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To my limited understanding, additive synthesis adds "simpler" sound waves together to create a more rich and complex sound wave.

I've read that FM synthesis uses another sound wave to manipulate another waveform to create a more complex sound. I cant grasp the difference, doesn't both methods fundamentally add sound waves together to create a more complex sound? Whats separates them?

Very grateful for any answers!

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FM and additive synthesis have almost nothing in common. The only common aspect I can think of is that many FM synths allow using several oscillators or "operators" summed i.e. mixed together in adjustable mixture ratios, which is not in principle even a part of FM synthesis. The thing that FM synthesis conceptually does not do is add waves together, even though real-life FM synthesizers allow for that to some extent.

In FM synthesis, the frequency of an oscillator is modulated by another audio rate signal. https://en.wikipedia.org/wiki/Frequency_modulation_synthesis

Think about the tuning knob of a guitar. Pluck a string and start turning its tuning knob back and forth - the string's pitch goes up and down. You are modulating a frequency. If you could do this up/down tuning at a rate of, say, 1000 times a second, and if the guitar could actually do this, you could say that you're doing frequency modulation. Or actually, if one string's oscillating wave motion could turn the tuning knob of another string, you would have an FM guitar.

The set of frequencies created by the modulation depends on the accuracy of the oscillators and operations involved, and the precision needs to be very high so that it creates the same frequencies reliably enough for musical applications. That's why in practice, frequency modulation got very popular only when it was done with digital circuits which allow for mathematically perfect accuracy and timing. By perfect I mean that digital calculations always produce exactly the same numerical output for the same input, and with discrete timing, so the operations produce stable results that are not subject to the analog world's tuning instability.

The sound created in FM, when you can modulate an oscillator at an audio rate is not at all intuitive. I don't think anyone could imagine the sounds created by FM synthesis - they're very surprising, rich and complex, and the amount of overtones added can be very large. Small changes of parameters and "algorithms" in FM synthesis can change the sound dramatically like in quantum leaps. This is why some people see FM synthesizers as wild beasts they can't control.

In additive synthesis, sine waves are added together. https://en.wikipedia.org/wiki/Additive_synthesis It's a bit like a Hammond organ or church organ where you can create a mix of overtones/partials/multiples of a fundamental base frequency. This is a very intuitive and simple way of molding sounds. You can dial in more or less highs and lows etc.

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    Scary memories!! You've just reminded me of my first forays into DX7 programming… totally non-intuitive until Steinberg started making their editor software. Years later, in a quite bizarre coincidence, I got Dave Bristow's job when he left Yamaha for Emu. In the early DX7 years, the Bristow presets were known for being able to use lower case in the titles. The onboard editor couldn't do that. – Tetsujin Jan 19 at 18:50
  • @Tetsujin So did you learn to make sounds with FM? :) Some people are able to handle the beast. For example this guy creates all sorts of sounds with FM synthesis youtube.com/watch?v=P6CgLXrkMXI youtube.com/watch?v=eLTJlesVBhk I think that's completely insane! – piiperi Reinstate Monica Jan 19 at 19:17
  • I was a 'poker' never an expert. I was better with the 'berg editor, but never anything like Dave B was. he could 'imagine' a waveform & build it. – Tetsujin Jan 19 at 19:33
  • "In practice, frequency modulation can only be done with digital circuits which allow for mathematically perfect precision and timing." That's incorrect. Analog FM implementations (including audio synthesis applications) are very common, not sure where you got the idea that it can only be done digitally. It is less expensive to implement a system that includes several operators (modulators + carriers) digitally, but where did you get the idea that "in practice frequency modulation can only be done with digital circuits which allow for mathematically perfect precision and timing"? – Von Huffman Jan 20 at 1:43
  • @VonHuffman Better now? I think you knew perfectly well what I was trying to say. – piiperi Reinstate Monica Jan 20 at 6:36
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To my limited understanding, additive synthesis adds "simpler" sound waves together to create a more rich and complex sound wave.

Yes - specifically, additive synthesis is about adding sine waves together to create a more complex resultant waveform.

I've read that FM synthesis uses another sound wave to manipulate another waveform to create a more complex sound.

Yes - specifically, it uses one wave to control the frequency of another wave. In some implementations of FM these waves are only sine waves; in other implementations, each of these waves might themselves be more complex waves.

So as piiperi Reinstate Monica's answer says, at the simplest level, the techniques are different.

Let's take a look at the algorithms in the Yamaha DX7, the best-known FM synth:

FM synth algorithms http://powerfx.assets.s3.amazonaws.com/images/uploads/fm-synth-algorithms.png

The blocks (operators) at the bottom represent carriers - the 'initial' waves being modulated. In the DX7, each of these is a sine wave. If we look at algorithm 32, and ignore the fact that operator 6 can modulate its own frequency, you could use that as a simple 6-sine additive synthesizer. So there is a degree of similarity there, even though the techniques are entirely different.

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