3-operator Digital FM

Audio Generators

1. Tuning Knob Sets the reference frequency when the Pitch input is at 0V. Double-click for middle C.
2. Fine Knob ±1 semitone adjustment around tuning frequency.
3. Hertz Knob ±5 Hz adjustment around tuning frequency.
4. Vel Input Modulates the amplitude of the operator’s ADSR envelopes.
5. Trig Input When triggered, restarts the operator’s ADSR envelopes. If the Gate input is unconnected, starts the envelope in free-running mode.
6. Gate Input On rising edge, starts the operator ADSR envelopes from the attack segment. While the gate is high, the envelopes go through attack and decay segments, and then remain at their sustain level. On falling edge, they go to the release segment.
7. Pitch Input Calibrated for 1V/octave pitch signals.
8. Pitch-to-decay Knob Changes the decay and release times operator ADSR envelopes relative to the input pitch.
9. FM Input Per-operator external FM input, with attenuator. Use this to create complex FM algorithms with other oscillators.
10. Ratio Knob Per-operator frequency multiplier.
11. Fine Knob Fine-tunes the frequency multiplier.
12. FB Knob Controls the amount of FM feedback. It has the effect of changing the operator waveform from sine to sawtooth-like to white noise.
13. Out Knob Operator output volume. Depending on the FM algorithm, this may control either the amount of FM applied to another operator or the mix of this operator sent to the module Out jack.
14. Env Input Overrides the operator’s ADSR envelope with an external amplitude envelope signal. Expects a signal between 0V and 10V.
15. A, D, S and R Knobs Attack, decay, sustain and release for the operator amplitude envelope. No effect when an external envelope is connected.
16. Vel Knob Controls how much the signal on the Vel input affects the ADSR amplitude. No effect when an external envelope is connected.
17. Pitch Env Knob Amount of pitch envelope applied to operator. Pitch envelope is disabled when the knob is centered (default position).
18. Time Knob Length of the pitch envelope. No effect when Pitch Env knob is centered.
19. Curve Knob Pitch envelope curve. From linear to exponential. No effect when Pitch Env knob is centered.
20. Key-to-vol Knob Controls how the Pitch input affects the operator volume. No effect when centered; lower notes become louder when turned counterclockwise, higher notes become louder when turned clockwise.
21. Algorithm Selector Changes the internal FM topology. Depending on the algorithm, each oscillator may be used to modulate another one or may be routed to the module output.
22. Oscillator Output Output signal.

Overview ⚓︎

In the 80s and early 90s, digital FM synthesis took the world by storm, finding its way into professional keyboards, home organs, portable keyboards, video game consoles and early PC audio expansion cards. A radical departure from analog subtractive synthesis, it could not only cover the same sonic territory with rich basses, pads and leads, but it also excelled at creating expressive electric pianos, crisp metallic bells, and punchy percussions.

The main drawback of digital FM is its complexity: creating those iconic sounds requires adjusting many parameters for each operator (the term for an oscillator in an FM engine). In the 80s, this meant spending substantial time navigating cryptic menus on a small LCD screen to adjust each parameter individually.

When designing this module, we had two goals in mind:

• Immediacy: We limited the module to three operators so that we could expose all synthesis parameters as knobs instead of hiding them in panels or menus. We also added amplitude and pitch envelopes to each operator, allowing complete sounds to be created simply by connecting the module’s Pitch and Gate inputs to the Keyboard, and connecting its output jack to the Output Mixer.
• Flexibility: While three operators driven by three ADSR envelope generators are enough to produce a wide range of sounds, the additional FM and external envelope inputs allow for FM patches of any complexity.

The module can be used in two ways:

• Full-synth mode When a cable is connected to the Gate or Trig inputs, the module behaves as a fully contained synthesizer. The sound will start when the ADSR envelopes in the operators are triggered by the gate or trigger signal, and it will stop when the envelopes reach the end of their release time after the gate falls back to 0V.
• Free-running mode When no cable is connected to the Gate or Trig inputs, the ADSR envelopes are bypassed and the operators always run at full volume.

Quick Start ⚓︎

Full-synth mode

• Connect the Keyboard Pitch output to the Pitch input at the bottom-left of the module.
• Connect the Keyboard Gate output to the Gate input above the Pitch input. This triggers the built-in envelopes in the operators.
• Connect the Out jack at the bottom-right of the module to the Output Mixer.
• Digital FM synthesizers were generally polyphonic, so set the Mode module to Poly for an authentic experience.

Now you can experiment with using different settings for the operator’s Out, Ratio and ADSR knobs to produce an infinite number of sounds. Connecting the Vel input and adjusting the operator’s Vel knobs will add even more control over the sound.

You can use the CV Quick-connect feature to quickly connect the Pitch, Velocity, Trig and Gate inputs by double-clicking on them.

Free-running Mode

In this mode, the module always produces sound on its Out jack, like other oscillators that don’t have a Gate input.

• If you need pitch tracking, connect the Pitch input to the Keyboard Pitch output or to another pitch source like a sequencer.
• Connect the Out jack at the bottom-right of the module anywhere you would connect a free-running oscillator. You may want to process it with a filter or shaper and then control it with a VCA or a LPG connected to an ADSR.

Superficial Introduction to FM ⚓︎

FM is short for frequency modulation. An FM synthesizer needs at least two oscillators: one that we hear, and another one to modulate its frequency. We call the first a carrier, because it carries the sound we hear, and we call the second a modulator, because its role is to modulate another oscillator.

When the frequency of the carrier is modulated, its timbre becomes more complex. Different ratios in frequency between the modulator and the carrier will produce different timbres.

In digital FM synthesis, complex timbres with plenty of high frequencies are more likely to cause dissonant aliasing artifacts, which is why most digital FM synthesizers use simple waveforms based around sine waves.

When more than two oscillators are involved, things become more complex. We could imagine a topology where one modulator affects two carriers that run at different frequencies, or one modulator affecting a second modulator, affecting a third, and so on, until the last modulator modulates the carrier. In the 1980s, the term algorithm was popularized to refer to these topologies, along with the term operator to refer to the individual oscillators that are part of an algorithm. The bottom section of the module lets you choose between four different algorithms to connect the three operators.

Technically, there are two kinds of frequency modulation: linear and exponential. Linear FM shifts the carrier’s frequency by adding or subtracting a value proportional to the modulator’s amplitude, while exponential FM scales it based on the exponential of the modulator.

Fun fact: digital FM synthesizers use neither linear nor exponential FM. Digital FM is actually phase modulation, where the modulator shifts the phase of the carrier rather than its frequency. This was easier to implement on early microprocessors, and can produce sounds identical to linear FM when working with sine waves.

So with the Classic VCO’s linear FM, the State Variable Filter’s exponential FM (using it as an oscillator by setting its Q fully clockwise) and this module’s digital FM, Multiphonics covers the whole spectrum of FM synthesis.

In Depth ⚓︎

The 3-operator Digital FM module is so densely packed with controls that it might seem intimidating, but it can be understood easily by breaking it into five simple sections:

Tuning ⚓︎

Tuning is controlled by the main Tuning knob, the Fine and Hertz knobs, their respective modulation inputs, and the Pitch input. See Oscillator Tuning for more information.

The actual output pitch of the module depends on the current algorithm and relative ratios between operators. FM can produce sub-harmonics, especially when using the Ratio Fine knob.

Note Control ⚓︎

The note control inputs (Vel, Trig, Gate and Pitch) will usually be connected to a Keyboard module to trigger the oscillator.

Trig and Gate trigger the amplitude and pitch envelopes that are found in each operator, while Vel can affect the level of the amplitude envelopes according to each operator’s Vel knob. This works exactly like the corresponding inputs in the ADSR module.

The 1V/octave Pitch input sets the current note played by the oscillator, as described in the Oscillator Tuning section of the manual.

The Pitch→Decay knob affects the decay (D) and release (R) length of the operator ADSR envelopes according to the current note being played. When fully counterclockwise, the decay and release will be the same for all notes. As the knob is turned clockwise, the decay will become shorter for higher notes and longer for lower notes, as would be expected in an acoustic instrument.

Operators ⚓︎

Operator Amplitude

Arguably, the most important knob in the operator section is the Out knob, which controls the amplitude of that operator. Its effect depends on whether the operator is a modulator or a carrier.

In the algorithm section, modulators are depicted as connecting into another operator and carriers are at the bottom of the structure.

• For carriers the Out knob controls the output volume of the operator. If there are more than one carriers, the relative volume of these carriers will adjust the output mix. The module will only produce sound if at least one carrier has a non-zero output volume.
• For modulators the Out knob controls by how much the modulator affects the timbre of the operator to which it is connected.

The operator volume will also be affected by the Key→Vol (key-to-volume) knob, which adjusts the volume according to the signal on the Pitch input:

• When centered, the volume is the same for all pitch inputs.
• When turned clockwise, a higher input pitch will increase the operator volume, and a lower input pitch will decrease it. Use this on a modulator to create a versatile sound with mellow basses and bright highs. Note that this may increase digital aliasing artifacts when playing high notes.
• When turned counterclockwise, a higher input pitch will decrease the operator volume, and a lower input pitch will decrease it. Use this on sounds that are too agressive or that produce too much aliasing artifacts when playing high notes.

Operator Amplitude Envelope

Each operator has a built-in ADSR envelope to control the output volume when a gate or trigger signal is detected on the Gate or Trig inputs.

Read the Overview section of the ADSR module for a description of what the A, D, S and R knobs do.

Instead of the built-in envelope, you can connect any envelope signal to the operator’s Env jack. The external envelope can be triggered separately from the built-in envelope, and the Env jack also supports bipolar signals like the output of a LFO. When the Env jack is connected, the Vel input and knob are disabled; velocity sensitivity is expected to be handled by the external envelope.

When the module is in free-running mode (Trig and Gate inputs unconnected) and the operator has no external envelope, then the ADSR knobs will have no effect and the operator will always play at the amplitude set by the Out knob. However, even though the built-in ADSR envelope is disabled, the Vel input still works, allowing dynamic timbre and volume changes even in free-running mode.

Harmonic Content Control

The harmonic content of the output sound depends on the ratio between the modulator(s) and the carrier.

The ratio is set with the Ratio selector knob and the Fine knob. The Ratio selector starts at ½ and then goes from 1 to 32 in steps of 1. The Fine knob fills the gaps between the ratio values. For example, when the ratio is set to 1, then the range of the Fine knob will be from ½ to 2. When the ratio is set to 20, the its range will be from 19 to 21.

The operator pitch always follows the module tuning. If you need a modulator with a fixed pitch, use the sine output of a Classic VCO and connect it to the FM In jack of the target operator. The perceived pitch of a carrier depends on its ratio and that of its modulator(s). As a rule of the thumb, if the greatest common diviser of the carrier and modulator(s) ratio is 1, then the percieved pitch will be the tuning frequency of the module. If the greatest common diviser is above 1, the carrier will have a higher pitch. If fractional ratios are set with the Fine knob, the pitch may be lower or higher.

Pitch Envelope

Each operator has a built-in pitch envelope. Whenever the module is triggered by the Gate or Trig input, the operator will be detuned by the amount set with the Pitch Env knob. The pitch will then gradually settle back to the operator’s selected ratio over the time period set with the Time knob and following the selected curve (from linear to exponential).

Feedback

In most digital FM synthesizers, one of the operators is able to modulate itself. In the 3-operator Digital FM module, all operators have this capability with the FB (feedback) knob.

When the FB knob is turned clockwise from 0%, the operator waveform morphs from a sine wave to a sawtooth. When past the mid-point, the sawtooth starts breaking down and gradually turns into noise.This can be used on carriers to create richer sounds, which is especially useful for carriers with no modulators as found in some algorithms.

The feedback amount is also affected by the built-in ADSR envelope or by the external envelope.

External FM Input

The FM In jacks let any external oscillator act as a modulator to any operator. The knob controls the modulation depth. With these inputs, you can create an infinite number of algorithms by combining multiple 3-operator Digital FM modules, or by using the sine outputs of Classic VCOs as extra modulators.

The FM In jack can also be used to produce a vibrato effect with a LFO.

Remember that although the input is labeled FM In, the module actually does phase modulation, not frequency modulation. This has two consequences for external modulation signals. First, the modulation depth will depend on the frequency of the input signal: higher frequency inputs will produce a deeper modulation. Second, waveforms other than sine will not have the expected behavior because, as previously mentioned, phase modulation is similar to linear frequency modulation only when using sine waves. For example, the triangle output of a LFO connected to the FM In of an operator will actually sound like a square wave.

Algorithms ⚓︎

The algorithms section controls the routing of the operators, which affects what is heard on the module output. Each box in an algorithm pictogram corresponds to an operator, with the number of dots in the box matching the operator’s number (one dot for OP1, two dots for OP2…) Click on an algorithm to select it.

1. In algorithm 1, the output of OP1 modulates OP2, and the output of OP2 modulates OP3. Only the output of OP3 is routed to the Out jack.

2. In algorithm 2, the output of OP2 modulates OP3. A mix of OP1 and OP3 is routed to the Out jack.

3. In algorithm 3, the outputs of OP1 and OP2 are mixed. This mix modulates OP3, and only the output of OP3 is routed to the Out jack.

4. In algorithm 4, all operators are independent. Their outputs are mixed and routed to the Out jack.

Troubleshooting ⚓︎

If there is no sound on the output:

• Make sure that the Out volume of the operator(s) at the bottom of the selected algorithm diagram is set high enough.

• If you use the internal ADSR envelope generators, check that at least one of Gate or Trig is connected to a working gate or trigger source.

• If you use an external envelope generator, make sure that it gets triggered properly.

• If the main output isn’t connected directly to the Output Mixer, the problem may be elsewhere in the patch. Try connecting directly to the output.