FM instigator Dr John Chowning outlines the birth of digital to Paul Colbert.

The father of FM synthesis was on holiday.

Strictly speaking, a sabbatical from California's Stanford University where he lectures: an educational break to refresh the mind and rekindle the imagination.

Not many of us would have selected an upstairs bar at the British Music Fair as a site to revitalise the synapses, but Dr John Chowning was attendant for another reason. To advise on, speak about and predict for the offspring of his experiments — the Yamaha DX7.

Chowning, of the slightly chubby frame, enquiring eyes and enthusiastic manner, stumbled upon the basic principles of musical FM in 1967. He did it "by ear training", wasn't and isn't a mathematical or computer science genius — "my background is altogether musical", and still believes that ear-judgment is the best way of setting up a DX7. Number crunching is not the path.

I tell him at the end of our interview that he's fast turning into a cult hero in the synthesiser business. He blushes and denies it becomingly. After all, he invented the basis for FM almost 20 years ago while Bob Moog was reaping his glory with voltage control.

Talking to Chowning, and contracting his excitement, you'd believe he'd discovered FM yesterday, not a decade plus ago.

Stanford is as unusual a hall of academia as Chowning is an uncommonplace scientist. The University, in his words, is "the kernal" of California's Silicon Valley. One slice of the silicon even leases land from the campus, and collaboration between industry and university are close.

"A lot of people seem to think I just sat down and thought it up. Well, of course, it wasn't that way at all. I was exploring with very rapid and deep vibrato, and the computer I was using allowed me to push that to arbitrary limits. I listened to a vibrato of, say, 10 cycles per second with a depth of 10Hz on a tone of, say, 100Hz — 'whhoowhhoowhhow', that's the sound you get.

"Because the computer imposed no limits I tried to make the depth 100, and then not ten cycles per second but 20, 40, 50 or 100.

"What happened, as we now know, is at 100 cycles per second and a depth of 100Hz I had a ratio of 1:1 and a modulation index of one. On the output of DX7 that's about 70 output level. What it sounded like to me was no longer a tracking change in pitch, but just a timbral difference. Then I doubled everything and it sounded like I'd transposed it up in pitch, but with the same spectrum."

After talking to an engineering friend, and poring over radio physics books, he found a mirror for FM in broadcasting where there's a carrier wave (the original 100Hz tone) and a modulating wave. In broadcasting the carrier is in the Megahertz, but in Chowning's form both waves were in the auditory range, and in cases the carrier was well below the frequency of the modulator — unheard of in broadcasting, but the beginning of the operator system.

"This was simple sinusoidal modulation, though in the the real world, the sound we hear everyday, the modulating wave, is a complex wave — the orchestra, the human voice, whatever."

In 1964 Chowning had been working with computers to create spatial illusions using only three elements — direct signal, reverb signal, and panning between four speakers. He was looking for a psycho-acoustic way of making sounds appear to leave the room and realised (in simplest terms) that you could do it by panning towards one speaker, reducing the direct signal strength (as the object moves away from you), but keeping the reverb level the same. Add a slight pitch change to imitate the doppler shift, control it all from a joystick, and there you go.

It was this system that lead him to contact Stanford's patent department. When FM came along in '67, and he realised, with some admitted surprise, its full musical potential, he was ready to talk to them again.

Patent costs are high, so Chowning signed to Stanford who could afford to register the patent and then look for possible manufacturers interested in developing the system. They tried Hammond and Lowrey, but both found the material difficult to grasp and concluded the necessary technology to make the theory work commercially was still far away.

Finally, almost by chance, they communicated with Yamaha, at that time far from a major force in American keyboards. But Yamaha had been carrying out their own investigation into digital sound creation, and the engineer they sent to Chowning reportedly seized the concept in ten minutes. A licensing deal was struck, and work on taking FM from the lab to the public, commenced.

"For most people who use FM a lot — the best programmers — the theory is in the background, but there are rules of thumb.

"In simple modulation — one carrier and one modulator — the frequencies produced are based on the simple relationship of their ratios such that you have the carrier component plus or minus integer multiples of the modulator.

So if you have a ratio of 1 for the carrier and 2 for the modulator, you have a waveform that is only composed of odd harmonics (for this law anything minus you make positive).

"So it's 1 plus or minus 2 which gives '3' and '-1' (1); then 1 plus or minus 2 times 2 which is 4 and that's '5' and '-3' (3); then 1 plus or minus 3 times 2 which is 6 so that's '7' and '-5' (5), etcetera.

"So all these integers turn out to be odd numbers. That will be true for modulator/carrier ratios that are odd to even, for example like 3:2 or 3:4. You'll only have odd harmonics, but you may not have all of them.

"Even harmonics come when all harmonics are transposed up an octave, for example 2:2 is the same as 1:1. All harmonics occur when the modulation ratio is 1 and the carrier is anything else like 1, 2, 3, 4 or 5, if the output level is large enough. It gets a little more complicated if you add another modulator. Then you have double combination frequencies.

"All this is perfectly easily explained by the rules of thumb, but that's not the way programmers think. It's really the more global aspects — what happens to the spectrum in general ways."

When Chowning was originally plotting these rules, there was no such thing as an FM Keyboard. It could take as long as a minute for the Stanford computer to absorb the instructions he'd given it and eventually produce a sound. That, more than any aspect of Yamaha's development of his idea, is what startles him. The instantaneous production of FM sounds from pressing a key, and the immediate reaction to new programming details.

"I call it real time squared.

"You open up the DX7 and there are two chips doing 96 oscillators, envelopes and the waveforms... 96 oscillators I think at about 60KHz sampling rate, which is high. There's some very substantial intelligence embedded in those chips... some very clever realisations of the algorithms."

During the interview. Chowning often referred to his ear training, and how it had lead him to FM. The time came to ask how the rest of us could educate our auditory extremities in this manner.

"It's intuitive, physical thinking. Looking at an oscilloscope doesn't tell you what the ear needs to know.

"Back in the early days there was a lot of thinking about it in the physical domain. Take bell tones. Think what happens and what you hear. First the clapper hits the bell and what you hear is lots of of high frequencies — the 'clang' tone. These small modes of vibration quickly diminish and you get the mid range tones; the volume drops. Then finally, right at the end, there are the very low hum tones.

"What you have is a spectrum that's always becoming simpler. I knew the volume envelope had an exponential decay, and that a bell tone was made up of enharmonic components (not integer or semitone steps) so that meant a ratio of a carrier to a modulator that's more complex than one simple integer — something like 1:1.4 using the fine frequency on the DX7. And I knew that if the output level of the modulating operator was great at first and also decayed away, perhaps with the volume envelope, then the right thing would happen. When there's no modulation you then have a sinusoid, which is what you want at the decayed end.

"By changing the ratios, you can produce different gong sounds. If you use the same envelope but use a ratio like 1:1 now it sounds like a plucked string which has similar characteristics — very complicated at first but then coming back to a damped sinusoid.

"That's the way I think about it; letting my ear make a quick analysis based on a little bit of physical experience and trying to find out what the relative parameters are.

"Spectral evolution, that's important, too: what happens globally to a sound? If you have a trumpet that starts very softly and makes a crescendo, what do you hear happening? We hear it getting louder, but there's something else. If you record a soft trumpet and just turn up the volume, it won't have the same effect. Something happens. It also gets brighter. If we can translate this subjective term into some physical change, like an increase in the bandwidth, we know what to do with the output of the right operators.

"As another example, take the tone of a soprano voice which would have three prominent resonances (formats — all voices have them at particular frequencies, they help identify us.) They fall around particular harmonics so the interval between each of these components under the spectral envelope is constant. So immediately I think, if we have a modulation operator at a fundamental frequency and there's some resonance around the eighth harmonic and I put a carrier at eight times the fundamental frequency with not too much output, then you're going to get a little bell shape curve there that looks pretty much like a resonance. Then you add those together and they work pretty well."

Notice that all this time we've only been dealing with one carrier and one modulator. Chowning is keen to encourage all DX7 owners to spend a long time experimenting with just two operators, admitting that if he'd been 'blessed' with six or even four or five at the start, he'd still be trying to work out the rules. Different algorithms might extend the power of the DX7, but he's dubious that dozens of operators would make that much difference. The law of diminishing returns.

"Maybe eight or ten operators but beyond that the curve really dips. Maybe we don't even need more than six. It can get so complicated, it just saturates the spectrum beyond what the ear can perceive.

"One of the more important steps I look for is independent frequency control over the operators so you can have that global LFO applied not only to one algorithm but to the whole keyboard.

"Source identification — that aspect of perception which tells us there are three different clarinetists playing at the same time — that has to do with what I call micro-frequency fluctuation.

"Even if there's no vibrato, there's a little bit of frequency variation in every natural tone. Ask the very best violinist to play a perfectly constant note and record it; then take out one period of that and reproduce it and play one against the other and you can still tell the difference.

"It has to do with these small changes in frequency which are incredibly important and that will be a very great step when the integration is such that we can have the power to be able to apply that vibrato, both periodic and random, a function of key scaling. It would a wonderful advance.

"The worth of the TX816 is more than eight times a DX7 in power, because each module can be programmed with a slightly different vibrato rate and depth. When you activate them all on one voice, it's bigger in tone than eight DX7s all on the same setting. "Other advances... well there are other forms of algorithms we know about that with a little more computational power..." And computational power was where we had to leave it until the sabbatical's over. For now it was back to the Yamaha stand, after politely requesting a couple of copies of One Two. There were lectures and clinics here and in Paris, plus a book on the DX7 to complete with co-author Dave Bristow. It will be the for once and exhaustive work on the keyboard, explaining the machine for the ear-novice and, as the pages flip by, descending into the mathematical relationships of FM.

And when you speak to the father, the son actually begins to make sense.