Synthesis types

After watching some of the "intro to synthesizer" videos, it's interesting to ponder all the types that have evolved over the years--additive, subtractive, sampling, AM, FM, yadda, yadda, yadda.

With all the math references, modulation, frequencies, etc. I've often wondered why there was never synthesis based on multiplication or division, or maybe even geometry. And if we can use AM and FM, why not Short Wave, UHF, or RADAR synthesis as well?

I've thought of that before as well: geometric synthesis. Not sure entirely how it would work, but now I have something to think about.

Okay plan: you invent UHF/Short Wave and I'll work on geometric.

Okay plan: you invent UHF/Short Wave and I'll work on geometric.

I'll see what I can do.

I was also thinking, since Yamaha makes outboard motors, they could develop "marine band" synthesis.

Excellent concept. I'll work on the synthesis based on differential equations.

(Actually, I bet modeling, particularly for acoustic instruments, requires some of the good ol' calculus...)

Ring modulation is basically multiplication of two signals. But it falls under AM.

Convolution is superimposing of two signals in time domain (which translates to multiplication in frequency domain). And vice versa. So in a way, multiplication has been done.

Physical modeling is based on a lot of differential equations solving, too.

Perhaps this was an early "ring modulator."

Haha!

No, "ring modulation" is called like that because the schematic for it looks like this:

See the ring of diodes? Yeah, that.

That's also why some synth nerds will get in a tizzy about "true" ring mod vs. balanced modulation vs. AM vs. whatever else someone came up with

Damn and here I always thought it had something to do with an algebraic ring.

Damn and here I always thought it had something to do with an algebraic ring .

Sure, mod a ring and you get a finite field which will have a well-defined frequency of some sort...

You could always mess with Kurzweil's FUN's. They go back to the K2000 series:

"A discussion of V.A.S.T. would not be complete without mentioning "FUNs". "FUN" stands for "function", and these are mathematical equations that take two values (a and b) as inputs and perform an operation on them. FUN equations include "a+b", "a*b", "b/(1-a)", and many others of varying complexity. They also allow for self-modulation; some FUNs introduce a variable "y" which represents the most recent output of the FUN. The Kurzweil evaluates each FUN every 20 milliseconds, hence it can take that value and plug it back into the equation if the equation has "y" as an input variable. Any modulation source can be assigned to a or b (or both at the same time) in a FUN. This can be used to mix two modulation sources, cause one to multiply the effects of another, and so forth. Internally, the K2000 rescales whatever value is currently being sent by the control source to a number between -1 and 1 (for bipolar control sources. Unipolar sources are scaled between 0 and 1), then applies the function and returns an output value. Using FUNS, therefore, more than three control sources can be assigned to modulate a parameter in a block since you can assign a FUN as a modulation source for "Src1", "Src2", or "Dptctl". Four FUNs are available per layer and FUNs can be assigned as inputs to other FUNs. The Kurzweil evaluates the FUNs sequentially, hence for this to work you would want to assign FUN1 as an input to FUN2, but not vice-versa."

^^^^From here - http://en.wikipedia.org/wiki/Kurzweil_K2000

More for modulation manipulations than proper synthesis - but still.

Nerd spoil-sport alert: Short Wave, UHF, and RADAR would all be forms of FM (if taken literally) since those all happen in various frequencies of the ER spectrum. And, most of that would not have sidebands in the audible spectrum. But they all sound cool as names. If I'm going to invent a form of synthesis, I'ma call it "public access cable channel guide" or something like that.

One fun thing would be to mess with various arbitrary symmetries in a waveform and spin samples around those symmetries. For instance, take a non-repeating waveform (like a piano sample) and arbitrarily pick a dB level. This is a "symmetry" point around which you can spin the samples (and there could be various mapping algorithms to determine what "spin" means. Like up, down, strange, charm, bottom, top...). Assign some sort of continuous controller to do the "spinning" and wah-la -- basic cable channel guide synthesis. Now, establish multiple symmetries and spin them at the same time, morph one into another, do the spinning at audio rates, project them down onto various 2-d planes, etc. That's the premium cable channels...

Wouldn't that just be a fancy waveshaper then?

No, "ring modulation" is called like that because the schematic for it looks like this: See the ring of diodes? Yeah, that.

I never knew that, thanks.

Some of us learned something new today.

FM is based on 'ratios'. The relationship between modulator and carrier determines the sideband frequencies that are produced. The math can get hairy though.

Ratios is essentially all about multiplication and division, so... there you go. Mission accomplished!

Hmm..... Ring Modulation.

Click on door stopper

Hmm, looks like an earlier reply got lost...

AM and FM are modulation methods.

Short wave, UHF and Radar are frequency bands.

Haha! No, "ring modulation" is called like that because the schematic for it looks like this: See the ring of diodes? Yeah, that.

Aha -- I'd been meaning to ask about the difference between cross modulation and ring mod when it came up earlier, but thought I'd google it first. You beat me to that. Thanks! Still not sure exactly what ring mod is (though I do remember trying it on early moog and/or arp synths in shops) but this makes it clear why it's not "just" cross-modulation. I think ... I'll have to ponder it a bit!

Cross modulation is analog-style FM, whereas ring modulation is AM.

I wrote a convolver once, but oddly enough it was for virtual reality avatar animations, not audio. It was just the simplest way I knew to make a lowpass filter that didn't introduce phase delays. Differential equations hurt my head. I have a book I've been meaning to study called something like "differential equations for dummies" but I'm not quite smart enough. (I had to review my basic calc first, argh, been so damn long!) But for you math folks, convolutions are multiplication, but it takes differential equations to really understand how to program them in nontrivial ways.

The trivial way is to use it to duplicate a linear system, and all that takes is using the step response of the system as the filter kernel. Thus, fire a starter pistol in Carnegie Hall, record it, use that for the filter kernel, and viola: you can hear yourself play piano in Carnegie Hall! But convolutions can do way more than that. I have another book (Shannon) I don't understand that goes into great detail, but requires facility with diff-eq. wheee. So much math, so few hours in the day!

The first part of that makes perfect sense (and I wondered about that). The second part I still need to think on, but I'll take your word for it. Thanks again!

http://en.wikipedia.org/wiki/Ring_modulation

Says it all, right here.

"Wave Terrain Synthesis" is a kind of geometric synthesis: you make a "terrain" from a two-dimensional function, and then your oscillators draw paths through it.

One of the classical functions (if I remember correctly) is (x+1)*(x-1)*(y+1)*(y-1)*(x-y). I think people have even used photographs as functions.

Photographs can also be used as sources for additive synthesis (see Camel Audio Alchemy).