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A Beginner's Guide to FM Synthesis

Written 2000/01/06

C.S. Graves

Ever played an FM synth but have been too intimidated by all the esoteric terms and parameters to program your own FM sounds? Who hasn't? For years I would tinker with my Yamaha PSS-680, but that board really doesn't have the extensive parameters of synths like the DX series and other, more sophisticated, synths. It wasn't until Gary loaned me his DX-100 that I finally understood the basics of the standard Yamaha-style FM synthesis architecture (what other style of hardware FM synthesis is there?). Mind you, I'm obviously not John Chowning, but I think I've learned enough to help out anyone out there who might be trying to figure out how to get into creating their own FM sounds, but you're still going to need some basic knowledge of general synth terminologies (q.v. my article in Nightwaves issue 4, A Beginner's Glossary of Synthesis Terminologies).

As you may know, FM synthesis relies on one oscillator (the modulator) modulating the frequency of another (the carrier). What might throw some people off is that in Yamaha-style FM, oscillators are referred to as operators. Okay, no problem... now you want to establish how your particular synth displays which operators are active and which are affected by the parameters you will be fiddling with. For the DX- 100, there is a sequence of four digits on some pages to show which operators are active. The digits are either 1 for active, or 0 for inactive. The first digit will represent the first operator, the second represents the second operator, etc. For most parameters you should be able to use a certain button (possibly called operator select or something similar) to see the settings for that same parameter for each of the operators. The DX follows the parameter value with "1 OP", "2 OP", '3 OP", or "4 OP" which indicates what operator is currently selected for parameter editing.

Another of the cryptic things about Yamaha's FM synths is the various configurations to choose from. These are often graphically depicted on the synth itself for easy reference, but it doesn't do a lick of good if you don't know what it means. Here's how you can decipher these: choose one of the configurations (often a number will correspond with the graphic depictions) and then isolate a single operator to play on its own. If you hear a sinewave, then the operator you have selected is a carrier. Any operators that you cannot hear when you isolate them are modulators, unless you forgot to turn up the volume! As you do this, take note of where the carriers and modulators are shown in the diagrams for each configuration. This way you will be able to understand the configuration just by looking at the diagram and can pick the desired one for your patch. One last thing about these diagrams is an operator depicted with a line going out of, and back into, itself. This operator can utilize feedback, that is to say that it can be set to modulate itself to varying degrees. It is with this operator that sawtooth tones can be attained if you have the feedback and frequency ratio settings right.

So you've picked a configuration, now what? Well, now it would help to undestand the many parameters that will affect your FM sound. There are amplitude values that change the static volume of each operator. Take note that the volume of the modulators will have a dramatic effect on the carrier's timbre. This is called the modulation index.

Next is the frequency ratio. This is a value that represents the frequency of the operator relative to the default value (usually 1). So a ratio of .5 means the frequency is half that of an operator with a ratio of 1, and a quarter of that of an operator with a ratio of 2. Everytime the ratio is doubled, you move up an octave. In the case of the DX series there are a variety of preset ratios which the folks at Yamaha no doubt have determined to be most suitable for making musical sounds. This may seem limiting if you've used other hardware or software synths, and wish to tweak the modulators to xxx.xxxx hertz like in Visual Orangator, but you've got to work with what you've got. Try different combinations of carrier/modulator frequency ratios until something strikes your fancy. If they all sound harsh, try changing the modulation index, or just read on...

Using the synth's amplitude envelopes you make the overall volume and/or the modulation indices dynamic. This is where the real fun of making FM synth sounds begins. You can make a sound have a loud, harsh attack and then fade out to nothing. For this sort of thing you want the decay of the modulator to be quicker than that of the carrier. Or you could opt for an eerie pad sound that starts with gentle sinewave tones slowly being complexified by a modulator that increase in amplitude with the attack. These are just two examples of what the envelope section offers. Like any good sound designer (not that I qualify as such) EXPERIMENT!

You may also be able to assign an LFO to the amplitude and/or frequency of each operator. You can choose the type of waveform as well as how much the pitch or volume of the operator will be affected by it, adding even more comlexity and life to your sound.

To top it all off, many FM boards have additional parameters to allow modulation via velocity or breath controllers. While not many people are likely to use or even have heard of the latter, the velocity parameters can make the sound even more responsive if your Yamaha keyboard is velocity sensitive, or if it's being controlled through MIDI by one that is. For this reason alone I hope to get my hands on a used DX someday so that I might make shiny FM patches whose modulation indices are radically changed depending on how hard I hit the keys of the controller board.

That's all I can think of considering I don't have Gary's DX-100 sitting in front of me right now. I think I hit the important aspects of FM, though it may still seem a little esoteric until you get your hands into it and hear the results of the theory. I discovered that once you get past the obstacle of understanding the under-appreciated, non- subtractive, seemingly alien FM architecture, designing sounds for it will become as natural as with any other popular kind of synthesis. I hope that I've helped make that obstacle a little less daunting.

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