{"query": "Tuning — equal temperament and the comma", "count": 20, "results": [{"id": "card_music_tuning", "title": "Tuning — equal temperament and the comma", "shelf": "codex", "surface": "secular", "snippet": "Twelve-tone equal temperament sets every semitone at the irrational ratio 2^(1/12); it is a deliberate compromise that spreads the Pythagorean comma evenly so every key is playable. A tuning is a CHOI", "authority_tier": "engine_derived", "source": "Narrow Highway — music", "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_theory_tuning_systems_comma", "title": "Tuning systems & the Pythagorean comma", "shelf": "theories", "surface": "secular", "snippet": "Tuning systems & the Pythagorean comma — an engine domain that can touch it: music_theory. Calibration: seals — a deterministic verifier can CONFIRM or BREAK checkable claims drawn from it, and seal t", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_n_ff27b07c4577", "title": "Fluid dynamics as the behavior of the axes", "shelf": "concepts", "surface": "secular", "snippet": "Matt: 'Fluid dynamics as behavior of axes? something along that line.' The axes are not static — they FLOW and redistribute as the map grows. Fluid dynamics may describe their behavior: a turbulent fl", "authority_tier": "matt", "source": "Operator's seed (Matt) — honest grade: resonance", "readable": false, "generated": false}, {"id": "card_n_cdb747a427d2", "title": "Electronics — the resonant chain, from Ohm's law to the radio wave", "shelf": "science", "surface": "secular", "snippet": "One sealed chain runs the whole bench: Ohm's law (V = I·R), the capacitor's\nexponential clock (one time constant → 63.2% charged), the diode's exponential gate (current\ndoubles every ln2·nVT ≈ 17.9 mV", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_bridge_theory_tuning_systems_comma__fundamental_theorem_of_arithmetic", "title": "Bridge: Tuning systems & the Pythagorean comma  ↔  Fundamental theorem of arithmetic (unique factorization)", "shelf": "bridges", "surface": "secular", "snippet": "Tuning systems & the Pythagorean comma and Fundamental theorem of arithmetic (unique factorization) are the same form in different domains. pitch ratios are integer factorizations; the comma is 3^12 a", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_alm_connection_syntonic_comma", "title": "Almanac: The syntonic comma: the pure third and the Pythagorean third disagree by 81:80", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  Music has TWO ways to build a major third, and they do not match. music_theory confirmed the pure (just) major third is the simple ratio 5:4 (64 Hz to 80 Hz) -- the one nature gives in the", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_n_9d42516b140c", "title": "Quartz at 32,768 Hz — a power of two on the wrist", "shelf": "science", "surface": "secular", "snippet": "Every quartz watch cuts a tuning fork to hum at exactly 2^15 = 32,768 Hz, sealed, and\n32768 / 2^15 = 1: run the signal through fifteen binary flip-flops, each halving the frequency,\nand the last ticks", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_c_106861f9474c", "title": "Varactor — tuning by voltage ↔ Oscillator — LC resonance, the bench's own S", "shelf": "connections", "surface": null, "snippet": "since f ∝ 1/√C, halving the capacitance raises the frequency by exactly √2  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_c_b432c299ac6e", "title": "Varactor — tuning by voltage ↔ Electronics — the resonant chain, from Ohm's", "shelf": "connections", "surface": null, "snippet": "since f ∝ 1/√C, halving the capacitance raises the frequency by exactly √2 ... and the tempting error 'halving C halves f' seals BROKEN with residual √2 − 1/2  — a concord the card itself states; mine", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_n_f9e74aa145cc", "title": "Varactor — tuning by voltage", "shelf": "science", "surface": "secular", "snippet": "A reverse-biased junction is a capacitor whose plates move with voltage — so voltage\ntunes frequency. The law that seals is exact: since f ∝ 1/√C, halving the capacitance raises\nthe frequency by exact", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_seal_c4ba7c9a50a6c988c0dbde3b1d64ac57b5fbf95aa4d92d83cc9da63a292e462a", "title": "Receipt c4ba7c9a50a6… — sealed: record", "shelf": "seals", "surface": "secular", "snippet": "{\n \"anchors\": [],\n \"axis_coords\": {\n  \"axis\": \"mathematics\",\n  \"dimensions\": [\n   \"reasoning\"\n  ]\n },\n \"gate_results\": [\n  {\n   \"details\": {\n    \"broken_at\": null,\n    \"confirmed_steps\": 1,\n    \"error", "authority_tier": "engine_derived", "source": "Narrow Highway engine — sealed record", "readable": false, "generated": false}, {"id": "card_floor_music", "title": "Music — interval, tuning, and the harmonic series", "shelf": "codex", "surface": "secular", "snippet": "Music is number made audible: the consonant intervals are small whole-number frequency ratios (octave 2:1, fifth 3:2, fourth 4:3), and a scale is a tuning that divides the octave — equal temperament b", "authority_tier": "engine_derived", "source": "Narrow Highway — music", "readable": false, "generated": false}, {"id": "card_src_book_17571", "title": "Piano Tuning: A Simple and Accurate Method for Amateurs — J. Cree (Jerry Cree) Fischer", "shelf": "gutenberg", "surface": "secular", "snippet": "Piano Tuning: A Simple and Accurate Method for Amateurs, by J. Cree (Jerry Cree) Fischer. Subjects: Piano -- Tuning. Read the full text (public domain): https://www.gutenberg.org/ebooks/17571", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "readable": true, "generated": false}, {"id": "card_src_word_tuning", "title": "tuning", "shelf": "dictionary", "surface": "secular", "snippet": "a. & n. from Tune, v. Tuning fork (Mus.), a steel instrument consisting of two prongs and a handle, which, being struck, gives a certain fixed tone. It is used for tuning instruments, or for ascertain", "authority_tier": "reference", "source": "webster-1913", "readable": false, "generated": false}, {"id": "card_src_word_temperament", "title": "temperament", "shelf": "dictionary", "surface": "secular", "snippet": "temperament: (noun) your usual mood — syn: disposition · (noun) excessive emotionalism or irritability and excitability (especially when displayed openly) · (noun) an adjustment of the intervals (as i", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_book_57354", "title": "Theory and Practice of Piano Construction With a Detailed, Practical Method for Tuning — William Braid White", "shelf": "gutenberg", "surface": "secular", "snippet": "Theory and Practice of Piano Construction With a Detailed, Practical Method for Tuning, by William Braid White. Subjects: Piano -- Tuning; Piano -- Construction. Read the full text (public domain): ht", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "readable": true, "generated": false}, {"id": "card_src_pron_tuning", "title": "tuning", "shelf": "pronunciation", "surface": "secular", "snippet": "tuning: pronounced (ARPABET) T UW1 N IH0 NG. From the CMU Pronouncing Dictionary — the standard machine-readable pronunciations of North American English.", "authority_tier": "reference", "source": "CMU Pronouncing Dictionary (cmudict) — BSD-2-Clause, Carnegie Mellon", "readable": false, "generated": false}, {"id": "card_src_rfc_7363", "title": "RFC7363 — Self-Tuning Distributed Hash Table (DHT) for REsource LOcation And Discovery (RELOAD)", "shelf": "rfcs", "surface": "secular", "snippet": "RFC7363: Self-Tuning Distributed Hash Table (DHT) for REsource LOcation And Discovery (RELOAD) (September 2014). Status: PROPOSED STANDARD.", "authority_tier": "reference", "source": "The RFC Index (RFC Editor / IETF) — public domain", "readable": false, "generated": false}, {"id": "card_n_b824114e7478", "title": "Easton: Shekel", "shelf": "dictionary", "surface": "secular", "snippet": "Weight, the common standard both of weight and value among the Hebrews. It is estimated at 220 English grains, or a little more than half an ounce avoirdupois. The “shekel of the sanctuary” (Ex. 30:13", "authority_tier": "external_aligned", "source": "Matthew Easton, Illustrated Bible Dictionary (1897)", "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_music_tuning"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}