FM Synthesis – an overview…

The Yamaha DX7 (Mk 1) may be thought by some to be an unusual candidate for these pages as it can hardly be classed as a rare, collectable vintage analogue keyboard (however my point of view is that keyboards are to be played, not collected). But as it was originally produced in 1983 and was the first affordable digital synthesizer then now seems as good a time as any for a re-appraisal of this enigmatic keyboard. I say enigmatic as I am sure that a vast number of current and past owners of DX7’s probably never will understand how they work.

I still find that this is the keyboard for percussive bell sounds, excellent electric pianos and extreme bass sounds. For the rest of the time (with the Special Edition ROM) it makes an excellent master keyboard. However for real in depth FM search out the SY77 or it’s module equivalent, the TG77.

The DX7 was first produced in 1983 (after several years of apparent inactivity from Yamaha on the synth front) it followed the extremely expensive and completely preset GS1 and GS2 and took the synth market by storm. This was for several reasons, firstly it sounded good out of the box with sound that were less ‘electronic’ than other synths, secondly it was touch sensitive (with a decent keyboard to match), thirdly it was affordable (£1500 / $1800 approx). For these reasons it was soon the keyboard to be seen with during the mid-eighties and was so popular it even got a second chance with the DX7 MkII (not many synths get that honour). In total Yamaha went on to make something like 160,000 of them. As Yamaha held the patents on FM (developed by Professor John Chowning at Stamford University, USA) they went on to make about every possible flavour of FM synth from the portable DX100 through to the massive (professionals only) DX1. The range consisted of:-

  • DX1 – Voice structure of two DX7’s but with larger LCD and better user interface, seperate controls for envelopes, weighted 73 note keyboard with poly-aftertouch, high quality wooden case and a list price of 9500. A true professional’s instrument.
  • DX5 – similar in function to a DX1 but in a more conventional case (like a larger version of the DX7). With a 76 keys, this time without the poly-aftertouch, this instrument is still a large keyboard but in my opinion if you had the space for it this is an ideal studio master keyboard and it is easier to understand than the DX7 because of the improved control layout. A bargain especially at the sort of silly prices you sometimes see them go for second-hand.
  • DX7 – The ideal all rounder of the range for both studio and live.
  • DX7-IID – Not a simple upgrade but a complete range of redesigns, only loosely based on the success of the original, that was released in 1987. One version, the DX7-IIFD, included a floppy disc drive for voice parameter storage. The DX7S was also released at the same time for the semi-pro market which was nearer to a straight re-hash of the original DX7 (complete with small LCD, although it was back-lit this time). A module (19″ rack mount this time) called a TX802 was also made available.
  • DX9 – same size and case as a DX7, this original partner to the DX7 was an odd part of the range as it was a four operator synth without velocity. This makes it much easier to understand but also eventually quite limited. Expect to pick one up for next to nothing, although I personally would go for a DX21 or DX11 for a cheap 4 operator FM synth.
  • DX11 – part of the third wave of FM synths, a much more compact keyboard and now multi-timbral. Effectively a keyboard version of the TX81Z module, which strangely came out long before the DX11. Four operator but with additional waveforms other than sine waves, this is the best bet of the cheaper FM synths.
  • DX21 – Part of the second wave of FM synths. At this point Yamaha had seemed to have decided that no-one was going to get the hang of programming these synths so they included 128 sounds in ROM that could be retrieved into the normal program locations. Only four operator the DX21 could, for the first time on an FM synth, produce splits and layers as well as having a chorus. Sadly velocity could only be sent via MIDI, as the keyboard fitted was not capable of sensing velocity itself.
  • DX27 – similar to the DX21 but without the split / layer facility. 192 presets in ROM that could be accessed directly and only needed to be put into user RAM if edited.
  • DX100 – mini-key version of the DX27 and could be used as a strap on MIDI remote keyboard, complete with conveniently placed real time controllers that fell to hand when being played standing up. Great fun – used to have one and regret selling it now.
  • TX816 – Has to be mentioned for the total overkill factor as this was a 19″ rack mount setup with eight TF1 modules in it, each module was equivalent to a DX7. The only time I ever had a chance to use one of these it was being driven by a DX7 so that was equivalent to NINE seperate DX7’s! As each TF1 can remember a tuning offset then calling up a patch on the DX7 controlling the rack would, through sysex, put the same patch in each TF1 but with the tuning offset intact. This results in truly monstrous sounds. Was also available as the TX216 with just two TF1 modules.
  • V50 – odd one out as although not a synth with ‘DX’ in it’s model number this was the last of the pure FM synths and the only one that was a workstation. In effect this was two DX11’s plus a drum machine, sequencer, disc recorder and effects.

Although Yamaha no longer produce a pure FM synth elements of FM turn up in some of their newer products. The range is diverse with some lower end products such as the SY35, TG33 as well as some of the high end products such as the SY77, SY99 and TG77.

It should be noted that the SY77 and TG77 (the one I still use) was one of the few FM synths that also had a filter, allowing you to filter the results of the FM synthesis section (these two synths also have sample based AWM sources as well).

The principle of operation of all DX keyboards, including the DX7, is called FM (which stand for Frequency Modulation) and the principles on which is based are remarkably simple. A practical example will help. Take ANY analogue synthesiser and patch a single VCO to the VCF, select a waveform that is low in harmonic content (on most synths this will be a triangle) and set the VCF so that it has no effect (ie Frequency = max, Resonance = min, all modulation = zero). Set the VCA / Envelope controls to give an organ style envelope. This is probably the most ‘bland’ sound you have ever programmed but this is equivalent to a DX7 carrier (the carrier is the sound that you can hear). If you now patch the LFO into the VCO at a speed of about 7Hz a pleasant vibrato should result (the LFO is equivalent to a DX7 modulator). This is FM at sub audio and is perceived by the ear / brain system as vibrato (no surprises yet). As the rate of the LFO is increased then the the change in the sound becomes perceived as a change of timbre instead of a change of pitch (this will depend on the frequecy range of your LFO). If you can patch another VCO (also sine / triangle) into the modulation input of the first VCO (often labelled ‘Cross-Mod’, ‘Poly-Mod’ or ‘X-Mod’) instead of the LFO then you will find this is a source of some fairly alarming bell like noises whose timbre depends on the relative volumes and frequencies of the two VCO’s. A similar effect can be extracted from a self-oscillating VCF (a sine wave) being modulated by a VCO (sine or triangle). If you actually get round to trying this you will find that the resulting two oscillator system is fairly unstable and unpredictable (but good fun).

DX7 Operators - Modulator / Carrier pair

Diagram showing a pair of DX7 operators in a Modulator / Carrier configuration

But what has this to do with the DX7? Well as mentioned earlier the basic building block of any FM synth is the ‘operator’ which is a sine oscillator / envelope combination whose frequency can be controlled by the keyboard or by other operators. An important thing to note is that the operator is generated digitally so it’s behaviour is very predictable. This is important when these operators are made to interact with each other (remember the instability of the VCO’s in the above experiment). The way these operators (there are six on a DX7) are connected to each other are known as ‘algorithms’ and Yamaha saw fit to provide thirty two (although there are many more possible combinations thirty two seem to be enough to be getting on with).

Algorithm Example

Algorithm Example – see text for explanation

So how do you put all this together? Well lets take an example, something like an electric piano (which the DX7 is quite good at!). First you select your algorithm. This is decided by the type of sound you wish to produce, in our example we wish to produce the ‘thud’ of the hammer followed by a fairly pure, but warm, tone that reacts to keyboard velocity. To do this you choose an algorithm that has the constituent parts you need. I would suggest number 5 (see diagram above) as it has three pairs of operators all in a simple carrier / modulator set up. This allows us to have a sound with three constituent parts, the ‘thud’ is produced by operator pair 5 plus 6 with operator pairs 1 plus 2 and 3 plus 4 producing the warm chorused fundamental. Operator 5 and 6 are used for the thud as operator 6 has the feedback loop around it that allows unstable waveforms such as noise to be produced. As the thud is unpitched then the operators are set with a fixed frequency relationship and are not controlled by the keyboard. the envelope of operator 5 (the carrier) is adjusted to give a small click for the attack of each note. The envelope, level and feedback of operator 6 (the modulator) are adjusted to give the correct tonal quality to the thud. Once happy with the ‘thud’ the two operators responsible can be muted temporarily and the body of the sound can then be worked on. This is created by having a carrier envelope that is longer in duration than the modulator envelope which results in a sound that emulates the harmonic content of a struck tine. Using the copy function it is very simple to create two pairs of operators with the same parameters and then use the fine tune parameter to get the two ‘virtual tines’ to beat and sound less clinical. By using velocity sensitivity on the modulator levels then the timbre of the instrument can be made velocity dependent (just like a real electric piano). This is the secret of the success of the DX7 that also makes it a very difficult keyboard to sample correctly (it is also the reason why I still have an FM synth) as you can create sounds that vary in character in a most unpredictable way dependent on keyboard velocity.

This cannot be a complete description of how to program FM (that would take a complete book) but if you have a DX here are a few different things to try:-

1. For fatter “analogue” pads use a fixed frequency sub-audio carrier.

2. For “vocal” formants use a fixed (audio) frequency modulator, somewhere in the middle of a stack of operators.

3. Subtle use of the pitch envelope can be used to enhance the attack phase of a note (good for wind instrument emulations).

4. White noise and decent analogue sawtooth sound can be obtained from use of operator feedback.

5. Envelope bias can give the effect of an opening filter if applied to modulator sustain levels.