If you've been paying attention to the trends in synthesizer design for the past few years, you've probably noticed some curious twists and turns. Analog synths, which were declared dead in the mid-'80s, are making a decisive comeback. And yet, strict analog isn't enough to satisfy many of the musicians who are gravitating to analog-style instruments. Many of the new analog-flavored synths — the digital ones, at least — are tricked out with a knob or two for adding more types of tone color with frequency modulation (FM).
That's ironic, because it was FM that killed analog synths the first time around. When Yamaha's DX7 burst onto the scene in 1983, its lively, detailed sound rang the death knell for a whole generation of analog keyboards.
After a few years, though, listeners wearied of the FM sound, which can be a bit squeaky-clean. The fashion wheel turned again and sample playback synths became king. But FM never entirely slid from view. Yamaha continues to build FM synths (its current model is the DX200 groove box), and numerous other manufacturers, from Access to Propellerhead, have added FM to their hardware and software synths' timbral resources.
FM keeps bouncing back because it's such a useful synthesis technique. It's a fast, efficient way to generate an enormous variety of expressive tones. And with a little roughing up from a modern distortion effect, it doesn't have to sound squeaky-clean at all.
Native Instruments' FM7 is the ultimate FM synthesizer. On one hand, it's closely based on the design of the DX7 and can load and play preset data from the DX and other vintage Yamaha FM synths. (Dozens of banks of DX7 presets are available for free online. A good place to start your search is at www.synthzone.com/yamaha.htm.) Yet FM7 goes much further than the DX7 thanks to its dual filters, saturation stage, and flexible signal routing. Also, the DX7 was not the easiest synth to program, with its single data-entry slider and skimpy two-line LCD. Programming the FM7 is a breeze by comparison.
Even so, FM programming isn't entirely intuitive. Finding the right waveform for a particular sound is not as easy as picking it out of a menu. In this article, I will start by describing the basics of FM synthesis, using FM7 for our experiments. The concepts in the first part of the article apply, with only minor tweaking, to any synth that features FM synthesis. The latter part of the article will cover advanced concepts that are specific to FM7, such as looping envelopes and modulation routings.
THE BIG IDEA
The musical applications of digital FM synthesis were first developed in the early '70s by Dr. John Chowning at Stanford University. At that time, digital synthesis was performed on large, slow mainframe computers. One second of audio could take many minutes to compute. Chowning explored the fact that frequency modulation not only gave him a wide variety of tone colors but allowed him to compute the desired waveforms much more quickly than was possible with other types of synthesis, such as additive synthesis.
Even the most hidebound classical musicians are familiar with frequency modulation: it's nothing but our old friend vibrato. In vibrato, the frequency of a tone increases and decreases — the pitch goes up and down — in a repeating, periodic way. You can hear this effect on a synthesizer simply by modulating the frequency of an oscillator using a repeating LFO waveform.
Chowning discovered that when the modulating wave is fast enough, our ears can no longer hear the discrete rising and falling cycles of the vibrato. Instead, we perceive the changes in the pitch of the main oscillator (called a carrier) as changes in tone color. When the modulating wave (called a modulator) is faster than 20 Hz, new overtones are added to the sound of the carrier. The strength of the overtones will depend on the amplitude of the modulator: stronger modulation means more overtones. And the frequencies of the newly generated overtones will depend on how the carrier and modulator are tuned with respect to one another.
Confused yet? Don't be. Launch FM7 and follow the exercises below. Before you know it, you'll be an FM whiz.
Begin by clicking on the library (Lib) button. Before going any further, click on the Save All button in the upper-right corner of the Library display and save your bank of presets under a new name.
Now, choose a preset and click on the Init Edit Buffer button. When you play the keyboard, you'll hear a simple sine wave tone — the raw ingredient of FM synthesis. Although pure sine waves have no overtones, they are good for a few things, such as adding suboctaves and high, ringing overtones. For most purposes, however, a sine wave will sound more interesting when we mess with the tone a little.
Now click on the green F button in the top row. If the right half of the window (as shown on p. 75) doesn't look like Fig. 1, click on the Matrix button, located near the upper-right corner. The Matrix display is your window into a vast world of FM programming.
Right-click (Windows) or control-click (Mac) on the letter E near the middle of the matrix. It will turn bright yellow.
Left-click (Windows) or click (Mac) in the black field just below E and directly to the left of the F. While holding a key on your MIDI keyboard, and without releasing the mouse button, drag the mouse upward. Your screen should look like Fig. 2. As the numerical value in this field (which is called the FM index) increases, the tone will get progressively brighter and more piercing. As you drag the mouse up and down, you will get a wah-wah kind of sound. Just about everything you do in programming FM7 will be a variation on this simple mouse move.
What you are doing in the above example is listening to the oscillator in F as the waveform of E's oscillator is modulating F's frequency. But because the frequency of E's oscillator is greater than 20 Hz, the frequency modulation causes changes in the tone color of F. (In the Init patch, both oscillators are tuned to the same frequency.) As the output of E increases in amplitude, the waveform of oscillator F acquires more and more overtones. The Waveform display at the upper-right corner of the FM7 panel shows a rough picture of what's happening to the sound.
OPERATORS ARE STANDING BY
If FM synthesis were limited to simple wah-wah sounds, it wouldn't be used very often. The power of FM synthesis lies in combining signals in various ways to create complex musical tones.
The signals come from operators. In Fig. 1, the letters A through F represent six individual operators. Each operator has two basic parts — an oscillator and an envelope generator. The oscillator creates a raw waveform, and the envelope generator shapes the loudness of the waveform over time. The following exercise will demonstrate how this works.
Start with the Init program and right-click (Windows) or control-click (Mac) on E, which switches operator E on. Raise the FM index in the box directly below E and to the left of F (see Fig. 2) to 40. When you play the keyboard, you'll hear a somewhat nasal tone.
Next, left-click (Windows) or click (Mac) on the E in the matrix, or click on the green E button in the top row (It will turn red). That will bring the controls for operator E into the main part of the window.
Left-click (Windows) or click (Mac) on Envelope in the upper-right corner. (From now on, I will use the word click on its own to mean left-click in Windows and a simple mouse-click on the Mac.) That will switch the display from Matrix to Envelope and Keyscaling screen for operator E (see Fig. 3). Now, click on the square handle in the upper center of the Envelope display and drag it straight down. That will reduce the envelope's sustain level to zero. When you play the keyboard, you should hear a tone with a pleasant knocking sound as its attack, followed by a sustain made up of the original sine wave. The shape of the attack will be visible in the Envelope display. If the entire tone fades out, or if the nasal tone sustains without changing, it's because you skipped a step above and you are editing the envelope of the wrong operator.
In this example, the signal from operator E starts at a high level, but quickly fades out because its amplitude is being shaped by the envelope generator. As E fades out, the waveform of F (which is what you're hearing) changes. Overtones are being stripped out of the tone, as if the sound of operator F were passing through a lowpass filter. Although FM7 has filters, we're not using them yet. This filterlike effect is accomplished by simply controlling the amplitude of operator E, which is the modulator.
Switch back to the Matrix display and take a look at all of those little black fields in the matrix. Each of them controls a signal routed between two operators. So far, I've been using operator E to modulate operator F. But by switching any operator on and then dragging in the field that connects it to another operator, you can easily create tonal changes.
There are two rules to remember when editing in FM7. First, an operator has to be switched on — illuminated bright yellow — for it to have any effect. Second, the row of fields along the bottom of the matrix connects the operators to the output. If an operator isn't connected to the output — either directly or because it's modulating another operator that's connected to the output — you won't hear it.
In the original DX7, you could choose from a set of 32 predetermined methods of connecting operators to one another and to the output. These were called algorithms. In FM7, the algorithms are entirely user-configurable using the Matrix display.
As mentioned earlier, the nature of the harmonic spectrum coming from the carrier operator in FM depends on the relationship between the frequencies of the carrier and the modulator. The following exercise demonstrates how that works.
Grab the envelope sustain handle for operator E, which you lowered in the previous exercise, and pull it back up to the top. This time, we want the modulator to sustain at its full level.
Switch to the Matrix display and make sure the FM index below E is set to at least 40. A setting of 50 might be even better.
Locate the frequency controls on the left side of the panel (see Fig. 4), and make sure the E button in the top row is still red. You're going to be changing the frequency of operator E.
Click once on the tiny up-arrow button directly below the word “Ratio.” You can do that while holding down a key on your keyboard if you like. The numeric display below the arrow will be 2, and the tone will change suddenly. If you're familiar with analog waveforms, you'll probably be able to identify the new tone as being similar to a square wave.
Switch back and forth between 1 and 2 a few times, using the up and down arrows at the left side of the Ratio display. Then try increasing the ratio still further, to 3, 4, 5, and so on. You'll hear progressively thinner but brighter tone colors.
For practical purposes, it's best not to go higher than 10 or 11 with the Ratio control. When you play in the upper range of the keyboard, higher ratios will produce aliasing, a clangorous effect that will interfere with your ability to play chords and melodies.
Aliasing has its uses, but FM7 also has tools for taming it. If you want to use a high ratio for a modulator and you need to play upper notes on the keyboard, use the Keyscaling display (below the envelope) to scale down the amount of the high-pitched modulator at the upper end of the keyboard. You can edit Keyscaling the same way you edit Envelope: click on the square handle at the right side of the display and drag it downward.
Now, set the Ratio of operator E back to 1 or 2 and click on the up or down arrow in the middle of the Ratio display. The tone will start to beat. One of the operators is now being detuned from the other. The beating effect is similar to what happens in any other synth when you detune one of the oscillators — the tone gets richer.
As you play up the keyboard, you'll hear the detuning get progressively faster and the sound becoming twittery. To avoid that, you can use the Offset parameter for detuning instead of the ratio. The Offset parameter detunes an operator by a constant frequency. Offset values between 1 and 1.5 are good for a rich chorusing effect.
Try turning down the ratio value for operator E to 0.0000. At this point, the modulator will have a fixed frequency of 0 Hz, so it won't affect the tone of the carrier at all. As you turn up the offset to 3.00 or 4.00, however, you'll start to hear vibrato. Increase the offset value gradually while holding down a key, and you'll hear the phenomenon described at the beginning of the article: when the frequency of the modulator reaches 20 Hz, the vibrato will meld into a tone color.
Reset the frequency parameters of operator E to a ratio of 1.00 with no offset, and use the up and down arrows beside the Ratio display to change the frequency of operator F (the carrier). Listen carefully to the variety of tone colors that are available.
Try setting the Ratio parameter of operator F (the carrier) to 0.00 and its offset to 1.00 or thereabouts. When the modulator is set to a low value you will get vibrato, but when the carrier is set to a low value the result sounds like chorusing. This technique is useful for creating rich FM sounds.
THAT DARN DX EP
In this exercise, we'll take some of the techniques we've learned so far, add a few new ones, and create a fair approximation of a classic FM sound — the DX7 version of the Rhodes electric piano. Start with the Init patch, as before. Edit the envelope of operator F so that it looks about like Fig. 5. That operator will make the main body of the piano tone.
Switch on operator E, then route it to operator F using the Matrix display and give it an FM index of 33. Tune operator E's frequency ratio to 10.00. This will create the bell-like tone.
Give operator E an envelope similar to that of operator F, but somewhat shorter. The bell-like overtone should die away while the main body of the tone is still audible.
Set operator F's Velocity Sensitivity slider to 50, and the same slider for operator E to 75. That will cause low-velocity notes to be softer and somewhat less bright.
Set operator F's Envelope Rate Velocity Scaling to 30, and the same slider for operator E to 50. At this point, you may want to go back and fiddle with the envelopes for these two operators to get a better approximation of the shape of an electric-piano tone. If your only experience with FM electric pianos has been with sampled ones, you'll hear something new and gratifying: an FM electric piano responds smoothly and evenly to MIDI Velocity data, in a way that not even the most expensive sampled electric piano on the market can duplicate.
Our piano still sounds a little wimpy, so let's add another color to the mix. Switch on operator D. In the matrix, route it to operator E, with a level of 35. Give operator D an extremely short envelope. The envelope should have an instant attack and then fall to zero in 0.02 seconds or less. In order to do this, you'll need to right-click (Windows) or control-click (Mac) on the Time ruler below the envelope and drag to the left in order to zoom in.
Next, tune operator D to some unusual ratio, such as 3.3980. This is the point at which FM programming becomes an art. The idea is to use operator D to imitate the sound of an electric piano's hammers striking the tines. It should make a brief percussive thwock. If it makes a tone with a perceptible pitch, the envelope is too long. Now, set operator D's Velocity Sensitivity slider to about 75.
To test whether operator D is doing its job, listen to a few notes with it switched on and then with it switched off. You can switch it on and off in the Matrix display or with the Operator On/Off button. You shouldn't be able to hear operator D as a separate element in the sound, but you should notice when it is missing, because without it the tone should sound a little too clean. (For more on this technique, see the sidebar, “Dissecting FM.”)
There are many ways to refine this program. A master FM programmer might even set up a real Rhodes and compare its tone with the FM sound one note at a time to get the envelopes and operator tunings just right.
You can use the general principles in this exercise for creating many types of FM sounds, not just that of electric pianos. The idea is to use different operators to craft different parts of a complex sound. In some FM patches, there may be only one carrier, and the primary modulator might be modulated by a second modulator. In other patches, the six operators might be configured as three carrier/modulator pairs. In still others, three or four carriers tuned to different frequencies might all be modulated by a single modulator. The possibilities are endless.
PUSHING THE ENVELOPE
FM7 provides an Easy page, which offers traditional synthesis parameters, such as ADSR envelopes for amplitude and timbre. However, if you confine your editing to those parameters, you'll miss out on much of the power FM7 has to offer. Here's a quick tour of the envelope section that highlights a few possibilities that you may not be aware of. For full details on FM7's envelopes, consult the owner's manual.
The DX7's envelopes had four level settings and four rate controls. But unlike a traditional ADSR, these envelopes didn't have to start and end with a level of zero, and the attack peak could be higher or lower than the sustain level. FM7's envelopes preserve that design, with one small exception: carrier envelopes always shut off, so you won't create stuck notes. FM7 envelopes also have more rate/level pairs (up to 31 per envelope), the ability to loop, and the ability to sync to a specific tempo. Let's begin by exploring the animated rhythms that you can create with looping envelopes.
Initialize the edit buffer, as before. Turn on operator E and set it to modulate operator F in the matrix. This time, set the modulation level at 60.
Select operator E for editing. If its Envelope display isn't visible, click on the Envelope button, which is in the upper-right corner.
Click on the Tempo Sync button. That will cause a grid of vertical lines to appear in the Envelope display, and the Time ruler below the display will switch from showing seconds to showing beat values.
Try dragging the square handle in the upper-left corner of the envelope to the right. That will increase the attack time of operator E, giving you a wah sound. Notice that the handle snaps to the grid as you move it. Park this handle on the line above the 1/8 marker.
Next, right-click (Windows) or control-click (Mac) on the red line along the top of the envelope. That will create a new handle. Drag this handle down to the bottom of the display and position it above the 2/8 marker. If the Mode parameter is set to Fix, you may need to click on the setting to switch it to SLD (slide), to create enough room.
Drag the handle at the upper-right corner of the envelope left or right as needed, so that it's positioned above the 3/8 marker. Click on the round handle in the middle of the right-hand envelope segment, and drag it downward so that the segment is linear rather than curved. At this point, your envelope should look like Fig. 6.
When you play the keyboard, you'll hear a repeating wah-wah sound. That is because the envelope for operator E is looping. The red lines indicate the start and end of the loop. So far, it's not a very interesting sound, but we're not finished yet.
Edit operator E's envelope so that it looks like Fig. 7. If you set it up correctly, you'll hear a catchy rhythm that loops every two beats.
Now activate operator D. Use it as a second modulator for operator F, as in the electric piano voice you created earlier. Give it a different rhythmic envelope, perhaps one that loops every five 16th-notes rather than every four eighth-notes, so that the two envelopes combine to make a longer rhythm. (If they also drift out of sync with one another, you need to download the version 1.1 upgrade of FM7 from the Native Instruments Web site.) Finally, tune operator E's ratio to 1.5 and operator D's ratio to 3.5. That will give the tone a fat suboctave growl.
Again, there are many other tricks that you can try with this patch. For instance, try running operator F through the filter, adding a rhythmic filter envelope, and panning the outputs of F and the filter slightly apart. You may have to experiment for a while to find combinations of envelopes that give you rhythms you like, but there's no shortage of possibilities to explore.
Most synthesizers let you control the filter cutoff frequency from the mod wheel or joystick. FM7 takes the concept much further. The output level of any operator can be controlled by the mod wheel, Pitch Bend, Aftertouch, Breath Control (Control Change 2), or either of FM7's two assigned MIDI Control Change types.
If an operator that's acting as a modulator is tuned below the carrier, you can use the mod wheel to bring in a suboctave. Because the modulator has its own envelope, the mod wheel can be assigned to add an attack transient to certain notes in a phrase. And because the carrier's level can also be controlled, you can easily set up a patch in which the mod wheel or another controller crossfades between two completely different tones.
To try out this concept, start with the rhythmic patch you created in the previous exercise. Select operator E for editing. In the Amplitude Modulation strip along the lower left (see Fig. 8), click in the data field below Mod and drag the mouse up. A setting of 80 or 85 will work well.
The mod wheel is already set up to create vibrato in the Init patch. For this example, we don't want that, so click on the green Mod button in the upper row. In the lower center of the large signal-routing matrix, you'll see a setting of 20 that routes the mod wheel (in the top row) to pitch (in the right-hand column). Turn this setting down to zero.
Now play the keyboard. Your patch should sound much more subdued than before, because FM7 has automatically lowered the level of operator E to give the mod wheel some room to maneuver. As you're holding a note, push the mod wheel up. The sound will become more aggressive as more of operator E's output is sent to the carrier.
In this article I've only scratched the surface of FM7 programming. Other areas you can explore include the choice of waveforms for each operator (using the Waveform selector shown in Fig. 8), the filter and saturator, the built-in delay/reverb effect, the audio input, and operator feedback, not to mention the many ways the six operators can be configured in different algorithms. If you're willing to take the time to learn FM7's tricks, you'll find yourself the master of a rich and endlessly creative sound palette.
Jim Aikinwrites about music technology for a variety of publications. His book Software Synthesizers is scheduled for publication in mid-2003.
The key to understanding FM patches created by other people is muting and unmuting the operators one at a time to hear how each contributes to the sound. By studying the Matrix display, you'll be able to see which operators are carriers and which are modulators. The carriers are connected to the Out in the right-hand column, as shown in the factory patch called Six-String (see Fig. A). If there's more than one carrier, start by switching off all but one of the carriers, so you can hear its contribution to the sound. Then switch its modulator(s) on and off, one by one.
In Six-String, operators C and F are carriers. Each of them has two modulators in a stack configuration: A modulates B, which in turn modulates C. The same thing happens with D, E, and F. When you mute F you'll hear only the bright portion of the sound, which is coming from C. When you mute C and unmute F, you'll hear that F is providing the dark body of the tone.
While listening to operator C, mute and unmute A. You'll hear that it's adding a lot to the brightness of the tone. Its frequency ratio is set to 20.0063, which is quite high. Try lowering this to 19, 18, and so on, and listen to the changes in the tone. Tuning each operator correctly is essential to creating a rich and lifelike FM tone.