Oora talked about complex and harmonic oscillators in his last video… he didn’t explain it in detail and I searched in Google but didn’t find a satisfying definition…
what exactly defines a complex oscillator?
and a harmonic oscillator?
how would you classify e.g. the 0-coast / Digitone / Analog Four / DPO / XPO
I don’t know all the definitions out there about Complex/Harmonic oscillators, but here are my few cents …
Complex Oscillator:
AFAIK the term “complex oscillator” has been coined after the Buchla 259 “complex wave generator” released somewhere in the 1980ties by Don Buchla and which is a module with two oscillators. One was dedicated to modulate the second at low and audio rates in AM and FM mode, to generate the waveform of the second oscillator. This waveform was also transmitted to a wave shaping and a wave folding section.
This concept generates a couple of typical “west-coast” style sounds, which would not be possible with subtractive synthesis and is available from Buchla/Tip-Top Audio for Eurorack, from Make Noise as DPO, Verbose Electronics, Frap-Tools and some others.
The recently released Spectraphon from Make Noise (May 2023), working with Fourier-Theorem based algorythms is a complex oscillator as well, as far as cross-modulation is concerned.
Harmonic Oscillator:
I know the Harmonic Oscillator from Verbose and it’s a bit like “additive synthesis” but only with few oscillators (8). But as far as “additive synthesis” goes there is Odessa from XOAC Devices, which adds up to 512 harmonics to built up one voice and allows to manipulate and modulate the spectrum/waveform dramatically. Same goes for the Cursus Iteritas Percedo from Noise Engineering.
The 0-Coast is west-cost, but without the “complex” of the 259 series, because there is one oscillator only. But it has the typical west-cost wave-shaping/wave-folding.
Digitone has pure FM synth voices, while Analog Four is a pure “subtractive synth” with analogue voices but digitally stabilised analogue VCOs - called DCOs.
To me “Complex Oscillator” ( as opposed to a complex oscillator, 'cuz the word ‘complex’ can be just an adjective ) means an oscillator with wavefolder.
I’ve been toying with learning complex oscillator patching with my small modular rig. It seems like it’s mainly 2 oscillators, one modulating the other, with wavefolding thrown in for fun. It’s pretty gnarly.
Thanks for that very good answer. Now i understand it finally!
…bitwigs polygrid is the perfect place to create and learn everything about and beyond all sorts of synthesis concepts…truu modular, truu complex, truu mind and ear boggeling…
This sentence just cost me $280.
I just ordered the West Pest, with the intention of patching DFAMs and Subharmonicon into before the wave folder.
this could cost you tens of thousands. Or not.
I just watched this Loopop Mavis video and in that he showed how wavefolders have little effect on saw and square waves which might lessen the effect on the SubH. More rounded waveforms like triangle and sine are better suited for more pronounced wavefolding. Though lowpassed squares and saws might work, as he demonstrates. Anyway, something to bear in mind.
Jorb mentioned that.
I’m trying to remember which Moog has which waveform.
But it doesn’t matter. I’m interested to see it for myself, and what happens if I apply negative filter amount and round out the sound.
Or even an LFO on the wave folder as I detune some oscillators.
Matriarch has S&H.
Or run the Malevolent into it. I’d love to see the baked in pwm and drive does to wave fold.
Thank you for mentioning that!
Just some side info for you. FWIW I had a Verbos Complex OSC and their Harmonic OSC, and I kept the Complex OSC much preferred the sound there. But I did notice that people tend to favor one or the other. The Harmonic gave you control of essentially stacking sine waves to create a more complex sound. (An interesting thing is that all sounds can be broken down into sine waves). The best thing I got out of West Coast synthesis was Low Pass Gates. That’s totally worth a look at understanding and the sound too, specifically with vactrols like LxD, MMG, QMMG etc. Though I did enjoy Natural Gate, and Sinc Bucina a ton too.
I wasn’t thinking this through… The Malevolent doesnt have a sine wave. Just sawtooth, triangle, and pulse.
So the Grandmother is a great start to see how the West pest interacts with detuned oscillators going in pre wave folder…I can even patch the audio out back into the spring reverb. Im excited to see what this is all about!
Fold Sines + Triangles
Filter Saws + Pulses
Folding is basically the inverse of filtering, adding harmonics rather than subtracting them.
Right, because they approach sines the more they are filtered, this is something I should try more actually.
You are right on the money! I just got it and i am looking over the manual… It has a triangle and sine, but also sawtooth… and the dynamics controller, well here is the copy from the website.
“The Dynamics Controller is a fascinating invention from the folks at Pittsburgh Modular Synthesizers. It combines the functionality of an envelope generator, VCA, and a low pass filter.”
So it has a lowpass baked into the dynamics controller, all probably to get a nice big sweetspot.
The Vector uses Harmonic Generators to create its sounds.
"Consider that each timbre is defined by its harmonic spectra – which overtone components are present and at what amplitudes – and how those evolve in time.
A sawtooth has both odd and even harmonics, so by mixing C and D you get exactly that.
Sounds with predominantly odd harmonic contents can be described as “nasal”. A square wave has only odd harmonics and it is the quickest way to get close to a reed instrument, such as clarinet, accordion etc. On the Vector, combine D with a bit of something else and you’ll get all sorts of nasally sounds.
Sounds with sparse harmonic content are “bell-like”. This is because IRL bells have only a few resonances, and in particular these resonances are often inharmonic. To create a bell-like sound start with a sparse pattern like A or F, and create a bit of inharmonicity by adding a touch of PM modulation from some other pattern.
A thing to consider is that odd and even harmonics aren’t really symmetrical. A signal with even-only harmonics is actually just a sawtooth wave one octave up! (+ a single undertone). So the symmetry is more like odd vs. even+odd.
Note the polarity (+ and - signs) on each pattern. If you add D and E, you’ll end up with a “super-odd” sequence.
After creating the base harmonic content you would continue with modifying the spectrum of each generator or their modulation result subtractively by adding a filter somewhere in the signal chain.
Of course as always, it’s best to observe these while playing a lower note rather than a higher note. The reason is that the top limit for partials is about 20kHz so if you play a high note there’s less space for them to occupy 
In other words: everything sounds like a sine wave when played high enough."
A wavefolder quite literally amplifies its signal and then folds the excess down, using a difference amplifier. Wavefolding a square or pulse will just reduce its volume, so that is pointless. Wavefolding a saw will have some effect, but because a saw is harmonically rich already, you are just altering the balance of those harmonics, and it is not so noticeable. Sine has no higher harmonics and triangle very few (filters don’t do much to them, unless they abruptly do too much), so wavefolding those adds more harmonics and is more apparent. Lowpassed square and saw have harmonics removed, and they can be put back in a different way with wavefolding. That is why the wavefolder in, for example, the Eurorack filter C4RBN can have more of an effect on squares and saws.
Interesting. And then you start wave folding wavefolded signals🙃
This thread actually got me wondering… Wavefolding-why? Stanford says it’s a sort of distortion. Other sources say more harmonics. Ok. Yeah. For what? I use the DPO folded out when I want dirty moving drones. I haven’t found another use. There’s a video of a guy making a Reese bass with it, but most of the demos I’ve seen of iit s straight up grindcore drone stuff. Was Buchla in to that, or is there a real use? I mean , I get the FM part when using a complex oscillator. The way the oscillator s can modulate each other, and then everything can modulate the modulator. But, why wavefolding?
A wavefolder is a relatively simple circuit that has a complex and musically useful effect on a signal. Wavefolding can achieve effects similar to FM. In my limited experience, if I use both wavefolding and FM at the same time, it had better be a very small amount of each, or I just get harsh noise. I get better results by using one or the other, or a lot of one and just a touch of the other.
It’s just the other way around to create timbres compared to typical subtractive synthesis.
Since both approaches are very different processes the timbres are very different as well. If you want the timbre of wavefolding you need a wavefolder. A filter won’t do the job 
I leave this here:
https://www.cim.mcgill.ca/~clark/nordmodularbook/nm_oscillator.html#waveshaping
Other chapters are juicy as well 