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Practically FM (Part 4)

Part 4 of our series for FM synth owners, in which Martin Russ gives away even more secrets of FM programming. Operators at the ready!

The FM brass sound has become almost as much a cliche as the analogue VCF-based brass sound. This month Martin Russ looks at both techniques.

After three months of reading this series you should be used to the style by now, so this month I am going to spend less time on the practicalities but will compensate by reviewing what has happened so far in a more analytical way. This time I am continuing the theme of programming 'classic' voice types with a Brass sound.

An unkind person once referred to the sounds made by analogue synthesizers as 'variations on brassy timbres', and to some extent, the characteristic sound made by using an Envelope to open and close the VCF (filter) is one of the major elements of the distinctive fingerprint of a particular synthesizer. When I was demoing synthesizers in the past, it used to be a point of pride to be able to identify a model by its VCF sound alone - Moogs had a distinctive distorted, fat sound, whilst ARPs had a thinner, cleaner sound, and the Yamahas were typified by a strongly resonant bandpass sound (yep, the big Y used to make analogue synths!), while Korgs sounded nasal and metallic.

Unfortunately, the first thing anyone did on an analogue synth was to turn the VCF resonance up to full, turn the VCF frequency down to minimum, and apply the maximum amount of envelope modulation. This is the recipe for the brassy timbres mentioned above, and until the DX7 appeared in 1983, it formed the mainstay of many a keyboard player's synth sounds. FM brought a different set of sounds - suddenly you didn't need to lug a heavy Fender Rhodes piano around with you, because of the DX7's 'E.Piano 1' preset, which spelled doom for tine bars and instant success for Yamaha. FM was capable of stunning imitations of real instruments but was rather weak in the 'any variation of synth brass you want' area. Personally, I was glad that we had a new set of sounds!

The FM brass sound depended not on the 'sound' of the filter, but on how the programmer arranged the Operators. It is a basic feature of FM that the sounds are derived from the arrangement of building blocks rather than the intrinsic 'sounds' of the blocks, meaning any manufacturer's version of FM will sound very similar. So the basic restriction of an analogue VCF - the characteristic sound - does not apply, and a more analytical approach is needed to construct sounds. The advantage of FM is that this flexibility enables the creation of a much wider range of sounds.

Does knowing anything about analogue synths help us programme an FM brass sound? Surprisingly, the answer is yes. (In the programming business, just about anything you know about sound can be exploited to your advantage.) So let's look at what makes a VCF so useful for creating brass sounds.

As you open a filter by increasing the cut-off frequency, you progressively let more and more harmonics through. When this happens at a rate slow enough for you to hear the evolving harmonics, it sounds very much like the way that a brass sound changes when you start to play it. The physics of open tubes tells us that you will get all the harmonics of the fundamental gradually decreasing in level with rising frequency, which gives rise to a sawtooth type of waveform, and this is indeed the usual source waveshape for synthesizing brass sounds.

In FM terms, we need a source with all the harmonics present and some means of altering the number of these harmonics dynamically. At the root of FM theory is the idea that as you modulate a sine wave with another sine wave you produce additional sine waves, and the bandwidth of the resulting sound is proportional to the amount of modulation. In other words, with a small amount of modulation you obtain only a few harmonics, but as you increase the modulation the number of harmonics present also increases. This is why the sound of an Operator becomes brighter as you increase the Output Level of the Modulator above it, and is why it is often stated that the Modulator Envelope acts somewhat like the Filter Envelope in an analogue synthesizer.

The example String and Piano sounds from previous months used only the Carrier Envelope to set their sounds - the Modulators were used at a fixed level, producing a more or less unchanging timbre. To create a Brass sound, all we need do is put an envelope onto the Modulator, and the envelope shape is exactly the same as you would use on the analogue synth, although the relative timings need some care. The only trick we need to know is that in order to get the harmonics to rise in a brassy way, we need to make sure that the Carrier Envelopes rise faster than the Modulator; that way we will obtain a dull sound at first, which will progressively brighten as the Modulator grows higher in level.

Patch dump from Lawrence Wilkes' DXpert program showing the 'Vanilla' DX7 voice.


As usual, we will use our 'Vanilla' voice as the starting point (see accompanying patch sheet). The only parameters we will be changing are the Envelopes, the Output Levels and the Detunes - you don't need to use all the features of FM every time!

The first item to consider is the Algorithm. In previous months I have scorned the choosing of algorithms and deliberately gone for an unsuitable one - this time I will be slightly more sensible.

The basic unit of an FM brass sound seems to be a Carrier and Modulator pair with the appropriate envelopes. Based upon this, Algorithm 6 would be a good choice, because it provides three such pairs. But we can improve on this - for example, Algorithm 22 is used by about 70% of the factory preset brass sounds and it provides the equivalent of four pairs, of which three share a common Modulator in Operator 6.

I will not use Algorithm 22 because it produces four parallel outputs, and so any detune will produce tremolo or beating effects in the output, which may or may not be desirable.

The current trend amongst FM programmers seems to be to go for exactly the opposite arrangement - Algorithm 13 for example. This provides a simple pair, and a set of three pairs sharing a common Carrier. There are thus only two Carrier outputs to deal with, making it much easier to control the final envelope and potential beating problems.

Coincidentally, Algorithm 13 also uses the same Operators for Carriers as in Algorithm 2, so we are on familiar territory in some respects!

And so to the envelopes. It takes a finite time to start air moving inside a piece of brass tubing, and so the envelopes supplied by 'Vanilla' are probably quite unsuitable for our purpose. The 'magic' critical region for envelope time occurs at around 50-60, where the envelopes stop opening immediately and you notice the time they are taking. Let's investigate just Operators 1 and 2 initially. Try setting these envelopes:

Op R1 R2 R3 R4 L1 L2 L3 L4
01 55 40 25 60 99 80 85 00
02 50 35 30 50 99 65 65 00

Both of these are typical brass-type envelopes - a relatively slow start, followed by a decay to a fixed or slightly rising level, followed by a rapid decay.

Figure 1. Graphic display of a suitable Brass envelope shape.

Also, the envelope for Operator 2 has slower Rates than Operator 1 in general - this produces the rising series of harmonics we want. Figure 1 shows the sort of shape you see on a graphic envelope editor. If you play the keyboard at this point you will find that this produces a very muted brass sound, and increasing the level of Operator 2 to about 85 should be about right for a brass pad sound. I usually attempt to make things nice and even across a voice, so set all the Modulator Output Levels to 85 to match. Whenever I add something, I also take something else away, and this time the Velocity Sensitivity is the victim. Setting this to 2 for all the Operators gives a good feel to my hands.

This is another basic theme to remember when programming FM - as you increase the Velocity Sensitivity and thereby reduce the volume, increase the Output Level to compensate for normal playing. This ensures that you have the volume you started with but with the Velocity Sensitivity centred upon your normal playing style. As a rough rule of thumb, each Velocity Sensitivity increment should be countered by an Output Level increase of between 5 and 10 - but this can vary with circumstance. Feel free at this point to try altering the Output Level of the Modulator, and altering the envelope Rates or Levels - learn by doing!

This is the basic Brass pair - a fundamental FM building block. You can change to Algorithm 12 if you want to investigate the effects of feedback on the sound. When you are ready to proceed, copy the envelope of Operator 1 to Operator 3, and the envelope of Operator 2 to all the other Modulators (Ops 4, 5 and 6). In order to add some movement and interest to the final sound, I would now add or subtract a little from the values of the Rates and Levels to 'naturalise' the sound. I increased Rate 1 of Operator 3 to 60 and decreased Rate 3 to 20, and slowed the Modulators of Operator 3 down a little: Rate 1 from 50 to 45, and Rate 3 from 30 to 25.

I made Operator 3 a little louder to suit its slower decay time by increasing Level 2 to 90. Op 4's Level 2 was increased to 85 to give some body to the sustain sound. Level 3 of Operator 5 was only adjusted slightly to 70 to give a rising effect which provides movement in the sustain sound, and this was taken further in Operator 6, where Level 2 was set at 75, and Level 3 at 90. Experiment for yourself with the Feedback value in Operator 6 - too much and the sound is too noisy, too little and the sound is not rough enough. I finally settled on a Feedback value of 3.

Since Operator 6 uses both feedback and the rising sustain envelope, this can be employed to provide a distinctive repeat start to the sound when you play harder, and so the Velocity Sensitivity was set to 4 using the 'add to one, take from another' idea.

When I finally ran through the combinations of Operators, listening to the separate parts in isolation, I found that one part of the sound was perhaps too bright, and so I reduced the Output Level of Operator 5 to 75. I prefer my brassy sounds to be bassy, so I cheated and transposed the keyboard to C2. The final tweaks were really just to round out the sound with some Detune: -1 to Operator 1, -3 to Op 2, +4 to Op 3, +7 to Op 5 and +5 to Op 6. Operator 3 is the reference here, since I made it the loudest of the above components, remember?

You should now have created SOS voice number 4 - 'BraSOSpad1' - a smooth, brassy fill sound with a myriad of uses in the busy studio (see patch dump).

Patch dump from DXpert showing the 'BraSOSpad1' voice for 6-Operator FM synths.

For the 4-Operator FM users our task is more interesting, since there really isn't a simple equivalent of Algorithm 13. We could use Algorithm 3, but this has a stack of three and is therefore going to be inclined towards harsh brass sounds. The next best alternative is probably Algorithm 5 - and the process is exactly the same for 4 Operators as for 6 Operators, except that we have not got Operators 4 and 5. The pair formed by Ops 1 and 2 will be the basis of the brass sound, with the other pair (Operator 4 has the Feedback) forming the rough raspy sound. The TX81Z screen dump shows very little else different from the 6-Operator version, except that all the values are scaled accordingly to cope with the different parameter ranges.

Screen dump from Soundbits' 4X4 program showing the 4-Operator 'BraSOSpad1' voice for the TX81Z.


We have already discussed the theory behind the Brass sound. So in this section I am going to attempt to tie together all the ideas so far in this series - a sort of progress report. As I have stated right from the beginning, the essence of any synthesis usually lies in the analysis. Without a clear idea of what you are aiming for, you are just groping in the dark. Surprisingly, so far, the main attention has been on the envelopes - they have been the major influence on the shape of the sound. Any knowledge you have of analogue synthesis is very useful here, because the basic ideas apply to FM and to samplers as well.

The String voice used a slow attack, long release envelope which set the feel of the whole sound, whereas our Piano voice used a percussive envelope to completely change the timbre. In this month's Brass sound, the ADSR shape of the envelope is an essential part of the sound. Remember that the Carrier envelope affects the volume of the final sound, while the Modulator envelope affects the timbre or tone. Armed with this information, we are able to be very specific in what we change for a particular effect. Tremolo implies changing the volume, so it involves a Carrier - specifically the 'beating' effect due to Detune; whereas vibrato is a cyclic frequency change, so it suggests altering the way a Modulator affects a Carrier.

The other major influence on the sound has played a much smaller part thus far and is the Frequency Ratio. This is the traditional bit of FM that people expect you to talk about. I prefer to wait until we have a firm foundation to build upon. I have deliberately restricted our use of Ratios to set the basic timbre, in order to keep things understandable. Even so, no single element is the key to effective FM synthesis, instead it is the combination of the many parts which makes up the whole. The right Ratio is only correct when teamed with the appropriate Envelope for the desired sound.

In the String voice I used a Fixed Frequency with an Operator pair above it. The Ratio of the pair was 1:1; in other words, the same basic sound that we have used in our Brass patch. The difference is in the Envelopes! One of the major differences between the Piano and Electric Piano sounds was the Frequency Ratio - the Piano used ratios of 5:1 and 9:1, whereas the Electric Piano used a much higher ratio. In general, the closer the ratio is to 1:1, the more harmonics you will produce and the sound will be thicker in character. In contrast, for higher ratios, the resulting sound will be thinner and more hollow or metallic.

If you experiment with the Ratio in a simple FM pair, you will be able to verify for yourself the range of timbres possible. FM's power lies in being able to vary the harmonic content of each 'pair' of a Carrier and a Modulator individually - you are not limited to a single VCF or waveshape from your oscillators. Algorithms with more than two stacked Operators can be thought of as being able to fill in the gaps left by the pairs - you can emphasise and add harmonics by choosing your ratios with care, by taking into account the ratios between all three Operators. You should spend some time accustomising your ears to the sounds of Ratios, particularly the way they change with variations in Modulator Output Level. This study will repay itself many times over when you want to create a particular sound - this is how I knew where to find a Piano sound - long hours of learning! Next month I will start to look at Frequency Ratios, concentrating first on simple values.

The 6-Operator voice dump is from Lawrence Wilkes' DXpert program. A shareware version of this featuring just the Librarian functions is available for £7. Contact SOS Shareware, (Contact Details).

The 4-Operator dump is from a Beta test version of a new product covering all the Yamaha 4-Operator FM synths except the FB01 (including the DX11) - the Soundbits' 4X4. Contact Soundbits Software UK, (Contact Details).

Series - "Practically FM"

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Part 1 | Part 2 | Part 3 | Part 4 (Viewing) | Part 5 | Part 6

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Sound On Sound - Copyright: SOS Publications Ltd.
The contents of this magazine are re-published here with the kind permission of SOS Publications Ltd.


Sound On Sound - Aug 1988


Synthesis & Sound Design


Practically FM

Part 1 | Part 2 | Part 3 | Part 4 (Viewing) | Part 5 | Part 6

Feature by Martin Russ

Previous article in this issue:

> Casio PG380

Next article in this issue:

> Win a SECK 12-8-2 mixer!

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