{"abstract":"A major third up from C is spelled on F (Fb4) instead of E4, because the letter advances one step too far.","category":"Music interval and transposition theory","checks":8,"contract":"Input [note, interval, direction]. note: letter, # or b accidentals, nonnegative octave. interval: quality letter (P, M, m, A, d) and generic number >= 1 with perfect-class numbers 1, 4, 5 (compounds reduce by 7). Direction up or down moves the letter by number-1 steps and the pitch by the interval size; the result is spelled with the moved letter, octave taken from the letter position. Results needing more than two accidentals, or a negative octave, return None.","contract_signature":"x","evaluation_group":"w2-music-interval-spelled-transposition","failed_approach":"Reducing the displacement modulo seven drops compound octaves and turns every downward move into an upward letter move.","family":"w2-music-interval-spelled-transposition-letter-step-count","id":"FA-80916","implementations":{"attempt":{"sha256":"92007f0f2d274e1561ac2f9df72d91f8e782ee1653d2b73280515cf33bdf9433","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    base = {'C': 0, 'D': 2, 'E': 4, 'F': 5, 'G': 7, 'A': 9, 'B': 11}\n    if not isinstance(x, list) or len(x) != 3:\n        return None\n    note, ivl, direction = x\n    if direction not in ('up', 'down'):\n        return None\n    if not isinstance(note, str) or len(note) < 2 or note[0] not in base:\n        return None\n    i = 1\n    acc = 0\n    while i < len(note) and note[i] in '#b':\n        acc += 1 if note[i] == '#' else -1\n        i += 1\n    if not note[i:].isdigit():\n        return None\n    octave = int(note[i:])\n    if not isinstance(ivl, str) or len(ivl) < 2 or not ivl[1:].isdigit():\n        return None\n    quality = ivl[0]\n    number = int(ivl[1:])\n    if number < 1:\n        return None\n    simple = (number - 1) % 7 + 1\n    perfect = simple in (1, 4, 5)\n    offsets = {'P': 0, 'A': 1, 'd': -1} if perfect else {'M': 0, 'm': -1, 'A': 1, 'd': -2}\n    if quality not in offsets:\n        return None\n    size = [0, 2, 4, 5, 7, 9, 11][simple - 1] + 12 * ((number - 1) // 7) + offsets[quality]\n    sign = 1 if direction == 'up' else -1\n    idx = 'CDEFGAB'.index(note[0]) + 7 * octave + sign * (number - 1) % 7\n    pitch = 12 * octave + base[note[0]] + acc + sign * size\n    letter = 'CDEFGAB'[idx % 7]\n    new_octave = idx // 7\n    new_acc = pitch - (12 * new_octave + base[letter])\n    if abs(new_acc) > 2 or new_octave < 0:\n        return None\n    return letter + ('#' * new_acc if new_acc > 0 else 'b' * -new_acc) + str(new_octave)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[(['C4', 'M3', 'up'], 'E4'), (['C4', 'M3', 'down'], 'Ab3'), (['B3', 'm2', 'up'], 'C4'), (['Cb4', 'd3', 'up'], None), (['C4', 'M9', 'up'], 'D5'), (['C0', 'm2', 'down'], None), (['C4', 'X3', 'up'], None), (['C4', 'M4', 'up'], None)], [(['C4', 'M3', 'up'], 'E4'), (['C4', 'M3', 'down'], 'Ab3'), (['B3', 'm2', 'up'], 'C4'), (['C4', 'm2', 'down'], 'B3'), (['C4', 'M10', 'down'], 'Ab2'), (['C4', 'M4', 'up'], None), (['C4', 'P3', 'up'], None), (['C4', 'M3', 'sideways'], None)], [(['C4', 'M3', 'up'], 'E4'), (['C4', 'M3', 'down'], 'Ab3'), (['B3', 'm2', 'up'], 'C4'), (['C4', 'm2', 'down'], 'B3'), (['E4', 'A4', 'up'], 'A#4'), (['F#4', 'A4', 'up'], 'B#4'), (['C4', 'P8', 'up'], 'C5'), (['C5', 'P15', 'down'], 'C3')], [(['C4', 'm2', 'down'], 'B3'), (['E4', 'A4', 'up'], 'A#4'), (['F#4', 'A4', 'up'], 'B#4'), (['C4', 'd5', 'up'], 'Gb4'), (['C4', 'd7', 'up'], 'Bbb4'), (['C4', 'd3', 'up'], 'Ebb4'), (['C4', 'M9', 'up'], 'D5'), (['D4', 'd4', 'down'], 'A#3')], [(['E4', 'A4', 'up'], 'A#4'), (['C4', 'd5', 'up'], 'Gb4'), (['C4', 'd7', 'up'], 'Bbb4'), (['C4', 'd3', 'up'], 'Ebb4'), (['Db4', 'd3', 'up'], 'Fbb4'), (['C4', 'P8', 'up'], 'C5'), (['C4', 'M10', 'down'], 'Ab2'), (['F4', 'A4', 'down'], 'Cb4')]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"oracle %d\" % i, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"025b196689b08770daa015dd9b7b548e535f0ea4557d0bd077ac02f0072e2674","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    base = {'C': 0, 'D': 2, 'E': 4, 'F': 5, 'G': 7, 'A': 9, 'B': 11}\n    if not isinstance(x, list) or len(x) != 3:\n        return None\n    note, ivl, direction = x\n    if direction not in ('up', 'down'):\n        return None\n    if not isinstance(note, str) or len(note) < 2 or note[0] not in base:\n        return None\n    i = 1\n    acc = 0\n    while i < len(note) and note[i] in '#b':\n        acc += 1 if note[i] == '#' else -1\n        i += 1\n    if not note[i:].isdigit():\n        return None\n    octave = int(note[i:])\n    if not isinstance(ivl, str) or len(ivl) < 2 or not ivl[1:].isdigit():\n        return None\n    quality = ivl[0]\n    number = int(ivl[1:])\n    if number < 1:\n        return None\n    simple = (number - 1) % 7 + 1\n    perfect = simple in (1, 4, 5)\n    offsets = {'P': 0, 'A': 1, 'd': -1} if perfect else {'M': 0, 'm': -1, 'A': 1, 'd': -2}\n    if quality not in offsets:\n        return None\n    size = [0, 2, 4, 5, 7, 9, 11][simple - 1] + 12 * ((number - 1) // 7) + offsets[quality]\n    sign = 1 if direction == 'up' else -1\n    idx = 'CDEFGAB'.index(note[0]) + 7 * octave + sign * number\n    pitch = 12 * octave + base[note[0]] + acc + sign * size\n    letter = 'CDEFGAB'[idx % 7]\n    new_octave = idx // 7\n    new_acc = pitch - (12 * new_octave + base[letter])\n    if abs(new_acc) > 2 or new_octave < 0:\n        return None\n    return letter + ('#' * new_acc if new_acc > 0 else 'b' * -new_acc) + str(new_octave)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[(['C4', 'M3', 'up'], 'E4'), (['C4', 'M3', 'down'], 'Ab3'), (['B3', 'm2', 'up'], 'C4'), (['Cb4', 'd3', 'up'], None), (['C4', 'M9', 'up'], 'D5'), (['C0', 'm2', 'down'], None), (['C4', 'X3', 'up'], None), (['C4', 'M4', 'up'], None)], [(['C4', 'M3', 'up'], 'E4'), (['C4', 'M3', 'down'], 'Ab3'), (['B3', 'm2', 'up'], 'C4'), (['C4', 'm2', 'down'], 'B3'), (['C4', 'M10', 'down'], 'Ab2'), (['C4', 'M4', 'up'], None), (['C4', 'P3', 'up'], None), (['C4', 'M3', 'sideways'], None)], [(['C4', 'M3', 'up'], 'E4'), (['C4', 'M3', 'down'], 'Ab3'), (['B3', 'm2', 'up'], 'C4'), (['C4', 'm2', 'down'], 'B3'), (['E4', 'A4', 'up'], 'A#4'), (['F#4', 'A4', 'up'], 'B#4'), (['C4', 'P8', 'up'], 'C5'), (['C5', 'P15', 'down'], 'C3')], [(['C4', 'm2', 'down'], 'B3'), (['E4', 'A4', 'up'], 'A#4'), (['F#4', 'A4', 'up'], 'B#4'), (['C4', 'd5', 'up'], 'Gb4'), (['C4', 'd7', 'up'], 'Bbb4'), (['C4', 'd3', 'up'], 'Ebb4'), (['C4', 'M9', 'up'], 'D5'), (['D4', 'd4', 'down'], 'A#3')], [(['E4', 'A4', 'up'], 'A#4'), (['C4', 'd5', 'up'], 'Gb4'), (['C4', 'd7', 'up'], 'Bbb4'), (['C4', 'd3', 'up'], 'Ebb4'), (['Db4', 'd3', 'up'], 'Fbb4'), (['C4', 'P8', 'up'], 'C5'), (['C4', 'M10', 'down'], 'Ab2'), (['F4', 'A4', 'down'], 'Cb4')]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"oracle %d\" % i, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"A deterministic bounded teaching model with a stipulated toy contract; it is not a complete music notation or theory engine. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-music-interval-spelled-transposition-letter-step-count","generated_at":"2026-09-29T14:49:58.077875+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Pitch spelling and interval arithmetic decide the notes that notation, transposition and analysis tools display or play.","root_cause":"The letter displacement uses the generic number itself, but a third spans only two letter steps.","sha256":"1062776b477cfcd85563f990593b6208d984f8b757236c030873b3a90a013bfe","title":"Spelled transposition by named interval: letter moved by the full generic number · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":42.458,"exit_code":1,"observations":[{"actual":"E4","check":"oracle 0","expected":"E4","passed":true},{"actual":null,"check":"oracle 1","expected":"Ab3","passed":false},{"actual":"C4","check":"oracle 2","expected":"C4","passed":true},{"actual":null,"check":"oracle 3","expected":null,"passed":true},{"actual":null,"check":"oracle 4","expected":"D5","passed":false},{"actual":null,"check":"oracle 5","expected":null,"passed":true},{"actual":null,"check":"oracle 6","expected":null,"passed":true},{"actual":null,"check":"oracle 7","expected":null,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": \"E4\", \"expected\": \"E4\", \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": null, \"expected\": \"Ab3\", \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": \"C4\", \"expected\": \"C4\", \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": null, \"expected\": \"D5\", \"passed\": false}, {\"check\": \"oracle 5\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": null, \"expected\": null, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":38.5,"exit_code":1,"observations":[{"actual":"Fb4","check":"oracle 0","expected":"E4","passed":false},{"actual":"G#3","check":"oracle 1","expected":"Ab3","passed":false},{"actual":"Dbb4","check":"oracle 2","expected":"C4","passed":false},{"actual":null,"check":"oracle 3","expected":null,"passed":true},{"actual":"Ebb5","check":"oracle 4","expected":"D5","passed":false},{"actual":null,"check":"oracle 5","expected":null,"passed":true},{"actual":null,"check":"oracle 6","expected":null,"passed":true},{"actual":null,"check":"oracle 7","expected":null,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": \"Fb4\", \"expected\": \"E4\", \"passed\": false}, {\"check\": \"oracle 1\", \"actual\": \"G#3\", \"expected\": \"Ab3\", \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": \"Dbb4\", \"expected\": \"C4\", \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": \"Ebb5\", \"expected\": \"D5\", \"passed\": false}, {\"check\": \"oracle 5\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": null, \"expected\": null, \"passed\": true}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}