FAILURE MAP
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FA-80841 / Music interval and transposition theory / Open access

Spelled pitch to MIDI key number: octave numbered from zero at middle C minus four · case 01

Every spelled pitch lands exactly one octave low, so C4 reports 48 and A4 reports 57.

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

ROOT CAUSE

The octave contribution multiplies the spelled octave by twelve without shifting the origin so that C-1 is key zero.

VERIFIED REPAIR

Restore the octave origin step so that it reads `(octave + 1) * 12`.

Unsuccessful approach: Special-casing only positive octaves collapses octave 0 onto octave -1, so C0 still reports 0 instead of 12.

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 '#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 * 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), ('C-1', 0), ('Cb-1', None), ('C0', 12), ('H4', None), ('C', None), ('c4', None), ('C-2', None)], [('A4', 69), ('G9', 127), ('C0', 12), ('D#0', 15), ('c4', None), ('C#', None), ('C4x', None), ('C--1', None)], [('C4', 60), ('A4', 69), ('C-1', 0), ('G9', 127), ('G#9', None), ('D#0', 15), ('A0', 21), ('C--1', None)], [('C-1', 0), ('G9', 127), ('G#9', None), ('Ab9', None), ('B#3', 60), ('Cb4', 59), ('A0', 21), ('C-2', None)], [('G#9', None), ('Ab9', None), ('B#3', 60), ('Cb4', 59), ('Fx4', 67), ('Ebb4', 62), ('C0', 12), ('C-2', None)]]
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 04860Failed
oracle 1None0Failed
oracle 2NoneNonePassed
oracle 3012Failed
oracle 4NoneNonePassed
oracle 5NoneNonePassed
oracle 6NoneNonePassed
oracle 7NoneNonePassed

SHA-256 / 6435dbaabd4f9555cadef02a920fedb59c66dda367e79deef9968e2516f09343

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':
        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 * 12 + 12 if octave > 0 else 0) + 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), ('C-1', 0), ('Cb-1', None), ('C0', 12), ('H4', None), ('C', None), ('c4', None), ('C-2', None)], [('A4', 69), ('G9', 127), ('C0', 12), ('D#0', 15), ('c4', None), ('C#', None), ('C4x', None), ('C--1', None)], [('C4', 60), ('A4', 69), ('C-1', 0), ('G9', 127), ('G#9', None), ('D#0', 15), ('A0', 21), ('C--1', None)], [('C-1', 0), ('G9', 127), ('G#9', None), ('Ab9', None), ('B#3', 60), ('Cb4', 59), ('A0', 21), ('C-2', None)], [('G#9', None), ('Ab9', None), ('B#3', 60), ('Cb4', 59), ('Fx4', 67), ('Ebb4', 62), ('C0', 12), ('C-2', None)]]
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 100Passed
oracle 2NoneNonePassed
oracle 3012Failed
oracle 4NoneNonePassed
oracle 5NoneNonePassed
oracle 6NoneNonePassed
oracle 70NoneFailed

SHA-256 / 1e32f28208f8c868ba7f5661eff186b9b81b3c5713fc7ffb9e11b79e3f1b444a

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), ('C-1', 0), ('Cb-1', None), ('C0', 12), ('H4', None), ('C', None), ('c4', None), ('C-2', None)], [('A4', 69), ('G9', 127), ('C0', 12), ('D#0', 15), ('c4', None), ('C#', None), ('C4x', None), ('C--1', None)], [('C4', 60), ('A4', 69), ('C-1', 0), ('G9', 127), ('G#9', None), ('D#0', 15), ('A0', 21), ('C--1', None)], [('C-1', 0), ('G9', 127), ('G#9', None), ('Ab9', None), ('B#3', 60), ('Cb4', 59), ('A0', 21), ('C-2', None)], [('G#9', None), ('Ab9', None), ('B#3', 60), ('Cb4', 59), ('Fx4', 67), ('Ebb4', 62), ('C0', 12), ('C-2', None)]]
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 100Passed
oracle 2NoneNonePassed
oracle 31212Passed
oracle 4NoneNonePassed
oracle 5NoneNonePassed
oracle 6NoneNonePassed
oracle 7NoneNonePassed

SHA-256 / b0b4bcbd9796f3696068ec2355ca0672698bc1336fdad0355bc52d50ed5a294c

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 2026-09-29T14:49:57.433633+00:00.

Case digest / e8dc075725e2accef32e024b58f5e9ca791614fc6b83bda783a4a099e96ece65