Investigate "all tunings half-step flat" — code is correct, add regression guard

[palvimaki]

Founder report

"all tunings are half step too low" — displayed note/target ~1 semitone flat vs. the actual pitch played, across every tuning.

Root-cause investigation

The hypothesis was a deterministic constant bug (wrong A4, off-by-one MIDI/octave, bin/sample-rate error, shifted note table). Every candidate was checked and ruled out. The codebase is mathematically correct end-to-end.

Verified accurate to <0.1 cents at A4=440 and all standard guitar frequencies (82.41 / 110 / 146.83 / 196 / 246.94 / 329.63 Hz):

Layer	File	Result
Reference pitch / MIDI formula	src/audio/note-math.ts:39-49	440 * 2**((midi-69)/12), 1200*log2() — correct
MIDI↔note name	src/audio/note-math.ts:22-37	round-trips E2↔40, A4↔69, E4↔64 — correct
Guitar presets	src/domain/instruments/guitar/presets.ts	E2=82.407, A4=440.000 exactly — correct
Nearest-string select	src/app/state.ts:104	picks the same note, no shift — correct
TS DSP (YIN + MPM)	src/audio/dsp/{yin,mpm}.ts	<0.5c on synthetic plucks — correct
Production worklet pitch chain (YIN + target-aware)	public/worklets/tuner-processor.js	<0.1c on synthetic plucks — correct

There is no semitone-flat constant or formula error anywhere in the source. No prior semitone fix exists in history; production is current with dev.

What this PR does

Adds a permanent regression test (test/unit/semitone-flat-regression.test.ts) that feeds exact reference pitches through frequency → MIDI → note and the nearest-string / cents path, asserting 0-cent agreement. A genuine semitone bug would surface here as ≈ -100 cents. The test passes, codifying correctness and catching any future regression.

No production-code change is made because the reported defect does not exist in the code. Fabricating a "fix" would introduce a real bug.

Most likely actual cause (for Founder follow-up, no deploy)

1. Stale PWA cache — an old cached service worker / tuner-processor.js from before the octave-gate fixes (21fbbf9). Hard-reload / clear site data and retest.
2. Reference source not at 440 — if tested against another tuner/app/string set that itself isn't A440, every reading would look uniformly flat.
3. Acoustic — strong low-string inharmonicity / room coupling at the mic; not a code constant.

Recommend the Founder hard-refresh tuner.fi (or bump the SW cache version) and retest before any further code work.

Tests

npm test → 80 files, 299 tests, all green (includes the new regression test).

🤖 Generated with Claude Code