[ii-impy]

Summary

A new operator, plucked_string: an extended Karplus–Strong string. Its controls are resonator's less structure, mapped the same way, so an instrument swaps one for the other by type.

pluck (gate edge) ─► one period of noise ─► 2-pole LP ─► circular position comb ─┐
                                                                                 ▼
in ─► × (1 − loop gain at f₀) ─────────────────────────────────────────────► + ─► line (N samples) ─► allpass (frac) ─► loss LP ─► × g ─┐
                                                                                 ▲                                                    │
                                                                                 └────────────────────────────────────────────────────┘ ─► out

• Tuning: the allpass is solved exactly at f₀ for what the line and the loss filter's phase delay leave.
• brightness: partial k decays 1 + h·(k − 1) times faster than the fundamental. The loss pole is fitted to that at the 8th partial, and the same control sets the pluck's colour.
• damping: the fundamental's ring time, on resonator's curve.
• in: normalized to unity at f₀.
• with_lowest_freq(hz): sizes the line, the way Delay::with_max_time does.
• Cost: a few operations a sample, whatever the pitch or brightness. resonator's cost grows with its mode count.

Wanted by ii-handhelds' Emotional Support Synth for a nylon-string sound. There it renders the four-string graph in 27% fewer instructions than four resonators.

Evidence

16 OpDriver tests in plucked_string.rs, among them:

• Pitch: within 3 cents of freq from 82 Hz to 2 kHz, dark and bright; partials 2–6 within 5 cents of harmonic.
• Ring time: the measured ring is within 15% of the mapped one.
• Position: plucking the middle cuts the 2nd partial over 10× against plucking near the end.
• Bowing: a sine at f₀ passes within ±1.5 dB of unity.
• Stability: never grows at damping 1 and brightness 1, from 20 Hz to 8 kHz; finite under NaN controls.

The two bugs the first draft had, each with the test that caught it:

• Before: a_pluck_rings_at_its_freq failed at 1046.5 Hz, dark. A fixed loss pole cut the fundamental 4% a period, so the string died in ~50 ms.
  After: the loss pole is fitted per partial, and the test passes.
• Before: a_dark_pluck_has_no_buzz measured an RMS frequency of 870 Hz on a dark 220 Hz pluck. A one-pole burst falls as 1/k, a sawtooth.
  After: a two-pole burst, settled over a period first, measures under 550 Hz.

Gates: cargo test and cargo test -p reuben-core --features bench green; cargo fmt --all --check and cargo clippy --all-targets -- -D warnings clean. reuben describe plucked_string matches the contract. breath-harp.json, with its resonators swapped for plucked_string, passes reuben validate.

Not ear-checked: the tests prove the oracle, not the sound.

Merge Danger

Door: two-way

Additive: a new operator and its bench workload, with no existing operator changed.

Blast Radius: none

sync-docs has not been run for it: authoring.md, the library index and the operator lists don't mention plucked_string yet.

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