{"abstract":"The perfect fourth C4-F4 is named M4 and the augmented fourth C4-F#4 becomes an A4 only by accident of offsets.","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.","evaluation_group":"w2-music-interval-interval-naming","failed_approach":"Removing the unison from the perfect class names C4-C4 M1 instead of P1.","family":"w2-music-interval-interval-naming-perfect-class-membership","id":"FA-80906","implementations":{"attempt":{"sha256":"e8336dea42b46fc90183687e4147a534aafabd5ce85f2c1613fbf831834a69dd","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\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 (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', 'Eb4'], 'm3'), (['C4', 'G4'], 'P5'), (['C4', 'Gb4'], 'd5'), (['C4', 'F#4'], 'A4'), (['C4', 'C5'], 'P8'), (['C4', 'F5'], 'P11'), (['D4', 'D4'], 'P1')], [(['C4', 'Gb4'], 'd5'), (['C4', 'F#4'], 'A4'), (['C4', 'C5'], 'P8'), (['C4', 'D5'], 'M9'), (['C4', 'C4'], 'P1'), (['C4', 'C#4'], 'A1'), (['B#3', 'C4'], 'd2'), (['C4', 'Fb4'], 'd4')], [(['C4', 'C4'], 'P1'), (['C4', 'C#4'], 'A1'), (['B#3', 'C4'], 'd2'), (['E4', 'F4'], 'm2'), (['C4', 'B4'], 'M7'), (['C4', 'Bb4'], 'm7'), (['C4', 'C6'], 'P15'), (['C4', 'F5'], 'P11')], [(['C4', 'B4'], 'M7'), (['C4', 'Bb4'], 'm7'), (['C4', 'Bbb4'], 'd7'), (['C4', 'C6'], 'P15'), (['C4', 'G5'], 'P12'), (['D4', 'C4'], None), (['C4', 'Fb4'], 'd4'), (['D4', 'D4'], 'P1')], [(['C4', 'C5'], 'P8'), (['C4', 'G5'], 'P12'), (['C4', 'F5'], 'P11'), (['D4', 'C4'], None), (['C4', 'B#3'], None), (['B3', 'C4'], 'm2'), (['F4', 'B4'], 'A4'), (['D4', 'D4'], 'P1')]]\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":"8535af2513db675d66b2629c1198f20f0bfd7a2c5ac0fc45a432ab94186f683c","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\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, 5, 8):\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', 'Eb4'], 'm3'), (['C4', 'G4'], 'P5'), (['C4', 'Gb4'], 'd5'), (['C4', 'F#4'], 'A4'), (['C4', 'C5'], 'P8'), (['C4', 'F5'], 'P11'), (['D4', 'D4'], 'P1')], [(['C4', 'Gb4'], 'd5'), (['C4', 'F#4'], 'A4'), (['C4', 'C5'], 'P8'), (['C4', 'D5'], 'M9'), (['C4', 'C4'], 'P1'), (['C4', 'C#4'], 'A1'), (['B#3', 'C4'], 'd2'), (['C4', 'Fb4'], 'd4')], [(['C4', 'C4'], 'P1'), (['C4', 'C#4'], 'A1'), (['B#3', 'C4'], 'd2'), (['E4', 'F4'], 'm2'), (['C4', 'B4'], 'M7'), (['C4', 'Bb4'], 'm7'), (['C4', 'C6'], 'P15'), (['C4', 'F5'], 'P11')], [(['C4', 'B4'], 'M7'), (['C4', 'Bb4'], 'm7'), (['C4', 'Bbb4'], 'd7'), (['C4', 'C6'], 'P15'), (['C4', 'G5'], 'P12'), (['D4', 'C4'], None), (['C4', 'Fb4'], 'd4'), (['D4', 'D4'], 'P1')], [(['C4', 'C5'], 'P8'), (['C4', 'G5'], 'P12'), (['C4', 'F5'], 'P11'), (['D4', 'C4'], None), (['C4', 'B#3'], None), (['B3', 'C4'], 'm2'), (['F4', 'B4'], 'A4'), (['D4', 'D4'], 'P1')]]\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"},"fixed":{"sha256":"0d2ae9a3515c9bd4d168a85662c150aad7fdaadfffd60586fce403b2a87cf69c","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\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', 'Eb4'], 'm3'), (['C4', 'G4'], 'P5'), (['C4', 'Gb4'], 'd5'), (['C4', 'F#4'], 'A4'), (['C4', 'C5'], 'P8'), (['C4', 'F5'], 'P11'), (['D4', 'D4'], 'P1')], [(['C4', 'Gb4'], 'd5'), (['C4', 'F#4'], 'A4'), (['C4', 'C5'], 'P8'), (['C4', 'D5'], 'M9'), (['C4', 'C4'], 'P1'), (['C4', 'C#4'], 'A1'), (['B#3', 'C4'], 'd2'), (['C4', 'Fb4'], 'd4')], [(['C4', 'C4'], 'P1'), (['C4', 'C#4'], 'A1'), (['B#3', 'C4'], 'd2'), (['E4', 'F4'], 'm2'), (['C4', 'B4'], 'M7'), (['C4', 'Bb4'], 'm7'), (['C4', 'C6'], 'P15'), (['C4', 'F5'], 'P11')], [(['C4', 'B4'], 'M7'), (['C4', 'Bb4'], 'm7'), (['C4', 'Bbb4'], 'd7'), (['C4', 'C6'], 'P15'), (['C4', 'G5'], 'P12'), (['D4', 'C4'], None), (['C4', 'Fb4'], 'd4'), (['D4', 'D4'], 'P1')], [(['C4', 'C5'], 'P8'), (['C4', 'G5'], 'P12'), (['C4', 'F5'], 'P11'), (['D4', 'C4'], None), (['C4', 'B#3'], None), (['B3', 'C4'], 'm2'), (['F4', 'B4'], 'A4'), (['D4', 'D4'], 'P1')]]\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-perfect-class-membership","generated_at":"2026-09-29T14:49:58.077160+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.","repair":"Restore the perfect class membership step so that it reads `simple in (1, 4, 5)`.","root_cause":"The perfect-class set lists 1, 5 and 8, but simple numbers are reduced to 1..7 so 8 never occurs and 4 is missing.","sha256":"0f57471c795dbda1e92cd1c0e6744276a2693e4234c675a22ca972118a4ee3d3","title":"Interval quality and number naming: fourth handled as an imperfect interval · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.799,"exit_code":1,"observations":[{"actual":"M3","check":"oracle 0","expected":"M3","passed":true},{"actual":"m3","check":"oracle 1","expected":"m3","passed":true},{"actual":"P5","check":"oracle 2","expected":"P5","passed":true},{"actual":"d5","check":"oracle 3","expected":"d5","passed":true},{"actual":"A4","check":"oracle 4","expected":"A4","passed":true},{"actual":"M8","check":"oracle 5","expected":"P8","passed":false},{"actual":"P11","check":"oracle 6","expected":"P11","passed":true},{"actual":"M1","check":"oracle 7","expected":"P1","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": \"M3\", \"expected\": \"M3\", \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": \"m3\", \"expected\": \"m3\", \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": \"P5\", \"expected\": \"P5\", \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": \"d5\", \"expected\": \"d5\", \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": \"A4\", \"expected\": \"A4\", \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": \"M8\", \"expected\": \"P8\", \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": \"P11\", \"expected\": \"P11\", \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": \"M1\", \"expected\": \"P1\", \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.449,"exit_code":1,"observations":[{"actual":"M3","check":"oracle 0","expected":"M3","passed":true},{"actual":"m3","check":"oracle 1","expected":"m3","passed":true},{"actual":"P5","check":"oracle 2","expected":"P5","passed":true},{"actual":"d5","check":"oracle 3","expected":"d5","passed":true},{"actual":"A4","check":"oracle 4","expected":"A4","passed":true},{"actual":"P8","check":"oracle 5","expected":"P8","passed":true},{"actual":"M11","check":"oracle 6","expected":"P11","passed":false},{"actual":"P1","check":"oracle 7","expected":"P1","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": \"M3\", \"expected\": \"M3\", \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": \"m3\", \"expected\": \"m3\", \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": \"P5\", \"expected\": \"P5\", \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": \"d5\", \"expected\": \"d5\", \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": \"A4\", \"expected\": \"A4\", \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": \"P8\", \"expected\": \"P8\", \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": \"M11\", \"expected\": \"P11\", \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": \"P1\", \"expected\": \"P1\", \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":41.165,"exit_code":0,"observations":[{"actual":"M3","check":"oracle 0","expected":"M3","passed":true},{"actual":"m3","check":"oracle 1","expected":"m3","passed":true},{"actual":"P5","check":"oracle 2","expected":"P5","passed":true},{"actual":"d5","check":"oracle 3","expected":"d5","passed":true},{"actual":"A4","check":"oracle 4","expected":"A4","passed":true},{"actual":"P8","check":"oracle 5","expected":"P8","passed":true},{"actual":"P11","check":"oracle 6","expected":"P11","passed":true},{"actual":"P1","check":"oracle 7","expected":"P1","passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": \"M3\", \"expected\": \"M3\", \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": \"m3\", \"expected\": \"m3\", \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": \"P5\", \"expected\": \"P5\", \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": \"d5\", \"expected\": \"d5\", \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": \"A4\", \"expected\": \"A4\", \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": \"P8\", \"expected\": \"P8\", \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": \"P11\", \"expected\": \"P11\", \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": \"P1\", \"expected\": \"P1\", \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}