{"query": "Acoustics — waves, loudness, and harmonics", "count": 20, "results": [{"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_theory_acoustic_wave_theory", "title": "Acoustic wave theory (harmonics, Doppler)", "shelf": "theories", "surface": "secular", "snippet": "Acoustic wave theory (harmonics, Doppler) — an engine domain that can touch it: acoustics. Calibration: seals — frequencies, harmonics and Doppler shifts compute. Sound is a PRESSURE wave in a medium,", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_music_theory", "title": "Music theory (harmonic series, equal temperament)", "shelf": "theories", "surface": "secular", "snippet": "Music theory (harmonic series, equal temperament) — an engine domain that can touch it: music_theory. Calibration: seals — frequencies, intervals and temperament errors compute exactly. A vibrating st", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_bridge_theory_acoustic_wave_theory__electromagnetic_spectrum", "title": "Bridge: Acoustic wave theory (harmonics, Doppler)  ↔  The electromagnetic spectrum & modulation (radio to gamma, one axis)", "shelf": "bridges", "surface": "secular", "snippet": "Acoustic wave theory (harmonics, Doppler) and The electromagnetic spectrum & modulation (radio to gamma, one axis) are the same form in different domains. identical wave mathematics on a different car", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_music_theory__fourier_analysis___signal_processing", "title": "Bridge: Music theory (harmonic series, equal temperament)  ↔  Fourier analysis & signal processing", "shelf": "bridges", "surface": "secular", "snippet": "Music theory (harmonic series, equal temperament) and Fourier analysis & signal processing are the same form in different domains. timbre IS a spectrum -- what distinguishes a violin from a flute at t", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_fourier_analysis___signal_processing__acoustic_wave_theory", "title": "Bridge: Fourier analysis & signal processing  ↔  Acoustic wave theory (harmonics, Doppler)", "shelf": "bridges", "surface": "secular", "snippet": "Fourier analysis & signal processing and Acoustic wave theory (harmonics, Doppler) are the same form in different domains. the harmonic series IS the Fourier decomposition of a standing wave; the tran", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_elasticity__acoustic_wave_theory", "title": "Bridge: Elasticity (Hooke's law, stress–strain)  ↔  Acoustic wave theory (harmonics, Doppler)", "shelf": "bridges", "surface": "secular", "snippet": "Elasticity (Hooke's law, stress–strain) and Acoustic wave theory (harmonics, Doppler) are the same form in different domains. Hooke's linear restoring force gives the harmonic oscillator, and a contin", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_acoustic_wave_theory__wave_optics", "title": "Bridge: Acoustic wave theory (harmonics, Doppler)  ↔  Wave optics (Huygens, Snell's law, diffraction)", "shelf": "bridges", "surface": "secular", "snippet": "Acoustic wave theory (harmonics, Doppler) and Wave optics (Huygens, Snell's law, diffraction) are the same form in different domains. both are the wave equation in different media: Huygens' constructi", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_floor_hodge", "title": "The Hodge chain - from periods and topology to the classes that are not cycles", "shelf": "codex", "surface": "secular", "snippet": "Two trees. The transcendental: Riemann's periods (1857). The topological: Lefschetz's analysis situs of a variety and the (1,1) theorem (1924), de Rham's forms (1931). They become one in Hodge's harmo", "authority_tier": "engine_derived", "source": "Narrow Highway - a chain on the one map (operator seed)", "readable": false, "generated": false}, {"id": "card_alm_connection_tide_machine_is_fourier_synthesis", "title": "Almanac: The tide-predicting machine sums waves with gears -- Fourier synthesis made of brass, foretelling the sea", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  In 1872 Lord Kelvin built a machine of pulleys, wires, and gears that could predict the tides at any harbor for years ahead. It worked by Fourier SYNTHESIS: the tide is a sum of simple cos", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_bridge_theory_acoustic_wave_theory__celestial_mechanics_ephemeris_prediction", "title": "Bridge: Acoustic wave theory (harmonics, Doppler)  ↔  Celestial mechanics / ephemeris prediction", "shelf": "bridges", "surface": "secular", "snippet": "Acoustic wave theory (harmonics, Doppler) and Celestial mechanics / ephemeris prediction are the same form in different domains. small-integer ratio resonance: the octave is exactly 2:1 (440→880 Hz, s", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_dual_trigonometric__fourier_spectral", "title": "Duality: trigonometric  ↔  fourier_spectral  (harmonic basis)", "shelf": "bridges", "surface": "secular", "snippet": "A deep bridge between two forms — harmonic basis. Fourier analysis is trigonometry taken to a basis — any signal as a sum of sines and cosines", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_calc_molecular_vibration", "title": "Molecular bond vibration", "shelf": "calculations", "surface": "secular", "snippet": "Molecular bond vibration — chemistry. Formula: omega = sqrt(k/mu). Canonical FORM: periodic (x = A*cos(omega*t + phi)) — a chemical bond is a spring — the harmonic oscillator with the reduced mass mu ", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_calc_v_acoustics_harmonic_frequency", "title": "Harmonic frequency", "shelf": "calculations", "surface": "secular", "snippet": "Harmonic frequency — acoustics. Formula: f_n = n f_1. Canonical FORM: fourier_spectral (f(t) = sum c_n e^(i n omega t)) — engine verifier acoustics.harmonic_frequency — the deterministic check the con", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_alm_connection_major_triad_is_overtone_ratios", "title": "Almanac: The major chord is built into sound: harmonics 4:5:6 are the major triad", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  The major chord is not a human invention but a fact of physics that the engine confirmed across three domains. Any vibrating string or air column sounds a fundamental plus a series of harm", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_sys_wave", "title": "Waves & oscillation", "shelf": "systems", "surface": "secular", "snippet": "The same wave equation governs sound in air, light in the field, ripples on water, and a plucked string. The same harmonic oscillator is an LC circuit, a mass on a spring, and a pendulum — resonance a", "authority_tier": "reference", "source": "The recurring form — the system analogies (standard engineering) + the design they witness to", "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_src_mill_bochner_1946", "title": "S. Bochner 1946 — Vector fields and Ricci curvature", "shelf": "millennium", "surface": "secular", "snippet": "S. Bochner (1946). Vector fields and Ricci curvature. Bull. Amer. Math. Soc. 52 (1946) 776–797. DOI 10.1090/S0002-9904-1946-08647-4. Canonical: https://doi.org/10.1090/S0002-9904-1946-08647-4. Free co", "authority_tier": "reference", "source": "S. Bochner (1946), Bull. Amer. Math. Soc. 52 (1946) 776–797", "readable": false, "generated": false}, {"id": "card_calc_quantum_oscillator", "title": "Quantum harmonic oscillator", "shelf": "calculations", "surface": "secular", "snippet": "Quantum harmonic oscillator — physics. Formula: E_n = hbar omega (n + 1/2). Canonical FORM: periodic (x = A*cos(omega*t + phi)) — the oscillator quantized — evenly-spaced energy levels above a zero-po", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_calc_shm", "title": "Simple harmonic motion", "shelf": "calculations", "surface": "secular", "snippet": "Simple harmonic motion — physics. Formula: x = A cos(omega t + phi). Canonical FORM: periodic (x = A*cos(omega*t + phi)) — a restoring force proportional to displacement. Same form, different domain: ", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "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_floor_acoustics"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}