What's FM ?
FM is short for frequency modulation - it's probably a familiar term because of FM radio.
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 but the sound is clearer. However in FM digital 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 about organising several sets of modulated waves (six in the DX7) to produce musically pleasing sounds.
The DX7 Revolution
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 before you can draft an email, but to program the DX7 you've really only got two alternatives : use the presets or create your own sound patches from the ground up.
Even editing other peoples' patches requires some "nuts and bolts" understanding, unless you throw everything to chance. So, understandably, Yamaha's research showed that 95%+ of 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.
After many attempts to make FM more accessible, Yamaha and others moved on to sample based synthesis - essentially digital tape recorders - since it was easier to shape a pre-formed sound.
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 times the sound wave goes round its' cycle each second. Frequencies are measured in cycles per second. Amplitude is simply 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 the human ear 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. The difference between a sax and guitar sound is immediately obvious 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 (ie subtractive synthesis - as used in analog synths).
The time dimension: EGs and Operators
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 is the key to creating vibrant, original FM sounds.
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/timbre. At the other extreme from Alg32, Alg1 has a stack of four operators with the output from the bottom operator ( 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 by playing with the settings of these operators. And of course, in addition to stacking the operators, each operator has it's own EG to further shape its sound over time.
For the DX7 there's really only one reference book that justifies the title - Howard Massey's The Complete DX7 (Amsco Publications, 1986). It is a superbly detailed, totally comprehensive practical tutorial on every aspect of operating the DX7. Long since out of print, you may be able to get it on EBay, Google for a PDF, or try a bricks and mortar library: ISBN references are UK 0.7119.0996.2 or US 0.8256.1071.0. Massey also wrote The Complete DX7II .
Massey's book also discusses FM theory in some practical detail. For a more advanced thoretical discussion try John Chowning and Dave Bristow's FM Theory and Applications (published by the Yamaha Music Foundation,1986, ISBN 4-636-17482-8).
Both these excellent texts provide "rules of the road" for creating original FM sounds, 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.
Other References :
The history of the DX7 and it's many variants is detailed in these excellent articles from Sound on Sound magazine:
For a simple, practical introduction specific to the DX7 try :
Yamaha Easy DX7 - A Complete Guide to the DX Synthesiser, Hal Leonard Publishing Corporation,1986. ISBN 0-88188-452-9
The official Operating manual for any of the DX/TX and SY ranges is available from Yamaha.