Mechanism is the product boundary.
A Chiral plugin starts with a governing equation. The equation constrains the signal path, the parameters, and the kinds of motion the effect can produce.
Chiral Audio glossary
Mechanisms beneath the sound.
This glossary defines the scientific vocabulary behind the catalog. Each entry begins with the mechanism, then names the audio consequence: how a control parameter changes behavior, why the response is nonlinear, and where the equation becomes audible.
Parameters are control variables.
Coupling, carrying capacity, dispersion, and temperature are not cosmetic names. They are levers that move a system through defined behavioral regimes.
Audibility is the standard.
A mathematical mapping only matters when a musician can hear it. The catalog favors mechanisms with clear sonic consequences and broad performable range.
Catalog V1
Three mechanisms already inside the instrument.
The first catalog wave covers the clearest mappings: coupled oscillator synchronization, logistic resonance growth, and nonlinear wave propagation. Each panel below is an entry point into the larger vocabulary.
01 / Foxfire
Coupled oscillators
Sixteen voices exchange phase information. Below critical coupling they drift. Near the threshold they flicker into partial coherence. Above it they lock.
02 / Autocatalysis
Self-amplifying resonance
Resonators recruit themselves through an S-curve. Growth starts slowly, accelerates, then saturates against a capacity limit.
03 / Soliton
Balanced propagation
Dispersion spreads the repeat. Saturation refocuses it. At the balance point, the delay line sustains without collapsing into smear or runaway feedback.
Glossary
No terms match that search.
01
Studio Thesis
Structural isomorphism
Structural isomorphism is the requirement that the organization of a source phenomenon maps cleanly onto the organization of the DSP. The scientific system supplies the signal path, state variables, constraints, and parameter meanings.
Audio consequence: the effect inherits behavior from the mechanism itself. A coupled-oscillator chorus can drift, cluster, and lock because those are native behaviors of the Kuramoto model.
Governing equation
The equation that defines how a system changes over time. In this catalog, the governing equation is the design object: it determines state update, stability, feedback, and the meaningful parameter ranges.
Audio consequence: a control is strongest when it corresponds to a real term in the equation. Coupling, capacity, dispersion, and temperature carry more authority than arbitrary macro labels because they name actual system levers.
Control parameter
A variable that changes the regime of a system. Temperature moves a material through a phase transition. Coupling moves oscillators from incoherence toward synchronization. Capacity limits a self-amplifying reaction.
Audio consequence: a good control parameter does more than add more effect. It changes the kind of behavior the listener hears.
Order parameter
A compact measure of macroscopic order. In a Kuramoto network, the order parameter R measures phase coherence across the oscillator population. R near zero means incoherence. R near one means synchronized motion.
Audio consequence: an order meter can show the ensemble cohering while the ear hears the chorus tighten.
02
Nonlinear Dynamics
Nonlinear dynamics
The study of systems whose response is not proportional to input. Doubling the input does not simply double the output. Thresholds, saturation, hysteresis, phase transitions, and self-reinforcing feedback all require nonlinearity.
Audio consequence: nonlinear systems produce qualitative changes: a chorus snaps toward coherence, a resonator blooms after the attack, a delay stabilizes into a persistent wave.
Phase transition
An abrupt change in system-level behavior as a control parameter crosses a critical value. Water freezes. Magnets order. Oscillators that drift independently begin to synchronize when coupling crosses the threshold.
Audio consequence: the transition zone is performable. In Foxfire, the Coupling knob moves the chorus through incoherence, flickering partial sync, and locked motion.
Critical coupling
The coupling strength at which a finite fraction of oscillators begins to synchronize. Below this value the population remains mostly incoherent. Above it, the order parameter rises as the network coheres.
Audio consequence: critical coupling is the dramatic hinge in a coupled-oscillator chorus. It is where motion starts to feel intentional without becoming rigid. See the longer Kuramoto synchronization explainer.
Coupled oscillator
An oscillator whose phase or amplitude is influenced by other oscillators. Coupling can produce entrainment, clustering, traveling waves, and synchronized motion, depending on network structure and coupling strength.
Audio consequence: voices stop behaving as isolated LFOs. They become a population with collective motion.
Kuramoto synchronization
A model of how oscillators with different natural frequencies self-organize when they exchange phase information. In its common mean-field form, each oscillator follows \(\dfrac{d\theta_i}{dt} = \omega_i + \dfrac{K}{N}\sum_{j} \sin(\theta_j - \theta_i)\).
Audio consequence: Foxfire uses this model to make a chorus that can drift, cluster, flicker at the threshold, and lock as a system. Read the full audio explanation or the practical comparison.
Bifurcation
A point where a system changes the number or stability of its possible behaviors. Below the bifurcation, one regime is stable. Across it, a new regime appears or an old one disappears.
Audio consequence: bifurcations are useful for controls that should cross from following to oscillating, or from stable to unstable, with a clear threshold.
Hysteresis
History-dependent response. A hysteretic system does not return along the same path it took in. Magnetic materials show this as a loop between field strength and magnetization.
Audio consequence: distortion can remember recent signal motion. The transfer curve becomes path-dependent, which creates weight, lag, and asymmetric recovery.
03
Growth, Waves, and Propagation
Autocatalysis
A reaction where a product also catalyzes its own formation. Each unit of product increases the rate at which more product appears, until substrate limits or carrying capacity slow the reaction.
Audio consequence: resonators can grow from the signal they detect. Harmonics emerge after the initial event instead of merely decaying from it.
Logistic growth
A growth model where the rate depends on both current population and remaining capacity: \(\dfrac{dN}{dt} = rN\!\left(1 - \dfrac{N}{K}\right)\). Growth begins slowly, accelerates, then saturates into an S-curve.
Audio consequence: a resonant band can bloom with a physical time profile: lag, ignition, and self-limiting ceiling.
Verhulst equation
The differential equation for logistic growth, published by Pierre-Francois Verhulst in 1838. It refines exponential growth by adding a capacity term that slows growth as the system fills.
Audio consequence: the Verhulst shape gives Autocatalysis its controlled bloom. It grows with force, then stops where the model says it must.
Carrying capacity
The maximum state a growth process can sustain under its constraints. In logistic growth it is the K term, the ceiling that converts runaway exponential growth into bounded S-curve behavior.
Audio consequence: capacity sets how far resonance can bloom before it self-limits. It is the difference between growth and uncontrolled feedback.
Reaction-diffusion
A class of systems where local reactions and spatial diffusion act together. The result can be self-organizing patterns: stripes, spots, chemical waves, and morphogenetic gradients.
Audio consequence: reaction-diffusion is useful when spectral or spatial material should organize itself from local interactions rather than a global modulation curve.
Soliton
A solitary traveling wave that preserves its shape because dispersion and nonlinear steepening balance. The wave resists the usual fate of broadening, decaying, or breaking apart.
Audio consequence: Soliton uses the balance principle inside a feedback delay. Repeats reshape themselves instead of degrading into mush or screaming into runaway feedback.
Dispersion
Frequency-dependent propagation speed. In a dispersive medium, different frequency components travel at different rates, so a complex wave spreads over time.
Audio consequence: allpass dispersion can smear a delay repeat in a controlled way. Balanced against saturation, the same force that would blur the signal helps create a stable repeat.
Group velocity
The speed at which a wave packet's envelope moves. It differs from phase velocity, which tracks the movement of individual wave crests. Dispersive media separate these speeds.
Audio consequence: group velocity matters when delay lines and wave packets are treated as moving structures, not only as time offsets.
Korteweg-de Vries equation
A nonlinear partial differential equation for shallow-water waves, commonly written \(u_t + 6u\,u_x + u_{xxx} = 0\). The nonlinear term steepens the wave. The dispersive term spreads it. Soliton solutions appear where those forces balance.
Audio consequence: the KdV equation supplies the conceptual spine for a delay that stabilizes through dispersion and nonlinearity rather than brute-force feedback.
04
Roadmap.
Boltzmann distribution
A probability distribution where lower-energy states are exponentially more likely than higher-energy states: \(P(E_i) = \dfrac{e^{-E_i/kT}}{Z}\). Temperature controls how sharply the system favors low-energy states.
Audio consequence: pitch or rhythm selection can move continuously from stable and tonal to high-entropy and exploratory.
Anderson localization
Wave trapping caused by disorder. Instead of diffusing freely through a medium, a wave becomes localized because random scattering prevents long-range propagation.
Audio consequence: a spectral freeze can become gradual and material-like. Disorder determines which bands stay trapped and which bands keep moving.
Bragg diffraction
The condition where waves reflect constructively from periodic planes in a crystal: \(n\lambda = 2d\,\sin\theta\). Wavelength, lattice spacing, and angle determine which frequencies reinforce.
Audio consequence: frequency bands can be routed through stereo space by diffraction logic, with spacing as the governing control.
Birefringence
An optical property where a crystal splits light into ordinary and extraordinary rays with different refractive indices. The split depends on angle, material, and polarization.
Audio consequence: chorus or comb filtering can split by direction and material profile, producing movement that feels prismatic rather than mechanically periodic.
Crystal lattice
A periodic arrangement of atoms or ions. Lattice spacing, symmetry, defects, and temperature determine how vibrations propagate through the material.
Audio consequence: an FDN reverb can derive delay ratios, diffusion, and spectral gaps from material structure rather than arbitrary tuning.
Chemotaxis
Directed movement along a chemical gradient. Cells compare local concentration over time and bias their motion toward stronger or weaker signal depending on the organism and stimulus.
Audio consequence: resonators can wander toward spectral peaks, following the source as if the signal were a gradient field.
Osmosis
Movement across a semipermeable membrane driven by concentration differences. The membrane admits some species, blocks others, and creates pressure when the system is constrained.
Audio consequence: two signals can compete across a spectral membrane, with permeability controlling how much one source occupies the other's space.
The catalog is an argument for structure.
Conventional plugin categories describe surface behavior: chorus, delay, reverb, distortion. Chiral's vocabulary is lower in the stack. It names the mechanism that generates the behavior, which is where the defensible difference lives.