Through Zero Linear Frequency Modulation

The first video is over my head.

I don’t find this intuitively satisfying. The thing is, quite a bit of the math you guys use all the time was developed by “philosophers.” There is actually no such thing as a circle. A circle is a concept.

Positive and negative are not arbitrary for electricians. A circuit is a cycle but it is not a circle.

The second video is important. It captures the reversibility of flow. If we look deeper into the chemistry of the parts involved in motors/generators, there will be characteristics that share modalities. These structures interact within a field, just as equations represent inverse relationships. If you read about transistors you will find the concept of doping quite intriguing. I suspect that without this ‘barrier,’ compressors won’t work. The transistor creates a buffer in the flow which ‘charges’ the event. There is more energy present in that period.

Now, I am not correcting anyone. I am making conjectures so that I can reveal my hand. I want to stop here. Tell me where I am wrong.

But the rose has teeth in the mouth of the beast.

Is the circle in the center of the animation, that pulls the modulation across the vertical line, representative of phase?


My brain just said that while crossing that vertical threshold puts the parameters into “the past,” you could use such a source for modulating reverbs and delays in “real time,” since the tails are synthetic echos. But that all depends on what that centered circle represents.

1 Like

Diving further in with the same patch…

TZFM Tests 2.audulus (636.5 KB)

Your comments led me to consider approaching frequency modulation from a different perspective. We typically view FM as rapidly changing the frequency of an oscillator of some type, but it would be equally valid to regard FM as moving an observer back and forth relative to a wave of constant frequency. This is typically referred to as the Doppler effect, but is in fact frequency modulation. Imagine an observer sitting on a platform that can be moved back and forth at a high rate. Now imagine that a constant frequency oscillator of some type is turned on so the the observer can detect it. While the observer is stationary, the frequency of the signal is constant. If the platform moves toward the signal source the frequency will rise, and if the platform moves away the frequency will fall. Vibrating the platform will result in the observer perceiving an FM signal rather than the original constant frequency. As the platform moves away from the source at a velocity approaching the speed of sound, the observed frequency will fall to zero. What if the observer is moving away faster than the speed of sound? The observer will then detect the oscillator waveform in reverse. In essence this is the basis for through zero FM. It also offers an interesting possibility for implementation. Typically we perform through zero FM on periodic waveforms. Because we know their shape in advance, we can easily calculate their time-reversed form. In fact sine, square, triangle and other waves that are symmetric along the time axis don’t need to be reversed, since in their case a time reversal is equivalent to a change in phase. A ramp, however is not symmetric along the time axis and can be either rising or falling. More generally audio signals tend to be quasi-periodic and are not predictable and therefore not easily reversed. However with a suitable buffer that can be played forward or backward at varying rates, which is relatively simple in the digital world, one could apply a form of through zero FM to non-periodic signals. During the positive portion of the modulation one would move forward through the buffer, and during the negative portion one would move backwards. Hopefully A4 will be capable of this type of manipulation.


That, and presets. Here’s the exact patch above, but with a slight variation on the ADSR module.
TZFM Tests 3 - Sweet Spot.audulus (636.5 KB)

1 Like

I fixed up the mess a bit. Sounds more FM. Not sure if I have gone through zero though. If the modulator is bipolar and the carrier responds to negative waveforms, does that mean all is well?

TZFM Tests 4.audulus (697.9 KB)

This short article got my understanding of TZFM a little further along.


A minor adjustment. I took into account @robertsyrett’s point about amplitude modulating the modulator with a VCA. No great changes in sound yet though.
TZFM Tests 5.audulus (698.8 KB)


TZFM Tests 6.audulus (748.2 KB)

I believe in this one. :no_mouth:

1 Like

I was running a patch through some reverb and delay, then I realized that it was also getting more reverb and delay through some hardware. It sounded good so I tried this double stage before and after a filter strictly in Audulus. Then I used some lfo’s to animated the 4 pole k-pass. It sort of travels around nicely. Headphones recommended.

TZFM Tests 7.audulus (713.6 KB)


Really Interesting patch! I dig how the layers of filtering make the FM really gooey sounding.

1 Like

I plan to resume some work on TZFM. It seems like some of these synthesis techniques hold much more treasure than I have yet seen. This write up on the SSF Zero Point Oscillator peaked my interest again.

“Through-Zero FM is a form of frequency modulation that produces much deeper and useful FM tones than a typical VCO can accomplish. New techniques have been discovered that not only improve the performance of TZFM, but also grant additional benefits as will be explained. The ZPO’s modulation section is a hybrid involving both TZFM (frequency modulation) and TZAM (amplitude modulation). Coupling these two techniques substantially expands the performance and tonal shaping possibilities, beyond traditional TZFM. The results are more stable and balanced across the modulation bandwidth and both TZFM and TZAM can function together or independently, and anywhere in between.”

So I thought I would post this. Has anyone managed to get sonically further with TZFM than with just FM/PM? It would be cool if someone could share a convincing patch.

More info on the SSF site.

1 Like

I would assume that TZAM inverts the signal when the modulator goes negative . Don’t know if anyone has tried that with Audulus, but it would be pretty straightforward. The only practical way to implement TZFM in Audulus (at least that I’ve been able to come up with) uses a phasor as the oscillator core. This works fine if you’re using a sine as the carrier but using other waveforms will introduce some significant aliasing. I’m not sure how much of the final product is truly the result of TZFM and how much is a byproduct of the approach used to generate it.

1 Like

Sometimes I just keep going, even if I know I might be missing the point. I grabbed one of those TZFM patches and started switching old modules for newer ones. One discovery I made was that, in this patch, the injected wavefolder at that specific stage, really sharpens up the bass tones, but maintains the analog ‘weight’. Much credit, again, to @biminiroad for his amazing filter refaces!

TZFM Tests 6.2.audulus (859.4 KB)

I think it also matters that the physical speakers/headphones get properly driven at the end – ie. crank it.

1 Like

Indeed, that is one of the main reasons that most of these TZFM oscillators coming out have analog designs. The core will typically have some sort of quadrature waveform (trapezoidal or sinusoidal) and TZFM comes from manipulating these core outputs. The analog versions are still quirky I might add.

Well TZFM is just PM rephrased in terms of FM, so it’s not necessarily going to sound any different. I think the main interface difference is most TZFM will have a linear dc offset for the incoming FM signal (here it’s called zero point) that is basically a second channel of FM input.

You know what would be really nice on a TZFM/PM oscillator? Some sort of indicator that lights up, or reads some number, that tells you that you have gone through zero. Maybe even by how much.

That’s a pretty easy request. Here is a little recreation of my doepfer TZFM oscillator. I think they are great building blocks and the only thing to keep in mind is that the lower octaves are affected disproportionately to upper octaves because they are located closer to zero.

TZFM OSC MINI.audulus (205.1 KB)
TZFM patcholopy.audulus (587.6 KB)


Catching up on this thread and throwing this into the pot: Hordijk Mini Matrix – Node Proc


This sounds awesome.

1 Like