FAILURE MAP
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FA-80861 / Music interval and transposition theory / Open access

Spelled pitch to MIDI key number: double sharp glyph not consumed · case 01

Any spelling with an x double sharp (Fx4, Cx-1) is rejected as malformed.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The accidental scanner only consumes # and b, so the x glyph is left in the octave field.

VERIFIED REPAIR

Restore the accidental run step so that it reads `x[i] in '#bx'`.

Unsuccessful approach: Admitting x but capping the scan at two accidentals rejects legal triple accidentals such as Dbbb4 and Cxx4.

Case contract

Input a spelled pitch string: uppercase letter A-G, any run of accidentals (# = +1, b = -1, x = +2), then a signed integer octave where C4 = 60 and C-1 = 0. Return the MIDI key number, or None for malformed text or results outside 0..127.

Why this case matters

Pitch spelling and interval arithmetic decide the notes that notation, transposition and analysis tools display or play.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    names = {'C': 0, 'D': 2, 'E': 4, 'F': 5, 'G': 7, 'A': 9, 'B': 11}
    if not isinstance(x, str) or len(x) < 2 or x[0] not in names:
        return None
    i = 1
    acc = 0
    while i < len(x) and x[i] in '#b':
        acc += {'#': 1, 'b': -1, 'x': 2}[x[i]]
        i += 1
    tail = x[i:]
    neg = tail.startswith('-')
    digits = tail[1:] if neg else tail
    if not digits.isdigit():
        return None
    octave = -int(digits) if neg else int(digits)
    midi = (octave + 1) * 12 + names[x[0]] + acc
    if midi < 0 or midi > 127:
        return None
    return midi
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('C4', 60), ('A4', 69), ('C-1', 0), ('G9', 127), ('G#9', None), ('Fx4', 67), ('Dbbb4', 59), ('Cxx4', 64)], [('G9', 127), ('G#9', None), ('Ab9', None), ('B#3', 60), ('Cb4', 59), ('Dbbb4', 59), ('Cx-1', 2), ('Bx-1', 13)], [('B#3', 60), ('Cb4', 59), ('Fx4', 67), ('Ebb4', 62), ('Dbbb4', 59), ('Cb-1', None), ('B-1', 11), ('Cxx4', 64)], [('Dbbb4', 59), ('Cb-1', None), ('B-1', 11), ('E4', 64), ('F4', 65), ('B4', 71), ('Cx-1', 2), ('Bx-1', 13)], [('Fx4', 67), ('Dbbb4', 59), ('F4', 65), ('B4', 71), ('Bb3', 58), ('C0', 12), ('D#0', 15), ('Cxx4', 64)]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("oracle %d" % i, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
oracle 06060Passed
oracle 16969Passed
oracle 200Passed
oracle 3127127Passed
oracle 4NoneNonePassed
oracle 5None67Failed
oracle 65959Passed
oracle 7None64Failed

SHA-256 / 91b8280f9c895b67512ff42d563ed243a41190f508bf7e789e4178a6631e9f19

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    names = {'C': 0, 'D': 2, 'E': 4, 'F': 5, 'G': 7, 'A': 9, 'B': 11}
    if not isinstance(x, str) or len(x) < 2 or x[0] not in names:
        return None
    i = 1
    acc = 0
    while i < len(x) and x[i] in '#bx' and i < 3:
        acc += {'#': 1, 'b': -1, 'x': 2}[x[i]]
        i += 1
    tail = x[i:]
    neg = tail.startswith('-')
    digits = tail[1:] if neg else tail
    if not digits.isdigit():
        return None
    octave = -int(digits) if neg else int(digits)
    midi = (octave + 1) * 12 + names[x[0]] + acc
    if midi < 0 or midi > 127:
        return None
    return midi
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('C4', 60), ('A4', 69), ('C-1', 0), ('G9', 127), ('G#9', None), ('Fx4', 67), ('Dbbb4', 59), ('Cxx4', 64)], [('G9', 127), ('G#9', None), ('Ab9', None), ('B#3', 60), ('Cb4', 59), ('Dbbb4', 59), ('Cx-1', 2), ('Bx-1', 13)], [('B#3', 60), ('Cb4', 59), ('Fx4', 67), ('Ebb4', 62), ('Dbbb4', 59), ('Cb-1', None), ('B-1', 11), ('Cxx4', 64)], [('Dbbb4', 59), ('Cb-1', None), ('B-1', 11), ('E4', 64), ('F4', 65), ('B4', 71), ('Cx-1', 2), ('Bx-1', 13)], [('Fx4', 67), ('Dbbb4', 59), ('F4', 65), ('B4', 71), ('Bb3', 58), ('C0', 12), ('D#0', 15), ('Cxx4', 64)]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("oracle %d" % i, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
oracle 06060Passed
oracle 16969Passed
oracle 200Passed
oracle 3127127Passed
oracle 4NoneNonePassed
oracle 56767Passed
oracle 6None59Failed
oracle 76464Passed

SHA-256 / 06cbb27ba75473c1b2bc286a7f25215eaac8678a03eb46591fc9432178f7ed82

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    names = {'C': 0, 'D': 2, 'E': 4, 'F': 5, 'G': 7, 'A': 9, 'B': 11}
    if not isinstance(x, str) or len(x) < 2 or x[0] not in names:
        return None
    i = 1
    acc = 0
    while i < len(x) and x[i] in '#bx':
        acc += {'#': 1, 'b': -1, 'x': 2}[x[i]]
        i += 1
    tail = x[i:]
    neg = tail.startswith('-')
    digits = tail[1:] if neg else tail
    if not digits.isdigit():
        return None
    octave = -int(digits) if neg else int(digits)
    midi = (octave + 1) * 12 + names[x[0]] + acc
    if midi < 0 or midi > 127:
        return None
    return midi
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('C4', 60), ('A4', 69), ('C-1', 0), ('G9', 127), ('G#9', None), ('Fx4', 67), ('Dbbb4', 59), ('Cxx4', 64)], [('G9', 127), ('G#9', None), ('Ab9', None), ('B#3', 60), ('Cb4', 59), ('Dbbb4', 59), ('Cx-1', 2), ('Bx-1', 13)], [('B#3', 60), ('Cb4', 59), ('Fx4', 67), ('Ebb4', 62), ('Dbbb4', 59), ('Cb-1', None), ('B-1', 11), ('Cxx4', 64)], [('Dbbb4', 59), ('Cb-1', None), ('B-1', 11), ('E4', 64), ('F4', 65), ('B4', 71), ('Cx-1', 2), ('Bx-1', 13)], [('Fx4', 67), ('Dbbb4', 59), ('F4', 65), ('B4', 71), ('Bb3', 58), ('C0', 12), ('D#0', 15), ('Cxx4', 64)]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("oracle %d" % i, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
oracle 06060Passed
oracle 16969Passed
oracle 200Passed
oracle 3127127Passed
oracle 4NoneNonePassed
oracle 56767Passed
oracle 65959Passed
oracle 76464Passed

SHA-256 / a927af4835099cbe02db21696cb8fe4a16b8e0616252500a93a665be30d24084

Verification & scope

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.

Observations recorded using Python 3.12.14 at 2026-09-29T14:49:57.730302+00:00.

Case digest / dac6b600aebf9f7696ad9bbd6e3839b4abe0c7b329c0fb489946f6e07fe3b2fa