19/ Mark Fell on his love of FM synthesis and algorithmic composition
www.factmag.com/2018/10/06/mark-fell-signal-path/

16/ Lord Kelvin’s Harmonic Synthesizer, Henrici’s Harmonic Analyzer
socks-studio.com/2011/08/16/more-on-the-harmonic-synthesizer-and-on-the-harmonic-analyser/

13/ The ANS Optical Synth & Tarkovsky Scores
www.musicofsound.co.nz/blog/the-ans-optical-synth-tarkovsky-scores

9/ Helmholtz’s apparatus for the synthesis of sound: an electrical ‘talking machine’
www.sites.hps.cam.ac.uk/whipple/explore/acoustics/hermanvonhelmholtz/helmholtzssynthesizer/

# Modular Diary – 034

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.

# Modular Diary – 033

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.

# Modular Diary – 032

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.

# Modular Diary – 026

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.