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.
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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| oracle 0 | 48 | 60 | Failed |
| oracle 1 | None | 0 | Failed |
| oracle 2 | None | None | Passed |
| oracle 3 | 0 | 12 | Failed |
| oracle 4 | None | None | Passed |
| oracle 5 | None | None | Passed |
| oracle 6 | None | None | Passed |
| oracle 7 | None | None | Passed |
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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| oracle 0 | 60 | 60 | Passed |
| oracle 1 | 0 | 0 | Passed |
| oracle 2 | None | None | Passed |
| oracle 3 | 0 | 12 | Failed |
| oracle 4 | None | None | Passed |
| oracle 5 | None | None | Passed |
| oracle 6 | None | None | Passed |
| oracle 7 | 0 | None | Failed |
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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| oracle 0 | 60 | 60 | Passed |
| oracle 1 | 0 | 0 | Passed |
| oracle 2 | None | None | Passed |
| oracle 3 | 12 | 12 | Passed |
| oracle 4 | None | None | Passed |
| oracle 5 | None | None | Passed |
| oracle 6 | None | None | Passed |
| oracle 7 | None | None | Passed |
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