FM - Fourier Synthesis

[brenton]

Does anyone know if there are any synths that construct sound from the basic frequency components rather than the usual subtractive and FM synth models?

I am a maths guy that drifted into signal processing and think of sound as a spectra that has been modulated - where as most synths seem to be designed by engineers who think in terms of filters and oscillators.

The way I am thinking of sound I would create a core frequency, thicken it up with various natural harmonics and then create an envelope. In effect creating the components of the fourier transform to create a frequency response - applying an inverse transform to get a signal - finally shaping it.

The engineering approach seems to be to create a signal rich with various harmonics and shape away what you don't want - sculpting perhaps.

Or are there reasons why things are not done this way - cpu intensive perhaps

[deastman]

Additive synthesis. There are many synths like that.

[BertKoor]

There's one in Caustic (available for PC, Android and iOS)
http://singlecellsoftware.com/docs/caus ... synth.html

Description of the algorithm:
http://zynaddsubfx.sourceforge.net/doc/ ... Dsynth.htm

[deastman]

There are countless examples of additive synths, or synths with an additive aspect to them, and I won't attempt to list them all here. But it dates all the way back to the drawbars of an organ. Not a new concept by any stretch.

[brenton]

Hadn't thought of an organ - but you are right .

The concept I had in mind of was far more general - a synth that could for example allow any sound to be constructed - rather than using sampling. something that would enable electronic music to sound - well not so electronic.

[cron]

The concept I had in mind of was far more general - a synth that could for example allow any sound to be constructed - rather than using sampling. something that would enable electronic music to sound - well not so electronic.

The problem with additive synthesis generally is that it's so fiendishly difficult to program without *very* high-level controls, and this high-level control sadly tends toward making fairly electronic timbres. While additive synthesis may well allow us to construct any new 'un-electronic' sound, it only really does so if we've got the patience to sculpt using *very* low-level controls - adjusting the amplitude envelopes/phase etc of every single sine which goes into it, let alone assumes we've got the ability to intuitively 'hear' the sound we want to create in this incredibly deconstructed way in our mind's ear.

There is third way however, and that's resynthesis - where we drop an existing audio file into our additive synth, let the additive synth work out how exactly how to recreate it, then play with the resulting data. Most additive synths on the market focus on this aspect today, whereas the ultra-low level editing was a little more common in years past. This kind of gets us back to sampling in one sense, but opens up a lot of interesting in-synth transformations that aren't possible in the time domain, many of which can indeed create novel acoustic(ish) spectra. How far up and down the piano keyboard that illusion holds as the resynthesis data gets further and further from its original state is another matter.

In my opinion, Harmor is the king of synths in the resynthesis/transform area. It's saddled with perhaps the worst, least intuitive toylike GUI you'll ever see - it's a shame that many will never see it's true power just because they never thought to right-click an element - but once understood it's frankly on another level to everything else out there. There are a few annoying limitations in there too - not being able to retune the resynthesis and 'from scratch' additive synth components is deeply unfortunate, and means you can't do loads of interesting effects that involve 'bending' between these two halves of the synth unless you're feeding the resynthesis engine with things tuned to a C, or don't mind the inevitable degradation that comes with pitchshifting and/or formant corruption that comes with 'tape-style' retuning of your samples before feeding them in. Still, it's amazing. Truly a thing of wonder.

Alternatively, if you'd like to try a 'pure' additive synth focused on building tones from scratch (albeit with the type of non-surgical, high-level controls alluded to earlier), the semi-modular Loom might be up your street. I've been a Harmor owner for ages, but recently picked up Loom (my first synth with the dreaded iLok protection) and I've been having a blast with it. I wish there were a few more modules aimed at modifying frequency data as well as amplitude data (there's currently just one bolted to the very end of an otherwise flexible module chain), but the focus on ensuring all partials stay harmonically related for the most part make it very accessible and easy to get good results fast.

Apologies if a lot of this post seems insultingly obvious to a maths guy with a clear vision of what he wants, but hey, it's the Getting Started forum after all

edit: forgot to add the paragraph about Harmor, making the 'alternatively' comment seem a bit odd

[cron]

This was going to be another edit, but there ended up being another posts worth of material here, so I'll go with it

On re-reading your original post, I'm getting the impression that you're not necessarily looking for realism or 'movement' as such, and are perhaps just looking more for 'static' spectra that lie outside the oscillator/filter norm which you can then further shape with amplitude/filter envelopes.

If this is the case, Serum might be another choice to look at. Although it's a wavetable synth, it has a partial editor inside its wavetable editor that lets you design your (static) spectrum in the oldschool barchart fashion. This spectrum is then saved as a 'frame' in the wavetable. You can have up to 256 of these frames which you scroll through with an automatable/modulatable knob on the main interface, so although your control over the spectrum is limited to the usual filter/amplitude envelope paradigm (incomparable to the dizzying possibilities of Harmor), you have up to 256 of them to morph through in addition to the filter/envelope stuff (and loads of other goodies like FM). However again, like Loom, it assumes all your partials are harmonically related. There's a sweet mathematical editor that lets you fill all 256 columns in one go if you know what you're doing though. I haven't got the foggiest what I'm doing with it, but as a maths guy I imagine you'll find a ton of power there. So it's not an additive synth as such, but it'll automagically convert any static spectrum you draw into a (usually) single cycle waveform for use in the wavetable.

Secondly, one of the transformations Harmor opens up is 'freezing' resynthesised sounds. By reducing the 'timestretch' knob to zero, you can play back just a single static snapshot from anywhere in your sound (or have playback of the sound slow down to a total freeze, or any other variation). You can then shape that with Harmor's amp/filter envelopes. As with everything in Harmor though, filters are 'faked' within the additive engine and can have a completely arbitrary frequency response which is then shifted by the cutoff knob - from a standard low pass to graphing the outline of your grandma's curly hair - and the fake resonance is similarly flexible. Another thing to consider if you're looking simply to play with 'acoustic-ish' spectra.

[xoxos]

The concept I had in mind of was far more general - a synth that could for example allow any sound to be constructed

hahaha i'll take a dozen eh.

the answer is, pick an audio sdk and start developing how else are your expectations to be precisely satisfied.

and that's the other answer, possibly. inexperience in the field? parameterisation, sensibility of use, as mentioned above, are big factors in synth design. if it takes you two months to patch or render it, you'll start thinking of economisations after you've done a few. when you think about natural/acoustic sounds, a sawtooth and a lowpass are brilliant really

i think there have been a few "your equation here" type vsts, but i'd suggest adopting an sdk. ......or engaging in an exploration of the synthesis platforms others make available to you (covers all the options dunnit). for the time being you could render sounds in a math app then arrange the samples in a host and do a bit of mixing