Thru-Zero FM Explainer

How to get the best results from your analogue thru-zero linear FM oscillator. An explainer in response to questions about the Doepfer A-110-4, but which is also applicable to other TZ-FM VCOs.



The A-110-4 seems to be more prone to pitching artefacts than other thru-zero (TZ) VCOs. That might partly be due to the specific design, but general considerations like the tolerances and sensitivities of analogue designs also play a role. Another issue might be perception, e.g. when certain modulation depths make it hard to discern the original pitch of the carrier.

DIGITAL FIRST

Ignoring the actual implementation (frequency- or phase-modulation), the reason digital FM is easy is because it’s clean. There are no DC offsets or pitch instabilities to ruin the result.

Here is an example using the Clavia Nord Modular G2. The carrier is always heard and only the modulator is enveloped. The frequencies of the two oscillators are fixed but the FM amount is manually increased: 01-TZ_clavia-digital

The carrier was tuned to B3 and the modulator D#5. I chose these pitches by ear to show an effect which might be confused for pitching at higher mod depths. When the modulation recedes, we get a sound similar to guitar feedback. This shows that it’s possible to find combinations of frequency relationships and modulation depths that will sound ‘wrong’ even when patched digitally. In an analogue system, frequency drift or tracking inconsistencies can worsen the problem.

DIRTY SIGNALS

But weird C:M ratios are not the main problem. The real enemy of dynamic linear FM is asymmetry caused by DC offsets. If the modulating wave is not centred about zero, the sound will churn. Here’s the same G2 patch, this time with some virtual DC offset added: 02-TZ_clavia-digital_virtual-dc-offset

To avoid this, some FM inputs are AC-coupled - the signal is filtered by a capacitor. But this is not a magic bullet. If the offset is large enough and being swept dynamically, the capacitor will have a hard time eliminating it. The most likely cause for DC offsets are the modulating oscillator itself, or more precisely its wave-shaping circuitry. I have had best results with Doepfer’s A-143-9 Quadrature sine-core oscillator.

SCIENCE, SWITCHES

Analogue TZ-FM involves switching to generate ‘negative frequencies’. No matter how finely timed, there is a moment of indecision which may be audible as a growl or rumble. DC offset makes this worse as it shifts the switching point. Lower initial frequencies (aka Bias, Symmetry or LFreq) allow more modulation and brighter sounds, but the cost is lower accuracy and more ‘bum notes’.

THE A-110-4

The Doepfer TZ-VCO switches between two oscillators. This method has pros and cons. If the two VCOs do not respond equally to modulation, the resulting FM will sound ‘off’, even if the modulator is clean and the switching point is accurate. This cannot be trimmed by the user. To mitigate pitching artefacts at the point of switching, calibrating the TZ transition can help.

WHAT IS IT?

As Cynthia Webster says in her humorous video showing the difference between thru-zero and normal linear FM, without TZ “half the modulation is gone”. As you’ll hear, the frequency relationship between carrier and modulator also plays a role.



The first VCO you hear in the next two examples is the Zeroscillator, then the A-143-9 which I have modified for standard linear-FM.

If the carrier’s initial frequency is high enough and/or the modulator is higher in frequency than the carrier, the tonal result is very similar:
03-TZ-high-initial-freq_ZO-A-143-9

The real difference between thru-zero and normal linear FM is apparent when the modulator is slower. As you can see above, instead of adding gentle folds, the modulator pushes and pulls the carrier through zero. TZ allows deep levels of modulation, even when the carrier’s initial frequency is low. When this is the case, there is a big difference between normal and TZ linear FM in the possible tonal result: 04-TZ-low-initial-freq_ZO-A-143-9

One last thought on this as the Zeroscillator video is much quoted when the question “what is thru-zero FM?” is raised: toggling the “Through Zero” switch on the ZO does not yield ’typical’ linear FM; normal linear FM does not sound like this: 05-TZ-not-typical

PATCH TIPS

I have concentrated on the audio effects here, but VCOs that can go thru-zero have other uses when they themselves are used as modulators. For an idea, try this patch for a thru-zero frequency shifter and listen to your sounds swap stereo sides.

I hope this explainer helps you with your TZ-FM experiments. The files folder is here. If you’re not sure about the analogue results you’re getting and need a digital ’control’, download the Clavia Nord Modular G2 demo. If you’re on a Mac and 10.7 or higher, you can run the demo under Wine. There is info here or an installer here.

Super Sawtor Demo

A review of Happy Nerding's Euro-format sawtooth animator.



As the name suggests, the Super Sawtor is designed to produce the sort of multi-oscillator unison sounds known from certain Roland synths and dance genres. Feed it a single saw, triangle or sine to get a dense, buzzing cluster. Too Trance for you? Have a listen:


The two tracks should give you an idea of the Sawtor's sonic scope. If you want to hear more, pay as-you-like to download the source files (10 tracks, @ 25 mins).

The Sawtor is solidly built and simple to use - the only parameters are the dry/ wet mix and the amount of spread. Its internal LFOs change speed in response to the incoming signal's pitch. That keeps the amount of spread even for most of our hearing range. The result is rich, vibrant and less prone to the phase-cancellations I know from my Roland Super Jupiter. Indeed, although it is analogue, the Sawtor emulates the beating of a digital super-saw.



It's this 'intelligent' modulation that sets the Sawtor apart from Doepfer's sawtooth animator and draws a parallel to Cyndustries'. It also limits its use. The only parameter you can affect is the 'spread' i.e. the number of stages. Once activated, the saw-multiples are constantly in motion. They can't be 'stopped' and spaced statically to produce new waveforms as is possible with Doepfer's A-137-2. To improve audio fidelity, the Sawtor is AC-coupled. This rules out certain CV-processing tricks.

So, does that make it a one-trick pony? Yes, but only in the sense that spring reverbs or fuzz boxes are too. Because you can't independently influence the modulation speed, the choice of input becomes important. Gated, sync'd, FM'd or even polyphonic sounds can make interesting fodder if you want to go beyond the Hardcore Hoover. But maybe that is to miss the point of the Super Sawtor: it makes one VCO sound like many and does so without fuss.

Many thanks to Igor for the module and for answering my questions.

WMD PDO Demo

Audio examples and review of the WMD Phase Displacement Oscillator. A sequel to this post.

The WMD PDO is a timbral oscillator with a twist. Three of its outputs can be discretely shifted in phase relative to the first. It can be used as a quadrature LFO, but the real fun starts when modulated at audio rates. This yields results similar to linear FM, but as the PDO’s creator William Mathewson says in one of his promo videos, phase modulation “gives you more”. Here it is in action:


The sounds in the multi-tracked demo track were generated by modulating the PDO either by itself, for wave-shaping, or an external VCO for PM effects. Buy the EP to access the full set of unprocessed demos (10 recordings, 30 mins duration).

As you can hear, the PDO is capable of a wide variety tones: deep acid basses, bright bells, wooden klonks, scraping steel strings, rasping super-saw/ PWM sounds, even digital noise. As with the Zeroscillator, panning two phase shifted outputs hard left and right can result in stunning stereo effects.

I found I could push the PM index harder and get brighter sounds than with either the analogue ZO or digital Hertz Donut. Like thru-zero linear FM, when the PDO is modulated with a bi-polar signal, its sign, or direction, changes. However, modulating the phase rather than the frequency results in less pitching artifacts.

That's not to say the PDO is artifact-free. At slower modulation rates I thought I could see/ hear the PDO 're-calculating' the phase offset, resulting in a mild siren effect. I asked William about this and he explained that this was the nature of phase modulation; what I was hearing was similar to the Doppler effect where moving the phase forward increases the frequency. At higher audio rates this was not apparent, but it might have an effect when using the PDO as an LFO. The digital wave-shaper means aliasing is apparent and the sound can break up at extreme frequencies or when FM-ed hard. However, I took this to be part of the PDO's character and, as you can hear in the demo track, it means you have another set of timbres to play with. I thought the saws and pulses were not as beefy as an analogue VCO and that it was a shame that one can't affect pulse width and phase simultaneously for 'shonky beats'. However this can be addressed by routing a shifted output to the reset input via a clock divider.

These are minor points given the wealth of sounds and possibilities packed into the PDO's 10HP. In fact, that would be my biggest criticism: it's pretty cramped! I'm sure I'm not the only one who'd gladly devote more rack space to a larger PDO, possibly with an onboard sine modulator and index VCA. As it is, the list of modules the PDO could replace in my system is shocking - it's perfect for a live set-up or desert island suitcase.

There is one last thing to consider: at almost €400 the PDO is in the same price category as the SynthTech E350 and Cylonix Cyclebox, which both offer increased fidelity. Whether they offer the same depth of phase modulation and character is something I look forward to testing in a future post.

Thanks to William for taking the time to answer my questions and for a great module!

PotD - Swings & Roundabouts

How to patch a thru-zero frequency shifter with two quadrature VCOs and ring modulators.



I love my Cwejman FSH-1 for its wide range and smooth analogue tone. The one thing it lacks is thru-zero capability. At slow settings, frequency shifters yield beautiful spatial effects. Thru-zero is the icing on the cake as it allows the up & downshift channels to 'swap sides'. Heard in stereo, this can sound great - or disconcerting, depending on the amount of shift!

So, how to go about patching one?

James Clark's Nord Modular tutorial on spectrum shifting explains the workings of a frequency shifter but stumped me on the need for all pass filters/ Hilbert Transformers. A post by Matt Jones at the Synthedit Yahoo Group offered the necessary clue:

"Out = (Input) * (Sine oscillator) + (Input shifted by 90 degrees) * (Cosine oscillator)
Changing the + sign to a - switches the amount of the shift from up to down …"

Here's the proof of concept:



In the recording you can hear me manually sweeping a DC voltage from positive to negative, biasing the modulator and causing the shifts to move from left to right.

My patch (see below) has three caveats: one, you need a Zeroscillator or similar to provide the thru-zero shifts (!). Two, unless you have the means of generating a cosine from your complex input signal, you're limited to simple sines. Three, it's fiddly and not 100% precise. That said, the results sound great:



The patch details: the ZO is used as the modulator. Set its bias to zero and patch the 0 & 90 degree outputs to the CV inputs of two ring modulators (e.g. A-133). I used the Doepfer A-143-9 QLFO as my signal as it provides the necessary outs. The 0 & 90 degree outputs were patched to the respective ring mods. The Toppobrillo TWF can be used to generate a cosine from another source, but I wanted to keep the patch as simple as possible.

To generate the upshift, I mixed the result of the 0 and 90 degree multiplications. To get the downshift, I subtracted the 90 from the 0 degree via an external inverter. The Cwejman VCA-4MX was used as the output to my final mixer. It's perfect for this task as it allows you to independently tap the mix of channels 1&2 and 3&4, which you can then pan left and right.

The fiddly bits: to bias the ZO correctly in both directions, I had to tune two voltages (+ve & -ve, Maths or Fonik's mh-01) and send them to the linear FM input via a sequential switch. It would have been easier to use the pulse output of the clocking LFO, but this didn't give me equal positive and negative bias i.e. the side-swapping effect was compromised. You can hear this in the first recording where I apply the bias manually. The second detail you have to watch is the mix/ subtraction balance to ensure clean up & down shifts, but this isn't too tricky. Just use your ears for both.

The ZO makes this patch possible. With zero bias, the oscillator comes to a stand-still. Any voltage you apply to the linear input will cause it to jump into action. Reverse the bias voltage and the ZO changes direction causing the shifts to swap sides. You could use a second A-143-9 as modulator, but would then lose this ability. Still, two QLFOs, an A-133 and mixer/ inverter offer an inexpensive single-sideband-modulation patch.

Buy Swings & Roundabouts.

Three Thru Zero

Comparing the thru-zero linear FM response of the Cyclonix Cyclebox to the Cyndustries Zeroscillator and Harvestman Hertz Donut.



I like timbral oscillators and use them in my live sets. The Zeroscillator is too big to gig with, so the Hertz Donut usually takes its place. While it packs a lot of features into a small space, the HD is less than hi-fi, so I was hoping the better-spec'd Cyclebox might be an alternative.

In this comparison, I've focussed on thru-zero linear FM as that is what I'm interested in. For demos of the Cyclebox's other features, look here.


dynamic, sine-on-sine. (0:00) zo, (0:09) cb (lead out)


ibid. (0:00) zo, (0:25) cb, (0:45) hd

Despite a firmware upgrade, the Hertz Donut tends to break up in the upper registers. Here's how the three cope with higher pitches:


(0:00) hd, (0:06) cb, (0:13) zo. (0:21) zo, (0:28) cb, (0:36) hd

I matched the pitches of the principal and modulating oscillators by ear, using mode 0010 on the CB for examples 2 & 3. On the ZO & HD I increased the modulation depth as far as I could before pitching artifacts were evident. The CB's FM index was set to full.

As you can hear, the CB doesn't seem to allow the same level of modulation as the ZO & HD, so it sounds muted by comparison. This can be addressed to an extent by increasing the gain, but as this feeds the wave-folder, the results are not the same. It's not clear from the manual whether the internal ratio setting is discrete or in semi-tones, but this might explain why it's easier to achieve clangorous/ bell tones on the ZO & HD. Overall, the CB's linear FM response reminded me of the Livewire AFG, namely better than most non-thru-zero VCOs, but lacking in brilliance.

The Cyclebox is more hi-fi than the Hertz Donut, but because I couldn't push the index as far in a dynamic FM patch, I found it lackluster. Both digital VCOs offer a built-in modulator, smaller footprint and more stable FM. However, despite the inaccuracies of analogue, I prefer the thru-zero linear FM tones of the Zeroscillator.

Patch Tips #19 - Morphase

A look at and listen to the Zeroscillator's quadrature outs.



Often overlooked and sometimes misunderstood, the Zeroscillator's morphase function can yield stunning sounds or be used as a complex modulation source.

The outputs offer four phase-shifted versions of the main oscillator (0, 180, 90 & 270 degrees). They can be wave-shaped from triangle to amplitude-compensated square via sine.

This morphing can be manually or CV controlled. A three-way switch determines how the outputs are affected: both, independent, inverse. The CV inputs (A & B) are unattenuated, the manual pots act as an offset.

With the switch left, an LFO patched to 'input A' sweeps the 0 & 90 degree outs from triangle to square and back. With the switch right, the 0 degree output morphs as before, but the 90 degree tap sweeps from square to triangle. With the switch in the middle position, two CVs are required, A & B, for independent morphing.

Here's how it sounds:

zo_morph1
zo_morph2
zo_morph3

Quadrature wave-shaping. 0 & 90 degree outputs panned left & right, dry.

The recordings give an idea of some of the stereo effects possible using just two outputs of the Zeroscillator. Example two features linear FM, while clips 1 & 3 show off one of my favourite patches: zero bias, modulator to FM in. This is another form of wave-shaping and is a great source of plucked string sounds.

The quadrature sines are not as pure as the main out and might need calibration to ensure similar waveforms at similar settings. Of course, as soon as one introduces dynamic wave-shaping, this is less of an issue. The quadrature outs can also be used in LFO mode for panning duties, but you might be better off getting an A-143-9 for this. Aside from the price difference, the QLFO is the best ZO modulator I've found, due to its clean sine and negligible DC-offset.

The Zeroscillator is a complex beast and needs some patience and care. However, the sounds it's capable of are worth the effort.

Patch of the Day - Define Time

Thru-zero linear FM fun with the Cyndustries Zeroscillator and Toppobrillo Sport Modulator.





Today's PotD showcases some of the lovely linear FM timbres and stereo effects that the ZO is capable of. It's a single-pass recording of the 0 and 270 quadrature outs, panned hard left and right, with only a little plate reverb from Audio Damage's Eos added. I used a self-oscillating Cwejman MMF-1 filter as modulator, manually offsetting its pitch with four pre-set voltages from a Fonitronik mh01.

The Sport Modulator drives the patch, delivering both CVs and gates. The cycle/ sample times were nudged manually, with some cross-modulation and the stepped random signal of a Wogglebug. The latter's smooth out modulated the attack time and loop trigger of a Cwejman CTG-VC. At high speeds, the envelope amplitude modulates the VCA-2P used as the final gate, adding further sidebands to the mix.