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Modular Diary

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.)

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Following on Hordijk’s fluctuation modulation, here’s a demo that I saw a while ago that’s been popping into my head, on how to program the lead sound for Vangelis’ Blade Runner theme. There’s a section on vibrato that starts around 4′23″.

I also took another look at the effects of uni and bipolar waveforms on linear FM in Robert Syrett’s Audulus Bahama oscillators – unipolar FM alters the perceived pitch (which makes sense for audible frequencies 1 since the modulation is only in an upward direction) while bipolar waveforms keep it centered. I noticed that the Moog Model 15 App has AC and DC frequency modulation inputs as well. In that case it’s simply a question of how strong the (exponential) effect is.

I was also curious to take a look at how the Model 15 App handles sync. Hard sync is as one would expect, but the weak (soft) sync is quite sublte and beautiful in the way that it gradually matches up the phase of the waveform while attempting to preserve its shape.

And finally a look at the Make Noise DPO which very much takes both linear and exponential FM into timbral texture territory. Robert Syrett has made an Audulus version of that as well.


  1. For LFOs I guess this isn’t a problem. 

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Phase Art: The picture above is of the Wikipedia 3:2 phase modulation example 1 and corresponding comparison with frequency modulation as displayed by an oscilloscope in X-Y mode.2 This is a mode typically used for testing phase relationships between signals and is well known as the method for displaying Lissajous curves – a sine wave on the X axis and a cosine wave on the Y creates a perfect circle, for example.

What I hadn’t realized is that a phase modulated signal against the same (unmodulated) reference frequency could create the kinds of shapes above. (The frequency modulated signal against the same unmodulated reference frequency produces a rotating oval.3) In this case the phase and (linear) frequency modulated signals are presented simultaneously, resulting in the bands of lines that look something like a staff in music notation.


  1. In this case 750:500 Hz 

  2. In this case the Goniometer in the MC Studio app.  

  3. Playing with the linear frequency index (the degree to which it approaches exponential frequency modulation) alters the number of lines present and their proximity. The more exponential the curve, the more one approaches familiar Lissajous territory. 

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Further down the phase/frequency modulation rabbit hole: I’ve played around a little more with the PM vs FM patch (uploaded to the Audulus forum) and got the levels set to recreate the Wikipedia phase modulation gif. The Audulus LFO waveforms are unipolar and I experimented at little, comparing the results with using a bipolar modulating waveform on the linear1 and exponential FM inputs.

I’ve also been looking at how the shapes change depending on whether the modulating frequency is higher or lower than the one it is modulating. The characteristic phase shapes (with amplitude sub-peaks within them) appear when the modulating wave is higher than the carrier, having a much stronger effect in this area than linear or exponential frequency modulation.


  1. This results in a folding effect similar to the phase modulation amplitude sub-peaks in the picture above. 

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It’s interesting how one can keep circling around a topic, slowly covering all it’s aspects and letting them sink in.

I’ve been taking a look at frequency modulation again – specifically the difference between phase and frequency modulation that I touched on in a previous post. Phase modulation (as used in the Yamaha DX synthesizers) has the same (linear) effect as linear frequency modulation, but while mathematically equivalent, the two sound very different. I came across a thread in the Audulus forum that I’d somehow overlooked before, in which Robert Syrett provides an example patch that helps clarify the differences.

Here’s my own slightly altered version of his patch that I’ve been playing around with. I haven’t quite managed to match the nice phase gif from the Wikipedia phase modulation article, but that can be explored further on another day.

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I particularly enjoyed the Cuckoo overview of FM principles that I came across in the Audulus forum thread on AM/FM/PM modulation.

I’ve since been wanting to take a closer look at the difference between linear and exponential frequency modulation and came across this video (also featuring an old ARP Oddysey Mk I) by Synthesizer Keith.

There’s a follow-up Reddit thread also clarifying that it’s linear modulation at play in the Yamaha DX style FM – the phase type of frequency modulation that Cuckoo refers to in his video – as well as a similar thread at KVR.

Keith refers to the Yamaha style linear FM as being “more musical” in his video, and there’s a Reddit thread, leading to a Muff Wiggler thread, on that question as well.

I found it interesting to look through the Wikipedia entry on Frequency modulation synthesis. I always associate FM with the 80s (the DX7!) but as the article points out Yamaha was already developing (and patenting) it (after famously licensing it from John Chowning1 ) in the mid 70s. It was only in 1980 that they’d developed the technology to a degree stable enough to release it commercially in the form of the curious Yamaha GS-1.

All of which was preceeded by Buchla with his own developments and implementations in the mid-60s.


  1. Chowning patented the digital implementation of FM in 1975.