About the Explorables

Reading about a filter tells you that resonance boosts the cutoff frequency. Dragging a resonance knob while the frequency response reshapes under your pointer tells you what resonance is. This section is a set of explorable explanations — in the tradition of Bret Victor’s reactive documents and 3Blue1Brown’s animated mathematics — where every plot is live, every number in the prose can be scrubbed, and everything you see can also be heard.

Two promises hold on every page:

1. The math is the library’s math. The widgets don’t sketch textbook approximations — they run the same formulas as Quiver’s Rust source: the PolyBLEP oscillator from oscillators.rs, the exact TPT filter response from filters.rs, the envelope stage machine from dynamics.rs. What you drag is what ships.
2. What you see is what you hear. The ▶ buttons play the very buffer being plotted, at the voltage conventions of the library (±5 V audio, scaled down to your speakers). Sound never plays until you ask.

The color language

Signals are colored by kind, consistently across prose, plots, and patch diagrams:

• audio — the sound itself, ±5 V
• CV — control voltages that shape it, like envelopes
• gate / trigger / clock — 0 or +5 V timing signals
• V/Oct — pitch, one volt per octave, 0 V = C4
• modulation — LFOs and secondary movement

When you see a dashed number in the text, drag it sideways (or focus it and use arrow keys) — the figures respond immediately.

The pages

• The Shape of a Wave — waveforms and their harmonic recipes, and why the oscillator must be bandlimited.
• Sculpting the Spectrum — the state-variable filter’s exact frequency response, from gentle rolloff to self-oscillation.
• Envelopes Shape Time — drag an ADSR by its corners and hear loudness become a contour.
• The Geometry of Pitch — one volt per octave, and why exponential pitch looks like a line on a log axis.
• Sidebands from Nothing — FM synthesis: two sines, a forest of partials, exactly where Bessel said they’d be.
• Follow the Signal — the full subtractive voice as a clickable circuit; scope any cable.

These pages need JavaScript (and a reasonably modern browser). Animations respect your reduced-motion preference; audio always waits for a click.

The math on these pages is a hand-checked JavaScript mirror of the Rust source — small and instant, but a mirror. When you want the actual compiled engine, open the Live Playground: the full synthesizer, running Quiver’s WASM build in your browser.