng Qi: One-offs
Following on my post on bipolar VCAs: Since there are some similarities between what’s going on with bipolar amplitude modulation and through-zero frequency modulation I thought I’d take another look at these topics in a little more detail.
Learning Modular has a nice post on Understanding the Differences Between Exponential, Linear, and Through-Zero FM, and from there I revisited @RobertSyrett’s Know your Nodes video on Comparing different types of FM.
One aspect that through-zero FM and bipolar AM modulations have in common is that they don’t freeze (or shut-off) output when the modulation signal falls below zero. Both do this by inverting the waveform in question. In the case of TZFM it is not the amplitude that is inverted but the phase of the waveform: In the Learning Modular video Chris Meyer describes this inversion as the oscillator ‘running backwards’ while @RobertSyrett in his Audulus demonstration talks of a reversal of the direction in which the waveform is being read. This means that there can be sudden changes in the direction of the waveform (in addition to it being sped-up/slowed-down) but without the potential jumps at the point of inversion that can occur with bipolar AM.
With both types of modulation sidebands are generated and this results in a change in the harmonic content of the waveform. In my previous post I noted Chris Meyer’s demonstration of the way in which the fundamental of the carrier falls away as bipolar AM (ring) modulation is increased, but remains present with amplitude modulation. Similar processes are at play in FM (of all kinds) and I came across a series of old Sound on Sound articles, one of which includes an good explanation of how the Bessel function can be used to describe the amplitude of each pair of side bands, and how they relate to the strength of the other partials and affect the relative strength of the fundamental.
@RobertSyrett demonstrates in his video how with TZFM sweeping the frequency also changes the character of the Bessel function (i.e. the timbre of the sound), while with PM the character of the Bessel function is uniform across the frequency range since the phase is not calculated in relation to the hertz value of the modulator – i.e. the timbre/harmonic structure of the waveform stays the same across the frequency range.
Phase modulation differs from TZFM in that the modulating waveform also changes the starting point of the carrier waveform. With TZFM the carrier remains in phase with modulating signal (through a continuously morphing Bessel function).
(I’ve also posted this on the Audulus forum.)
Beautiful, subtle performance by @Jespertralala Pedersen with his @MakeNoiseMusic and self built Serge systems at Sonic Festival CPH.
Rob Hordijk includes bipolar VCAs1 as part of both the Mini Matrix Node Processors and the Dual Fader and has demonstrated, in his various tutorials on these modules, the ring modulation effects that this makes possible.
Via a recent Reaktorplayer tweet I came across a nice Learning Modular tutorial demonstrating the difference between amplitude and balanced (ring) modulation.
Towards the end of the tutorial there’s also a nice demonstration of the way in which the fundamental of the carrier falls away with ring modulation but remains present with amplitude modulation.
I’ve uploaded some simple demonstrations using my Audulus versions of both the Mini Matrix - Node Proc and the Dual Fader to the Audulus forum.
I thought I’d gotten through all the Hordijk Modules, but of course there’s always one more thing…
Hordijk’s Mini Matrix – Node Proc
Inspired (like much else with Hordijk) by the EMS Synthi/Putney he gives his own take on the use of a matrix within a modern context.
Hordijk’s innovation is to use the well established technique of using a stereo cable to provide an insert point, here applied to each node in the matrix. This means that instead of a simple on/off connection, a level control or other kind of (more complicated) effect/processing can be applied to each node. Hordijk includes two level knobs as well as some ‘node processors’ alongside the matrix ready to be patched in for this purpose, but external sources can but used just as well. Concerning the size of the matrix itself (and the balance between flexibility and usability) he finds that a 6 x 4 grid is well suited to a typical 12 module (4 panel) Hordijk system since connections can also be made directly without necessarily having to go through the matrix.
I’ve been experimenting with how to set up something similar in Audulus: Stereo cables, the key element, are possible in Audulus, but unfortunately only in a single direction, i.e. it isn’t possible to use a single cable for both a send and a return. This means that one has to resort to manually making both parts of the connection, which is not quite as elegant as a single stereo cable and can easily get visually messy and confusing, even though it does open up even more possibilities for routings. (One trick that I’ve found useful to check on which connections have been made, is to zoom out slightly so that one shifts out of connection mode on iOS.)
Following Hordijk’s example, I’ve included 4 bipolar VCAs (using @RobertSyrett’s Audio Attenuator) for the ‘node processing’ – bipolar for the ring modulation and echo-like effects that they make possible, as with the Dual Fader. In my version VCAs 1 & 2 have controls to adjust the amount of modulation applied via the modulation input1, and 3 & 4 have controls to adjust the offset, which also makes them useful for scaling unipolar modulation signals.
As Hordijk points out a matrix can be useful not only for mixing signals, but also distributing them (multiples2), as well as creating complex (multiple) feedback loops.
I’ve posted a simple demo on the Audulus forum, as well as a basic version without the node processors.
This follows the version demonstrated in the Mallorca video – in the later NOVARS tutorial it appears the it is the modulation signal that can be inverted with a straightforward (non-centred) level knob for the VCA. ↩
Through clever use of mono and stereo cables Hordijk’s matrix can be used to mix signals as well as create multiples. ↩
Here’s a take on Rob Hordijk’s 24dB Filter – the last in my series of Audulus versions of his modules.
As usual Hordijk gives his own take on the classic Moog 4-pole ladder filter, creating a multimode filter through the addition of high-pass and band-pass inputs all mixed to a single output (rather than a single input with multiple outputs). This arrangement makes it possible to use the filter as a kind of mixer and spectrally cross-fade between the (independent) input signals.
One can also connect the same signal to all of the inputs1 and use the input controls to shape the curve of the filter. Ideally if the low- and high-pass inputs are set to the same amount they should complement each other and the cutoff frequency (and feedback resonance) should have no effect on the sound.2 Unfortunately, despite some head-scratching and various attempts, I haven’t managed to get this aspect to work, and one can hear a peak when sweeping though the frequency range. The high-pass with the cutoff frequency all the way to the left does however match the low-pass with the cutoff frequency all the way to the right, and spectrally crossfading between two different signals works well. With the same signal applied to all inputs the cutoff frequency (and potentially resonance) is clearly apparent on the band-pass input which can be used as a kind of equalizer.
Hordijk provides a good explanation of the principles on which the ladder filter is based in his NOVARS tutorial, and with that clear starting point I took the opportunity to dive into the The Art of VA Filter Design by Vadim Zavalishin – the ‘Bible’ of digital filter design as @stscheon puts it – as well as @stscheon’s Introduction to Digital Filters. I found the Introduction useful as an accessible complement to Zavalishin’s in-depth explanations with some good examples of Zavalishin’s diagrams patched in Audulus.
On the basis of @stscheon’s explanations I replaced the LPFs in the 24dB ladder filter with LPFs based on the Audulus LowPass node – and they indeed turn out to be more efficient. Comparing the node-based 1-pole low-pass filter with the patched version from the Audulus Module Library shows that they are almost identical: the node version does however have a slightly stronger attenuation – c. 2–3dB above 10 kHz, or thereabouts. This difference meant that in the 24dB filter the high-pass with the cutoff all the way to the left was slightly brighter than the low-pass with the frequency all the way to the right, and I ended up reimplementing the patched 1-pole LPFs in order to achieve the same brightness. (See above.) 3
Zavalishin interestingly describes (in Chapter 4.4) some of the multimode functionality that Hordijk builds on, warning however that:
The multimode functionality of the ladder filter is a rather exotic feature. If you’re looking for the bread-and-butter bandpass, highpass, notch etc. filters, you should first take a look at the multimode 2-pole state-variable filter discussed later in the book.
Exotic or not, Hordijk’s inclusion of independent inputs that simultaneously combine to a single output provides some unique functionality with the ability to spectrally crossfade between them. Although there is a diagram available on The Hordijk Modular Blog I’ve nevertheless been unsure of the details on how to combine the various filter modes. I’m not sure if I’ve solved this in the best way – but, with the exception of the HP and LP inputs perfectly complementing each other, it seems to cover the functionality that Hordijk demonstrates in the NOVARS video. Regarding the LP/HP asymmetry, my guess is that the four 1-pole LPFs each need to be converted to a HPF to achieve a ‘true’ HP ladder filter as Zavalishin explains in chapter 4.5 of The Art of VA Filter Design. The problem though is then how to maintain the LP signal simultaneously – unless one has a parallel ladder of filters… (which would seem to defeat the point of the design)?
An additional feature of Hordijk’s module is the addition of some subtle tube-like distortion that can help boost the resonant feedback peaks. He favours an all-harmonic distortion rather than one that only boosts the odd harmonics – as is the case with soft clipping and some tube-distortion models, as well as the tanh saturation that Zavalishin suggests in his diagrams. Hordijk generates his distortion through a process of FM feedback and I experimented with achieving something similar building on the techniques that I’d tried out in the Audulus version of his VCA-Shaper and Harmonic Oscillator. In the end I settled on using the JFET VCA in the Audulus library for the subtle all-harmonic distortion4 that it can provide (the Audulus Tube VCA provides odd harmonic distortion).5
The JFET distortion does however introduce a strong fundamental when applied to the high-pass input even though it is effective in boosting the peaks. The introduction of lower frequencies when resonance is applied to the high-pass is however a general problem with the ladder filter design and I haven’t found a satisfactory countermeasure (such as introducing a HPF in the feedback loop, as Zavalishin suggests) given the multimode nature of the module. Nevertheless, despite the rough edges in my version, I find it an effective and fun way of blending and shifting between different signals or different spectral areas of the same signal.
I’ve uploaded the module and various demos to the Audulus forum.
Hordijk has the low-pass input normalized to the high- and band-pass inputs. In my Audulus version those connections have to be made manually. ↩
The description in the Audulus docs of the LowPass node having a 12dB rolloff per octave had me confused at first since it matches the 6dB rolloff of the patched 1-pole filter. The 12dB rolloff does however apply to the Filter node. ↩
I’ve stuck to the standard (clipping) distortion SVG icon, even though I realise that it’s a little misleading in this case. ↩
I’m keen to do a little more experimentation with different saturation possiblities that Zavalishin diagrams for the standard ladder filter, some of which @SansNom has already explored – see the thread on the old forum. ↩