FM is short for frequency modulation - but you knew that anyway because of FM radio.
OK, so what's frequency modulation? It's a way of mixing two sounds together to create a third, different sound.
In FM radio a high frequency base or carrier wave is modulated by a much lower frequency audio wave and the result is similar to the original carrier wave - you just hear it better. However in FM synthesis both waves are audio frequency and the modulation can produce a sound that is totally different from the contributing waves.
Sounds reach our ears as pressure waves. These force our ear drums to vibrate and this generates electrical impulses that our brains register. FM involves putting two "pure" sound waves together in such a way that what you hear is not the original waves but the mix - or modulation.
FM synthesis is the black art of organising several sets (six in the DX7) of modulated waves to produce musically pleasing sounds.
What was so revolutionary about the DX7 when it came out in 1983 was that for the first time it made digital FM available in a powerful, flexible, and above all affordable package. Older, analog synthesisers use electronic components to generate ready-made complex waveforms which are then shaped using filters. In the DX7, the waveforms are just streams of numbers generated by the on-board computer to represent how the audio waveform would sound. All the mixing/modulation is done in the digital domain using FM synthesis.
So essentially a DX7 is a specialised computer - which in a way is where the problem starts. No-one expects you to understand the principles of the digital computer in order to be able to craft a Word document but to program the DX7 you've really only got two alternatives : use the presets or create your own sounds from the ground up.
Even editing other peoples' patches requires some "nuts and bolts" understanding, unless you throw everything to chance, so understandably 95%+ DX7s were never used to play anything other than presets or bought-in sounds. The growing frustration at the difference between the brilliant Presets and what you could achieve with half an hour's tweaking led most people to seek alternatives and of course they soon gave up.
Since then attention spans have declined exponentially. That ultimately that led to the rise of sample based synthesis - digital tape recorders - since these more easily satisfied the desire for instant gratification if not creativity.
But there is a third way and one that does satisfy both instincts. It does involve some understanding of the FM "operating system" but it recognises up front that no-one (not even Brian Eno or Rush) creates brilliant FM sounds from the ground up any more than anyone could create a brilliant word processor in machine code.
I designed DX Manager to make it easier to be creative in FM and at the same time make it simpler to understand what's going on as you make new sounds.
But that's getting ahead. First some more terminology you can't do without, so don't skip this bit.
All sounds can be completely described using just three terms: frequency, amplitude and timbre.
The first two are pretty intuitive - frequency just means pitch, how high or low the sound is : the term frequency is borrowed from wave terminology and means how many time the wave goes round its' cycle each second. So frequencies are measured in, yes, cycles per second. Amplitude is a measure of volume, how loud or soft the sound is, and this is measured in decibels - 1 db is roughly the smallest change in volume you can detect.
The third characteristic is timbre or tonal quality. Although you can't sum up timbre in a single measure like frequency or amplitude, perhaps harmonic content comes closest. You can instantly tell the difference between a sax and guitar even though they are sounding the same note at the same volume. Some sounds, like flute or organ, sound "pure" whereas others like the sax sound "rich" or "complex".
"Pure" sounds are dominated by a single frequency whereas "complex" sounds have many other frequencies which are (often deliberate) by-products of the sound creation process. For a sound to be pleasing to our ears under the western musical system, these other frequencies must have a regular relationship to the fundamental frequency - fixed multiples, double, treble and so on. The number of frequencies, their relative volume and the way these change over time are a sounds' tonal quality or timbre.
And this is where digital FM really scores. Frequency modulation synthesis is a very flexible and economical way of creating a wide variety of timbres that avoids having to build sounds by directly mixing each individual frequency (otherwise called additive synthesis) or by removing unwanted frequencies by filtering them (aka subtractive synthesis - as used in analog synths).
However no matter what method of sound synthesis is used there is also the time dimension to consider - sounds do not remain constant over time : the quality of a guitar note when it is first plucked is very different to the quality of the sustained note or the tremolo effect you add as it decays.
In FM synthesis, sounds are commonly shaped over time by changing the amplitude (volume) of their components. Typically a sound has an initial period in which it is developing (attack time), a period when it has matured, and a period when it decays - which may be before and/or after a key or string is released.
Together these sound shapes or settings make what's called an Envelope, which is just a representation of the boundaries (envelope) of the sound over time. The software in the DX that does this shaping is called the Envelope Generator (EG). Altering the rate at which these states are reached and their relative volumes goes to the heart of what's involved in creating vibrant FM sounds rather than yet another "Tines48" clone !
In the DX7 the basic sound - the one you get when you initialise a voice patch - is a sine wave. This is the purest tone you can get with (for all practical purposes) no harmonic overtones - after all it's just a stream of computer generated numbers. A tone generating unit, or Operator, consists of the input wave, a (digital) amplifier and an envelope generator. The DX7 family of synths have six operators (some later variants have only four) and the output of one operator can be fed into - ie modulate - another operator, and the output of that operator can be used to modulate another operator and so on.
With six Operators to play with there's obviously lot's of different ways in which the operators could be arranged. The 32 Operator arrangements Yamaha chose (known as Algorithms) are printed on the DX's top panel. The simplest arrangement is Alg32 which is just nothing more than the 6 Operators all lined up next to each other as carriers and not interacting - so there's no frequency modulation taking place. In every other case the Operators are stacked, placed above each other to varying degrees, so that the output of one Operator inputs to ( or modulates) the operator beneath it.
Altering the output of an Operator at the bottom of an algorithm stack - the Carrier Operator - alters the volume of the sound. But altering output of Operators above the carrier increases or decreases the sounds' harmonic content. Since at the extreme (Alg1) has a stack of four Operators with the output from the bottom operator (called the Carrier) providing further feedback to the top of the stack, it's possible to create some very rich harmonics or unpleasant racket without much effort. And remember, in addition to stacking our operators, each operator has it's own EG to further shape its sound over time.
Now here's where I cop out - since this is not a tutorial on how to operate a DX synth. If you want that here's some references and links that will take you further.
For the DX7 there's really only one reference that justifies the title - Howard Massey's The Complete DX7 (Amsco Publications, 1986). Long since out of print you may be able to get it through a bricks and mortar library: ISBN references are UK 0.7119.0996.2 or US 0.8256.1071.0. It cost me £16.95 and came complete with three plastic sheets of audio cues you could use to re-profile your hi-fi stylus with ! It is a superbly detailed, totally comprehensive tutorial on every aspect of the DX7 - practical and theoretical. Massey also wrote The Complete DX7II - which is now complete gold dust.
What I'll do from this point is assume you are now comfortable with the basics of FM and have done some simple editing - peering at the miniscule screen whilst tweaking the presets or something similar. The conclusion most of us come to from this is that a) there has to be a better way and b) the difference between being there and nearly there is small but the number of switch permutations standing between us and bridging that gap is infinite. So what are your alternatives ?
You can get a better grasp of the theory as applied to the DX7 by studying Massey's book and/or graduate to Chowning and Bristow's erudite FM Theory and Applications (published by the Yamaha Music Foundation,1986, ISBN 4-636-17482-8). It's the sort of guide to FM Stephen Hawking might have written.
Both these excellent texts give you some tools to narrow your search down - sort of general rules of the road for creating this or that type of sound, but both emphasise the importance of serendipity, which means the more or less accidental discovery of an original/exciting sound whilst following some general guidelines.
After many years trying to find this magic state of enlightenment, I am sorry to say that I don't think it exists for most people (although it may have done for Brian Eno and Rush). Like any art form there are some people who have a natural talent for it, which no amount of technique obscures, and there are the rest of us who need a helping hand.
Fortunately with the DX it is easy to shorten the odds by using our ears - the best arbiter of what sounds right. That was why, in developing my DX and SY Manager programs, I decided that "hear as you go" was a fundamental design principle. So not only can you see graphical representations of your sounds but, as you make changes you can hear the effect on the overall patch you're working with.
In DX Manager, I've taken this principle further by automating the sound creation process with a Patch Generator, but still of course leaving the final choice to your ears.
If you are interested in the history of the DX7 and it's many variants here's a couple of excellent articles from Sound on Sound magazine:
The Birth, Rise and Further Rise of FM Synthesis (Retro) The Yamaha DX1 & Its Successors (Retro)
A simple, practical introduction specific to the DX7 is: Yamaha Easy DX7 - A Complete Guide to the DX Synthesiser, Hal Leonard Publishing Corporation,1986. ISBN 0-88188-452-9
You can get the DX7 manual from Yamaha.
Finally here's an interesting article on programming the DX7 by Bo Tomlyn that appeared in Keyboard magazine in June 1985.