Proof behind the instruments.

Behaviour comes before labels

Voltage Synths begins with relationships inside an instrument. The position of a nonlinear stage matters. Filter feedback establishes another relationship; a capacitor sets an envelope time, and component variation separates related voices.

Musical consequence: useful control interactions survive beyond one tuned patch.

Filter structure defines the instrument

Substance uses a saturating 4-pole transistor ladder. Its pole-mixed outputs include compensation for low-frequency body.

Octet takes a 2-pole OTA state-variable structure. Mode crosses low-pass / notch / high-pass continuously, while band-pass stays separate. Resonance acts on the band around cutoff.

Musical consequence: the 2 instruments keep their own response under one engineering standard.

The oscillator meets its four audible-band targets.

The discrete saw core is checked at 48 kHz with legitimate harmonics removed from the analysis. Free-running saw, hard sync and full-depth pulse-width modulation all sit below their declared audible-band limits.

The full-band values are shown because they are materially higher in two of the four conditions, by more than 40 dB in each. A short band-limiting kernel has a transition region around Nyquist; later nonlinear processing can fold some of that ultrasonic energy back into the audible band. How much energy sits up there depends on where the harmonics fall relative to Nyquist, so the 3997.6 Hz row reads within 3 dB of its audible-band figure while the 1000.5 Hz row is nearly 50 dB above it.

Musical consequence: bright notes remain controlled in the audible band. The same applies to sync sweeps and pulse-width movement; the ultrasonic limit stays beside the result.

The filter follows an independent continuous-time reference.

The state-variable filter is probed from the outside with steady-state tones and compared with a separately evaluated continuous-time version of the same topology. It holds within 0.02 dB at the centre frequency and within 0.15 dB across the tested band. The check runs at 6 sample rates in the oversampling configuration the instrument uses.

What this establishes: the digital filter follows the intended circuit equations. Hardware comparison belongs to the calibration section below.

Musical consequence: the cutoff stays where the circuit says when a session changes sample rate.

The circuit sets the distortion points

Both integrator stages saturate at the operational transconductance amplifier limits inside their feedback loops. The output-stage supply rails bound self-oscillation amplitude.

The nonlinear system is solved together each sample with a fixed amount of work. Difficult settings cost the same as easy ones.

Musical consequence: resonance compresses at one level, blooms at another and can reach self-oscillation inside the same circuit.

Pitch and envelopes hold across 6 rates

Oscillator pitch is checked across 44.1–192 kHz to 0.005% relative error. Attack / decay / release follow resistor-capacitor trajectories over 1 ms–12 s. Timing holds within 0.5%; the sustain transition stays within 2%.

Musical consequence. A pluck keeps its timing. Long releases remain long, and a reopened project stays in tune.

Eight related voices move independently

The polyphonic engine owns voice allocation and stealing. Unison and glide operate inside that engine. Stable component variation comes from the patch seed plus voice index.

Musical consequence: chord width and movement return with the session.