Pickup Simulation

A pickup does not hear the whole string equally

The guitar setup owns pickup position, height, tilt, switching, and per-string routing. Position matters because a vibrating string has nodes and antinodes: sampling near the bridge produces a different harmonic balance than sampling nearer the neck.

The pickup module owns physical construction and electrical behavior, not placement. The same pickup can therefore be installed at bridge, middle, neck, or a custom point without embedding one guitar into its reusable design.

From motion to voltage

A magnetic pickup responds to changing magnetic flux. String displacement and velocity near the magnetic field create an induced signal, while aperture width, height, and magnetic geometry affect coupling. Those physical relationships describe the target model.

The current implementation uses a simplified string observation and then passes that signal through an equivalent circuit: series coil resistance and inductance driving parallel capacitance and load resistance. This produces a useful resonant loading model, but it is not yet a calibrated field simulation of flux, aperture, pole geometry, or pickup height.

Position samples harmonic motion

For an ideal string fixed at both ends, the contribution of each harmonic at a pickup is proportional to the sine of that harmonic’s observation position. The example makes the bridge-versus-neck difference visible without baking tone labels into the pickup.

ArcoBASICArcoBASIC communication example: observe string harmonics at a pickup position

' Observe one string at a physical point along its speaking length.
FUNCTION PickupObservation(harmonics, distanceFromBridgeMm, scaleLengthMm)
    position = CLAMP(distanceFromBridgeMm / scaleLengthMm, 0, 1)
    observed = 0
    harmonic = 1

    FOR amplitude IN harmonics
        ' A harmonic node at the pickup contributes little or no voltage.
        shape = SIN(Math.PI() * harmonic * position)
        observed = observed + amplitude * shape
        harmonic = harmonic + 1
    NEXT

    RETURN observed
END FUNCTION

motion = [1.0, 0.32, 0.18, 0.1]
PRINT PickupObservation(motion, 38, 647.7)

Construction families represented in the module model

The module and construction specifications can describe the families below. The active audio implementation is currently strongest for the single-coil equivalent circuit; the other families still require model-specific processing and physical validation.

Single coil and rail geometries
Series or parallel humbuckers with opposing winding and polarity
Stacked hum-cancelling constructions
Hexaphonic and other per-string voice layouts
Piezo bridge elements with their own capacitance and load
Passive output or explicit active preamp topology
Coil split, independent outputs, taps, and four-conductor wiring

Separating what a part is from where it sits

The RLC equivalent circuit and the sine-of-position harmonic sampling are specific to how a magnetic pickup listens to a vibrating string. A different domain will not have nodes, antinodes, or coil inductance. What generalizes is how the responsibility for where got kept separate from the responsibility for what.

The same separation shows up anywhere a component’s own behavior gets tangled with the context it happens to be deployed in: a UI widget that hardcodes assumptions about the page it currently lives on, a library function that silently depends on global state set by one particular caller. Decoupling what a thing is from where it is used is what makes it reusable at all.

Keep placement, bridge, neck, or a custom position, out of the reusable pickup construction entirely, so the same pickup definition works anywhere without special-casing one guitar’s geometry inside it.
Use a real relationship, such as the sine of harmonic times position determining how much of each harmonic reaches a point, rather than hardcoding tone labels like "bridge equals bright" that hide the actual cause.
Say explicitly which construction families, piezo, humbucker, hexaphonic, are represented in the model versus which are only structurally described, so "supported" does not quietly come to mean two different things.
Treat an equivalent circuit as a legitimate intermediate model, not a finished one. Calling the RLC loading "not yet a calibrated field simulation" keeps the roadmap honest about what remains between useful and validated.

LEARNING LAYER

Key terms, in plain language

You do not need a systems background to follow the work. These are the specialized terms used on this page.

Pickup aperture: The short region of a string that a pickup observes rather than one infinitely small point. Its width changes how strongly different harmonics contribute.
Inductance: An electrical property of a coil that opposes changes in current. Together with capacitance and resistance, it helps determine a pickup’s resonant character.
Capacitance: The ability to store electrical charge. Pickup winding capacitance, cable capacitance, and the connected load all affect high-frequency response.
Impedance: A frequency-dependent measure of how strongly a circuit opposes electrical current. Unlike plain resistance, it includes the behavior of capacitors and inductors.
Resonant frequency: A frequency where a system naturally responds more strongly. In a passive pickup, inductance and total capacitance help set this peak.
Q factorQuality factor: A measure of how narrow and pronounced a resonance is. Higher Q produces a sharper peak; lower Q produces broader, more heavily damped behavior.
DIDirect Injection: The direct electrical signal from an instrument before speaker and microphone coloration. ArcoAura keeps raw pickup DI separate from later effects and amplification.