{"abstract":"C4 to E4 is named AA2 instead of M3, because every generic number comes out one too small.","category":"Music interval and transposition theory","checks":8,"contract":"Input [lower, upper] spelled pitches (letter, # or b accidentals, nonnegative octave). The generic number counts letter steps plus 7 per spelled octave plus one; quality compares the semitone span with the major/perfect reference (compounds add 12 per octave). Perfect class for simple numbers 1, 4, 5: P, A, d, AA, dd; others: M, m, A, d, AA, dd. Descending letter order or unrepresentable quality returns None.","contract_signature":"x","evaluation_group":"w2-music-interval-interval-naming","failed_approach":"Adding the inclusive count only below the octave still names C4 to C5 a seventh and every compound interval one too small.","family":"w2-music-interval-interval-naming-generic-number","id":"FA-80891","implementations":{"attempt":{"sha256":"330435766426599facf031c466325a584d99b3673675fbb0a0b17251615bdab3","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    def parse(s):\n        if not isinstance(s, str) or len(s) < 2 or s[0] not in base:\n            return None\n        i = 1\n        acc = 0\n        while i < len(s) and s[i] in '#b':\n            acc += 1 if s[i] == '#' else -1\n            i += 1\n        if not s[i:].isdigit():\n            return None\n        octave = int(s[i:])\n        return ['CDEFGAB'.index(s[0]) + 7 * octave, 12 * octave + base[s[0]] + acc]\n    if not isinstance(x, list) or len(x) != 2:\n        return None\n    lo, hi = parse(x[0]), parse(x[1])\n    if lo is None or hi is None:\n        return None\n    steps = hi[0] - lo[0]\n    semis = hi[1] - lo[1]\n    if steps < 0:\n        return None\n    number = steps + 1 if steps < 7 else steps\n    simple = (number - 1) % 7 + 1\n    ref = [0, 2, 4, 5, 7, 9, 11][simple - 1] + 12 * ((number - 1) // 7)\n    d = semis - ref\n    if simple in (1, 4, 5):\n        q = {0: 'P', 1: 'A', -1: 'd', 2: 'AA', -2: 'dd'}.get(d)\n    else:\n        q = {0: 'M', -1: 'm', 1: 'A', -2: 'd', 2: 'AA', -3: 'dd'}.get(d)\n    if q is None:\n        return None\n    return q + str(number)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[(['C4', 'E4'], 'M3'), (['C4', 'G4'], 'P5'), (['C4', 'C5'], 'P8'), (['C4', 'G5'], 'P12'), (['D4', 'C4'], None), (['C4', 'B#3'], None), (['Cb4', 'B#3'], None), (['C4', 'Cx4'], None)], [(['C4', 'E4'], 'M3'), (['C4', 'Eb4'], 'm3'), (['C4', 'G4'], 'P5'), (['C4', 'Gb4'], 'd5'), (['C4', 'F#4'], 'A4'), (['C4', 'D5'], 'M9'), (['C4', 'F5'], 'P11'), (['C4', 'Cx4'], None)], [(['C4', 'G4'], 'P5'), (['C4', 'Gb4'], 'd5'), (['C4', 'F#4'], 'A4'), (['C4', 'C5'], 'P8'), (['C4', 'D5'], 'M9'), (['C4', 'C4'], 'P1'), (['C4', 'C6'], 'P15'), (['C4', 'D#6'], 'A16')], [(['C4', 'Gb4'], 'd5'), (['C4', 'C5'], 'P8'), (['C4', 'D5'], 'M9'), (['C4', 'C4'], 'P1'), (['C4', 'C#4'], 'A1'), (['B#3', 'C4'], 'd2'), (['C4', 'G5'], 'P12'), (['Bb2', 'C4'], 'M9')], [(['C4', 'F#4'], 'A4'), (['C4', 'D5'], 'M9'), (['C4', 'C#4'], 'A1'), (['B#3', 'C4'], 'd2'), (['E4', 'F4'], 'm2'), (['C4', 'B4'], 'M7'), (['C4', 'F5'], 'P11'), (['C4', 'A5'], 'M13')]]\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":"b5c8998a658aeccb4c444aed4756972e49cd84402495c58633dad43b19e90ed9","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    def parse(s):\n        if not isinstance(s, str) or len(s) < 2 or s[0] not in base:\n            return None\n        i = 1\n        acc = 0\n        while i < len(s) and s[i] in '#b':\n            acc += 1 if s[i] == '#' else -1\n            i += 1\n        if not s[i:].isdigit():\n            return None\n        octave = int(s[i:])\n        return ['CDEFGAB'.index(s[0]) + 7 * octave, 12 * octave + base[s[0]] + acc]\n    if not isinstance(x, list) or len(x) != 2:\n        return None\n    lo, hi = parse(x[0]), parse(x[1])\n    if lo is None or hi is None:\n        return None\n    steps = hi[0] - lo[0]\n    semis = hi[1] - lo[1]\n    if steps < 0:\n        return None\n    number = steps\n    simple = (number - 1) % 7 + 1\n    ref = [0, 2, 4, 5, 7, 9, 11][simple - 1] + 12 * ((number - 1) // 7)\n    d = semis - ref\n    if simple in (1, 4, 5):\n        q = {0: 'P', 1: 'A', -1: 'd', 2: 'AA', -2: 'dd'}.get(d)\n    else:\n        q = {0: 'M', -1: 'm', 1: 'A', -2: 'd', 2: 'AA', -3: 'dd'}.get(d)\n    if q is None:\n        return None\n    return q + str(number)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[(['C4', 'E4'], 'M3'), (['C4', 'G4'], 'P5'), (['C4', 'C5'], 'P8'), (['C4', 'G5'], 'P12'), (['D4', 'C4'], None), (['C4', 'B#3'], None), (['Cb4', 'B#3'], None), (['C4', 'Cx4'], None)], [(['C4', 'E4'], 'M3'), (['C4', 'Eb4'], 'm3'), (['C4', 'G4'], 'P5'), (['C4', 'Gb4'], 'd5'), (['C4', 'F#4'], 'A4'), (['C4', 'D5'], 'M9'), (['C4', 'F5'], 'P11'), (['C4', 'Cx4'], None)], [(['C4', 'G4'], 'P5'), (['C4', 'Gb4'], 'd5'), (['C4', 'F#4'], 'A4'), (['C4', 'C5'], 'P8'), (['C4', 'D5'], 'M9'), (['C4', 'C4'], 'P1'), (['C4', 'C6'], 'P15'), (['C4', 'D#6'], 'A16')], [(['C4', 'Gb4'], 'd5'), (['C4', 'C5'], 'P8'), (['C4', 'D5'], 'M9'), (['C4', 'C4'], 'P1'), (['C4', 'C#4'], 'A1'), (['B#3', 'C4'], 'd2'), (['C4', 'G5'], 'P12'), (['Bb2', 'C4'], 'M9')], [(['C4', 'F#4'], 'A4'), (['C4', 'D5'], 'M9'), (['C4', 'C#4'], 'A1'), (['B#3', 'C4'], 'd2'), (['E4', 'F4'], 'm2'), (['C4', 'B4'], 'M7'), (['C4', 'F5'], 'P11'), (['C4', 'A5'], 'M13')]]\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-interval-naming-generic-number","generated_at":"2026-09-29T14:49:57.993376+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 generic number is the count of letter steps between the notes rather than the inclusive count of letters.","sha256":"1f852b0ad8f225221a27cf0f0b3ba49a35687579a99ed7de4cbecc54cd98e1e7","title":"Interval quality and number naming: generic number counts letter gaps instead of letters · 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":41.892,"exit_code":1,"observations":[{"actual":"M3","check":"oracle 0","expected":"M3","passed":true},{"actual":"P5","check":"oracle 1","expected":"P5","passed":true},{"actual":"A7","check":"oracle 2","expected":"P8","passed":false},{"actual":"AA11","check":"oracle 3","expected":"P12","passed":false},{"actual":null,"check":"oracle 4","expected":null,"passed":true},{"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\": \"M3\", \"expected\": \"M3\", \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": \"P5\", \"expected\": \"P5\", \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": \"A7\", \"expected\": \"P8\", \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": \"AA11\", \"expected\": \"P12\", \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"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":38.507,"exit_code":1,"observations":[{"actual":"AA2","check":"oracle 0","expected":"M3","passed":false},{"actual":"AA4","check":"oracle 1","expected":"P5","passed":false},{"actual":"A7","check":"oracle 2","expected":"P8","passed":false},{"actual":"AA11","check":"oracle 3","expected":"P12","passed":false},{"actual":null,"check":"oracle 4","expected":null,"passed":true},{"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\": \"AA2\", \"expected\": \"M3\", \"passed\": false}, {\"check\": \"oracle 1\", \"actual\": \"AA4\", \"expected\": \"P5\", \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": \"A7\", \"expected\": \"P8\", \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": \"AA11\", \"expected\": \"P12\", \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"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."}}