What seems to be missing in comparison to discussions on Analog Synth VCOs are:-

Triangle Wave
Pulse (Width Modulated) Wave
Oscilator Synced (Phase Locked) Wave

Triangle Wave
You need a Modulator:Carrier stack
Set the Carrier Output Level = 99
Frequency Ratio = 1.00
Feedback = 0
Set the Modulator Output Level between 40-70

Pulse Wave
If you are good at math, then in geometry you know that about Quadrilaterals, Rhomboids, Parallelograms, Rectangles, Rhombus, Square, etc... well, in musical stuff the relationship between the Square Wave and the Pulse wave is such that all Square Waves are Pulse Waves. ()
There are many different four sided objects defined in geometry... and while all squares are rectangles, not all rectangles are square.
A ‘square’ wave is a special narrow definition of the pulse wave

A square wave is the perfect case of the pulse wave... much like a geometric square is perfect case of the rectangle (the adjacent and opposite sides and angles are all equal). All square waves are pulse waves, the perfect case where the signal in On 50% of the time and Off 50% of the time. The result is every other harmonic (only the Odd numbered harmonics)... as you change the % time On to Off, the timbre changes.

A pulse wave is defined as one that is On for a period of time and Off for a period of time. A 50/50 On/Off % is “square”; a pulse that is on 10% of the time and Off 90% of the time is a very narrow pulse.
Here’s a quick article on Synth Waves: SYNTH BASICS: All Squares are Pulse

If a Square Wave sounds hollow and woody - like a Clarinet
A Pulse Wave sounds narrow and nasal - like an Oboe, or Clavinet.
A Sine Wave is devoid of harmonics - and more like a tin whistle or flute

When the Modulator and Carrier share the same Ratio, as 1:1 — the result will be all harmonics (Sawtooth Wave).
When the Modulator is twice the frequency of the Carrier, you can get a Square Wave. Example M = 2, C = 1
As you increment the Modulator through the whole integer Ratio values, the Pulse gets narrower and narrower... you still only generate odd numbered harmonics but the timbre get more intense (nasal in quality). 3:1 gets nasal, 4:1 is pinched nasal, 5:1 even more pinched nasal... and so on.

Oscillator Sync
FM Synths and Analog Synths can both create this type of sound... the Analog Oscillator Sync requires 2 oscillators...one oscillator that tracks pitch for the pair according to the notes of the keyboard, the other oscillator is forced to sync to the pitch of its silent partner. In order for the “sync” sound the oscillator supplying the pitch reference should be higher in frequency than the audible slave oscillator. This gives the sound a very narrow, biting tone with a very distinct vocal-type resonance. The silent oscillator (high pitched) forces the slave oscillator to reset and follow the phase - as you change the frequency of the higher pitched master, it causes the timbre of the audible slave to take on the “hard sync” character.

Musical reference is The Cars - “Let’s Go”... classic “hard sync” sound.
In the Preset Waveforms you’ll find several “Sync Lead” Waveforms - for comparison. “Sync Lead4” and “Sync Lead5” are closest to the classic Cars recording... “Sync Lead3” has a lot of that ‘vocal resonance’ sound
Compare to the FM versions (in Manny’s tutorial) and you’ll understand just how they differ.. FM has more harmonics... this is where the right Filter will complete the emulation.

The FM-X Operators can do this type of sound but FM Operators tend to throw off many, many more sidebands frequencies (the forced synchronization does not happen in the same fashion therefore, the behavior is different), so the result is crazy richer in harmonics... in this case, with traditional FM the Oscillator Sync was so rich in harmonics (continuously variable) this changed the entire character of what is known as analog oscillator “hard sync”. That said, check out how Manny addresses this issue in the article).

Manny goes over creating Oscillator Sync with FM-X in one of the tutorials... (Manny's FM-Xplorations Article 5) and with artful use of the Motion Sequencer, too.

Extra Credit:
FM as in the DX7IIFD (1986) had the capability to expand on the original... you had many more people playing around with it. Back then this was the “10,000 monkey time”. Meaning so many people were exploring and making discoveries... It seemed new stuff was discovered all the time. FM Synthesis was taught in colleges and universities, it became the darling of academia.

It was ‘discovered’, (partly, out of necessity) you could use FM to create a kind of Reverberation (FM Reverb) — this was before synthesizers had any effect processing, at all. There was no need to follow up on this because proper Effects getting built-in to your synthesizer was on the immediate horizon...
_ I can remember the first time I heard the DX7IIFD say: “Ya-ma-ha dee ex se-ven” in response to the demonstrator playing seven notes on the keyboard! Robotic? Yes, sure, but the variety of tones that could be made with just a couple of Operators was truly amazing.

The first Yamaha Electronic Drums used a special FM Tone Generator.

By the end of the decade, they had it speaking and singing - products like FS1R (16 Operators, 1999), the PLG100-SG plug-in board, (with all the formant shaping and vocal analysis)... that then led to the Vocaloid software (2004). They’re up to Vocaloid 5 now...

The FM-X engine awaits a new generation of explorers, and a new set of discoveries. There have been many branches leading from the original DX7. Every time I ‘spin the wheel’ with the SmartMorph I find a half dozen more things to explore...

BTW: although samples of the different waveform shapes are in abundance on the internet -- so you can train your ear through online videos or websites -- you can also use your MODX. At least for non-modulated waveforms. The basic forms are sampled in Waveforms you can call up from an "Init Normal (AWM-2)" Performance replacing the piano element with an element that represents a basic "analog synth" waveform.

For SynLd/Analog categories you see:

"Sync LFO", "OB Saw", "Saw", "Saw Square" and "Square Saw" (morph between the two), "Tri Wave", etc.

Remember samples don't afford you the same kind of control - so these are just representative snapshots and fairly static (the basic waveforms).

Dear BM, J...

Super Duper info, thanks very much. I shall start trying these out.

Tony

Just wondering if the FM-X software code is Set-in-Stone. As in, "If feature 'X' could have been done, it would already have been done".

I notice in Manny 's FM-Xploration Tutorials he takes you to and shows you some of the limits of FM-X, then provides alternate methods/solutions.

One "limit" I recall was the absence of Phase Shifting ability between Operators, particularly for accurate PWM emulation.

Is this something, as an example, that could be easily implemented in FM-X code?

Yeah, phase shifting has to be faked a bit. PWM isn't native (ability to alter duty cycle of carrier periodic waveforms).

FM-X isn't necessarily etched in stone. I see an Ideascale FM item to add some features that's made it to the 3rd stage of consideration ("Assessment" ). Actually, 3 of the 6 items at this stage are FM-X related. Maybe there's some opportunities for extending FM-X.

I finally figured out what "ideascale" is and registered.

I noticed someone already posted a request to add Analog base VCOs to the existing All1, All2, Odd1 etc. This might be a tidier solution than adding "phase shift" or "oscillator sync" parameters to the code.

It's no biggy for me either way, although I suspect that FM super users would probably get more mileage from the "added parameter" route.

EDIT: I also see quite a few requests for the addition of a 3rd Modelling engine to MONTAGE/MODX which may make altering FM-X unnecessary.

It will be interesting to see what Yamaha do, if anything at all.

FYI: there has been some resistance to providing more waveforms although even previous Yamaha FM implementations had a wider (or lets just say, different) variety of FM basic waveforms to choose from. The thought is you can use feedback for sine (which you only get one modulator's worth - not every operator like the reface DX) or you can use the other waveforms with skirt to arrive at different waveforms. Sometimes what's required is two operators with appropriate ratios between. And the general thought is also that you have enough operators to realize what you want because you end up getting multiple parts you can always add to add operators - 8 at a time.

There's truth to that - Yamaha's pushback. But there's also truth/utility in the immediacy and conservation in using a single waveform to do the work of two -- or single waveform to get at better results. Using what's available gives one type of character to the resulting waveforms. I think single waveforms for traditional shapes (and some non-traditional) can make the engine easier to create with, conserve resources, and also give waveforms that are different/unique in character from the counterparts created by using what's there already. Also, adding waveforms of past FM implementations (these are not what you asked for, per-se) expands the "compatibility" of the current engine to legacy sounds based on the unique catalog of shapes previously available.

I guess we'll see. I'm sure the compatibility story is not compelling (to Yamaha, and I would argue perhaps not many users) as FM-X is more about combining the modulation possibilities as a forward-thinking vehicle than necessarily trying to be a super-set of the past.

One "limit" I recall was the absence of Phase Shifting ability between Operators, particularly for accurate PWM emulation.

Is this something, as an example, that could be easily implemented in FM-X code?

When the “limit” is properly placed in quotes, the discussion about whether it can be implemented is put in context. Another “limit” of FM-X is when attempting to emulate violins, it does not use a horsehair bow to initiate the sound. That is also a true statement. And if it did use a horsehair bow and cat gut strings to emulate the oscillator (violin oscillator) it would likely do a better emulation... but that ain’t gonna happen. (lol).

I make an exaggerated example, to make the point that an analog synth has its own characteristics and/or flaws (if you will) whether pulse width modulation can be emulated by operators in an FM synthesis, is not the point. If the same or similar situation was setup, using FM would the trade-off be worth it...without a major fundamental change, it is going to do it a different way.

Operators differ from Oscillators... some one who knows FM will be happy if in the discussion the newbie understands that they play a similar role. But they are not the same. A deep discussion will need to take into account the important differences. An Operator includes is own AEG, and its output can be dependent on the input from other Operators. Not the case in the analog world.
Pulse Width Modulation in an analog synth is a situation where one particular pulse width settings varies.... analog oscillators typically share the same AEG- so the structure is completely different.

So the answer is no, it would not be easily implemented. Could it be? If... only...
And while FM does PWM emulation in an entirely different way than analog synths - what is the goal? To emulate a specific synth sound from a classic hit or do everything an old analog synth did?

After all FM does the sound of a Rhodes tine and tone bar, in a completely different way, it does the plucked sound of a guitar in a completely different way, it does the sine waves of a B3 in a completely different way, it does the mallet strike on a bell, vibraphone, marimba, all different from the original instruments,... and so on. It’s a synth.

The other point is... samples can do PWM by taking a picture of it, but PWM is (in reality) a real-time interaction on an old style analog voltage controlled synthesizer, so when applying any stress to the analog waveform versus the snapshot of the waveform, it’s behavior will likely be different. Even when sampled you cannot always fully capture a sound — because once put it in musical motion the “behavior” comes into play - and that can be different.

For example, a sample of FM behaves differently than the actual FM — you have every thing you need to do this experiment. There are plenty of samples of FM classic sounds in the MONTAGE/MODX Element Wave ROM, see how they compare... a single standing note is very hard to tell the difference, but FM will change timbre differently than the sample snapshot.... When put into music motion. It’s response to varying velocity, for example. FM does not just get louder it initiates different musical sidebands (not necessarily available in the snapsot (sample) sound set).

Yes, you can probably mimic a specific type of change but still the FM could be varied in a more organic way. It is not emulating itself - it IS itself. It’s the AWM2 that is trying to emulate FM behavior.

So while the PWM samples represent what a PWM analog synth sounds like, put in musical motion you may quickly tell one from the other (or not). It is when folks begin to think any synth emulation is on-target - that they are really just willing to buy in because the markers they are using to judge it, have been mostly met.

Take a look at any of the Parts in the FM-X “FM PWM Pad” Performance
Study the Operator stacks - how they use detuning from each other and Fixed frequency modulation to emulate the change in pulse width.
It is not accomplished the same way as an analog synth, it is emulated, they are creating the illusion of varying the nasal-ness of the pulse waveform. For PWM strings, this is not bad - particularly with the three FM-X Parts...

Hope that helps.

Thanks BM for your insight.

I am quite possibly a unique user in the fact I have bought a 2020's modern synth, with the sole intention of reproducing sounds created by synths and keyboards of the 60's and 70's.

Limited budget was a huge factor, as well as the fact I had no prior experience with keyboards of any kind.

All my questions on here so far are definitely not gripes of dissatisfaction. Quite the opposite, I am in a state of awe, and my steep learning curve is generating a lot of curiosity. The MODX7 has massively exceeded my expectations.

I sometimes wonder if I might be mis-using this forum. I notice quite a few others use it as a "3rd Line Support" site i.e. "Why is smoke coming from my keyboard?" type affair. But I can't find any other resource on the web that has an equivalent level of participation or deep insight.

That said, I greatly appreciate yours and others time spent in addressing my curiosity.

You might have inadvertently bought the absolute best synth for this.

Have a look at Cuckoo's ways of importing a sound set of his own making, and then realise you can do this with all the samplings of old synths from the era you're interested in, and get the benefits of the effects and layering of the MODX, and FM-X, to add to those samples:

https://www.youtube.com/watch?v=76Vh2p9S2GE

On the FM front... Montage Expanded soundset... Webinars 1 live set, the second 'patch' is Oxygen.

This is a VERY good starting point to figure out how to make lush FM sounds that ring of 70's Analogue sounding ways.

I haven't seen the webinar that goes with it, but not sure you'll need it. The patch is very easily understood because it's four pairs of operators, each quite distinctively different.

I've been through Manny's FM-Xploration Tutorials, skimmed through Manny's Recreation of Acoustic Piano (FM-Xpert) and done the FM101. Manny has also done a series on the Reface DX which include real time Spectrum Analysis - check these also (YouTube Dr Synth "FM Over Modulation" to put you on track).

Long story short, if you go through all those you will find the FM methods for creating all the main food groups in relation to Analog Subtractive Synths, including different forms of noise. Bad Mister is correct that the principle/context/manipulation is different in FM, but the end product (aurally) can be the same - which is likely the ultimate goal.