{"query": "Harmonics — pitch, timbre, phonons", "count": 5, "results": [{"id": "card_acoustics_harmonics", "title": "Harmonics — pitch, timbre, phonons", "shelf": "codex", "surface": "secular", "snippet": "Pitch is frequency; a string also rings at integer multiples (the harmonic series), and their mix is timbre. The third harmonic of 220 Hz is 660 Hz (sealed). Quantized, a sound wave's quanta are PHONO", "authority_tier": "engine_derived", "source": "Narrow Highway — acoustics", "readable": false, "generated": false}, {"id": "card_calc_lattice_vibration", "title": "Lattice phonons", "shelf": "calculations", "surface": "secular", "snippet": "Lattice phonons — condensed_matter. Formula: omega(k) = 2 sqrt(K/m) |sin(ka/2)|. Canonical FORM: periodic (x = A*cos(omega*t + phi)) — a crystal's vibrations are a chain of coupled harmonic oscillator", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_bridge_master_harmonic_oscillator", "title": "Master equation: d2x/dt2 = -omega^2 x", "shelf": "bridges", "surface": "secular", "snippet": "a restoring force proportional to displacement — every oscillation is this, with omega^2 = restoring/inertia. ONE equation, 4 domains, connected by a change of variable: physics [omega^2 = k/m (spring", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_floor_acoustics", "title": "Acoustics — waves, loudness, and harmonics", "shelf": "codex", "surface": "secular", "snippet": "The physics of sound and hearing, standing between matter and mind. Sound is a pressure wave in a medium (v = f lambda); loudness is logarithmic (the decibel); pitch is frequency and timbre is the har", "authority_tier": "engine_derived", "source": "Narrow Highway — acoustics", "readable": false, "generated": false}, {"id": "card_seal_a3c4f4cba5d69229367a0cecb1eb33edbc5c419ab34d1da4ee09dbdde74b5751", "title": "Receipt a3c4f4cba5d6… — sealed: record", "shelf": "seals", "surface": "secular", "snippet": "{\n \"anchors\": [],\n \"gate_results\": [\n  {\n   \"details\": {\n    \"broken_at\": null,\n    \"confirmed_steps\": 1,\n    \"error_at\": null,\n    \"gap_at\": null,\n    \"steps\": 1,\n    \"verdict\": \"HOLDS\"\n   },\n   \"gat", "authority_tier": "engine_derived", "source": "Narrow Highway engine — sealed record", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_acoustics_harmonics"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}