A monophonic FM synthesizer for Max MSP that uses the Logistic Map as its modulation source, producing sounds that range from stable tonal textures to unpredictable, chaotic timbres.
Instead of a conventional sine-wave modulator, this synth feeds the output of a chaotic algorithm — the Logistic Map — into the frequency of a carrier oscillator. The Logistic Map is defined by:
where
The bifurcation diagram above is your roadmap. The horizontal axis is
The interface is split into three sections, each with its own role:
| Section | Location | Purpose |
|---|---|---|
| MOD | Top-right | Controls the chaotic modulator (the Logistic Map engine) |
| CARRIER | Middle-right | Selects the carrier waveform, envelope, and output level |
| GLOBAL PITCH | Bottom-left | Transpose, glide, and pitch-shift quality |
A waveform scope on the left displays the live output so you can see the relationship between your parameter changes and the resulting signal.
These controls shape the chaotic modulation signal before it hits the carrier.
This is the most important knob on the synth. It sets the
- 3.2 – 3.0 — Stable region. The map converges to a fixed point. The modulator outputs a near-constant value, so the carrier sounds clean and static. Use this as your "safe" starting position.
-
3.0 – 3.57 — Periodic region. The map begins period-doubling: first alternating between 2 values, then 4, then 8, and so on. You'll hear rhythmic, pulsing textures layered onto the carrier. Slowly sweeping
$r$ through this range reveals the bifurcations one by one. - 3.57 – 4.0 — Chaos region. The map becomes chaotic. Tiny differences in state lead to wildly different outputs. The modulation becomes dense, noisy, and complex. This is where the synth produces its most distinctive timbres.
Tip: The boundary near 3.57 is the most sonically interesting zone. Dial in slowly — small movements here produce dramatic timbral shifts.
Sets the central frequency (rate) of the chaotic waveform generator. This determines how fast the Logistic Map iterates and, by extension, the pitch-range of the modulation signal. Lower values produce slow, evolving modulation; higher values push the modulation into audio-rate territory for harsh, metallic FM textures.
Controls the modulation depth — how much the chaotic signal affects the carrier's frequency. At zero, the carrier sounds unmodulated. As you increase this, the logistic waveform exerts more influence. Paired with a high
Choose one of four carrier oscillator shapes:
- Sine (
cycle~) — Pure tone. Best for hearing the modulation's effect in isolation. - Saw (
phasor~) — Harmonically rich. Adds brightness even before modulation. - Triangle — Softer than saw, odd-harmonic content. Good middle ground.
- Square — Hollow, reedy character. Combined with chaotic modulation, can produce very aggressive sounds.
Standard four-stage amplitude envelope, each controlled by its own dial:
- Attack — Time for the sound to reach full volume after a note-on.
- Decay — Time to fall from peak to the sustain level.
- Sustain — Level held while the note is held.
- Release — Time to fade to silence after note-off.
Tip: Short attack + long release pairs well with chaotic modulation — you get an immediate hit followed by an evolving, unpredictable tail.
Master output level. The signal passes through a limiter (limi~) before output, but it's still wise to keep this in check when exploring extreme modulation settings.
These controls sit below the waveform display and affect the overall pitch of the output.
Shifts the pitch of incoming MIDI notes in semitones. Use this to quickly move the synth into a different register without retuning your controller.
Sets a portamento time. When you play a new note, the pitch slides from the previous note to the new one over this duration. At zero there is no glide; increase it for smooth, legato pitch transitions.
A dropdown menu that sets the quality mode of the internal pitch shifter (pitchshift~). Higher quality uses more CPU but produces cleaner pitch-shifting artifacts. For most use cases, the default is fine — experiment if you hear unwanted artifacts at extreme transpose values.
- Polyphonic voices
- Additional modulator sources
- Wavetable option for the carrier oscillator
- more chaotic algorithms