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I use tools including Ableton Analog, NI Massive and FAW Circle, with which I can produce more or less any sound I like, but I don't really understand how synthesis works and how to make a sound with it.

Can someone explain it please, and how I can use it to design custom sounds.

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up vote 3 down vote accepted

Do a Google search and you can find many references on Frequency Modulation (FM) synthesis and how to use it, compared to subtractive synthesis, additive synthesis, and other types.

Crude analog frequency modulation synthesis was a feature of some early analog subtractive synthesizers. However, a powerful form of FM synthesis in a digital implementation became extremely popular in the early 1980s with the release of the Yamaha DX7 family of synthesizers. There was a lot published on FM synthesis around that time.

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It should be noted that the Minimoog is a subtractive synthesizer, as are the vast majority of analog and VA synths. I'm also not sure you have the routing options necessary to achieve any sort of FM on the Mini. Maybe the modular? – Tim Lehner Mar 19 '13 at 12:42
Thank you for correcting my "typo". I meant to say "subtractive". But the Minimoog could indeed do frequency modulation synthesis on oscillator 3. Here is proof in a video. – user1044 Mar 19 '13 at 15:29
@WheatWilliams: The digital FM synthesis used in the DX series was very different from analog FM synthesis. Among other things, the internal sampling rates were insufficient to prevent significant aliasing of some frequency components in the generated signals, and such aliasing ends up playing a significant role in the sound of many patches. Were one to construct an analog equivalent of what the DX is 'supposed' to be doing, its sound would be very different from that of the DX. [note: my experience is with my DX21, but I expect the DX7 is similar in that regard]. – supercat Mar 19 '13 at 15:59
Of course you are right, supercat. I said that the FM synthesis on the Minimoog was crude and the FM synthesis on the DX7 was very sophisticated, and that one was analog and one was digital. I'm well aware that early Yamaha FM synthesizers were essentially 10 or 12 bit and very noisy. I had a TX81Z back then. I said nothing to make anybody think that the Minimoog and the DX7 would be equivalent or that they could make similar sounds. I just said that they were both examples of FM synthesis, which is perfectly true. – user1044 Mar 19 '13 at 21:54
@WheatWilliams: My point isn't that the Yamaha does FM synthesis better, but rather that because of digital aliasing effects it is totally unlike anything in the analog world, crude or otherwise. Incidentally, I wonder if the people who designed the DX7 ever played any arcade machines designed by Eugene Jarvis or featuring his sound board (Defender, e.g. debuted in 1979). The Jarvis sound board uses a 6800 microprocessor to generate waveforms by periodically adding various registers to other registers in a fashion conceptually similar to the Yamaha DX series. – supercat Mar 20 '13 at 16:38

Sound on sound magazine has an excellent series of free articles that explain synthesis from the ground up. Here's a link to the beginning of the chain.

They go from the very basic to the complex. It's a wonderful series and FREE!

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There are several ways of doing FM as well as a few different approaches to additive synthesis.

In the simplest form of two oscillator FM, a sinusoid modulates the frequency of the second sinusoidal oscillator. Depending on the ratio of the modulator to carrier frequency and the modulation index (strength of modulation), you get different sounds. Simple integer ratios such as 1:2 or 3:2 produce harmonic spectra, irrational ratios yield inharmonic spectra. The partials' amplitudes depend on the modulation index, and cannot be controlled independently. There are extensions to more than one modulator or carrier, cascaded FM and feedback FM, all of which extend the possibilities in various ways. For a very easy introduction to FM, try to find a copy of FM Theory & Applications by Chowning and Bristow.

Additive synthesis builds up sounds from sums of sinusoids with given frequencies and amplitudes that may vary over time. The advantage of additive synthesis is that any sound whatsoever can be represented. By doing a Fourier analysis of short windows of the sound you get a series of time frames of the spectrum at that moment. From that representation you would usually pick the strongest spectral peaks and synthesize the sound from a sum of sinusoids. This technique is known as the tracking phase vocoder. A popular extension is Spectral Modelling Synthesis (SMS) which incorporates noise.

Whereas additive synthesis has its corresponding analysis technique that lets you resynthesize (and modify) any sound, the situation is more difficult with FM. Traditionally, FM algorithms were tweaked by ear and by intuition. Then some researchers began searching for synthesis parameters that would match given sounds by genetic algorithms. That approach has mostly focused on harmonic sounds. In the early years of computer music efficiency concerns favoured FM over additive synthesis, but developments in algorithms and hardware makes that point moot.

Both FM and additive synthesis are useful for sound design, but there are of course other approaches worth knowing about, not least subtractive synthesis and physical modelling.

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