FA-81161 / Music interval and transposition theory / Open access

Chord symbol to pitch classes: flat roots not recognised · case 01

Bb, Ebmaj7 and every other flat-rooted symbol is rejected because the b is read as part of the quality.

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

ROOT CAUSE

Only # is recognised as a root accidental.

THE FAILURE

Only # is recognised as a root accidental.

Unsuccessful approach: Requiring more characters after the flat still rejects a bare flat triad such as Bb or Cb.

Case contract

Input a chord symbol: root letter with optional # or b, a quality from "", m, dim, aug, 7, maj7, m7, m7b5, dim7, sus4, mMaj7, 6, and optionally "/" plus a bass note (letter with optional # or b and nothing else). Return pitch classes root-first in template order; for a slash chord the bass moves to the front (removed from its old position if it is a chord tone, otherwise added). Unknown or malformed symbols return None.

Why this case matters

Lead-sheet, accompaniment and guitar-chart tools expand chord symbols into voicings.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(x):
    base = {'C': 0, 'D': 2, 'E': 4, 'F': 5, 'G': 7, 'A': 9, 'B': 11}
    shapes = {'': [0, 4, 7], 'm': [0, 3, 7], 'dim': [0, 3, 6], 'aug': [0, 4, 8], '7': [0, 4, 7, 10], 'maj7': [0, 4, 7, 11], 'm7': [0, 3, 7, 10], 'm7b5': [0, 3, 6, 10], 'dim7': [0, 3, 6, 9], 'sus4': [0, 5, 7], 'mMaj7': [0, 3, 7, 11], '6': [0, 4, 7, 9]}
    def root(s):
        if not s or s[0] not in base:
            return None, s
        if s[1:2] == '#':
            return (base[s[0]] + (1 if s[1] == '#' else -1)) % 12, s[2:]
        return base[s[0]], s[1:]
    if not isinstance(x, str):
        return None
    head, slash, tail = x.partition('/')
    r, quality = root(head)
    if r is None or quality not in shapes:
        return None
    tones = [(r + i) % 12 for i in shapes[quality]]
    if slash:
        b, rest = root(tail)
        if b is None or rest:
            return None
        if b in tones:
            tones.remove(b)
        tones.insert(0, b)
    return tones
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('C', [0, 4, 7]), ('Cm', [0, 3, 7]), ('Bb', [10, 2, 5]), ('Bb7', [10, 2, 5, 8]), ('F#m7b5', [6, 9, 0, 4]), ('Gdim7', [7, 10, 1, 4]), ('Aaug', [9, 1, 5]), ('Cb', [11, 3, 6])], [('Bbm7', [10, 1, 5, 8]), ('Ebmaj7', [3, 7, 10, 2]), ('Gdim7', [7, 10, 1, 4]), ('Aaug', [9, 1, 5]), ('Dsus4', [2, 7, 9]), ('C/E', [4, 0, 7]), ('C/Bb', [10, 0, 4, 7]), ('E#', [5, 9, 0])], [('Bb7', [10, 2, 5, 8]), ('C/E', [4, 0, 7]), ('C/G', [7, 0, 4]), ('C/Bb', [10, 0, 4, 7]), ('Am/G', [7, 9, 0, 4]), ('F/A', [9, 5, 0]), ('Bb/D', [2, 10, 5]), ('Bb/Ab', [8, 10, 2, 5])], [('Ebmaj7', [3, 7, 10, 2]), ('F/A', [9, 5, 0]), ('Bb/D', [2, 10, 5]), ('G7/F', [5, 7, 11, 2]), ('Cmaj7/B', [11, 0, 4, 7]), ('Cb', [11, 3, 6]), ('A6', [9, 1, 4, 6]), ('D/F#', [6, 2, 9])], [('C/Bb', [10, 0, 4, 7]), ('Cb', [11, 3, 6]), ('E#', [5, 9, 0]), ('A6', [9, 1, 4, 6]), ('AmMaj7', [9, 0, 4, 8]), ('C/E/G', None), ('C/Ebm', None), ('F#', [6, 10, 1])]]
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	`[0, 4, 7]`	`[0, 4, 7]`	Passed
oracle 1	`[0, 3, 7]`	`[0, 3, 7]`	Passed
oracle 2	`None`	`[10, 2, 5]`	Failed
oracle 3	`None`	`[10, 2, 5, 8]`	Failed
oracle 4	`[6, 9, 0, 4]`	`[6, 9, 0, 4]`	Passed
oracle 5	`[7, 10, 1, 4]`	`[7, 10, 1, 4]`	Passed
oracle 6	`[9, 1, 5]`	`[9, 1, 5]`	Passed
oracle 7	`None`	`[11, 3, 6]`	Failed

SHA-256 / a9ec91d59f1053adf78fc79b98544a71570a12f2b5359f09868c8410db0529ff

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(x):
    base = {'C': 0, 'D': 2, 'E': 4, 'F': 5, 'G': 7, 'A': 9, 'B': 11}
    shapes = {'': [0, 4, 7], 'm': [0, 3, 7], 'dim': [0, 3, 6], 'aug': [0, 4, 8], '7': [0, 4, 7, 10], 'maj7': [0, 4, 7, 11], 'm7': [0, 3, 7, 10], 'm7b5': [0, 3, 6, 10], 'dim7': [0, 3, 6, 9], 'sus4': [0, 5, 7], 'mMaj7': [0, 3, 7, 11], '6': [0, 4, 7, 9]}
    def root(s):
        if not s or s[0] not in base:
            return None, s
        if s[1:2] in ('#', 'b') and len(s) > 2:
            return (base[s[0]] + (1 if s[1] == '#' else -1)) % 12, s[2:]
        return base[s[0]], s[1:]
    if not isinstance(x, str):
        return None
    head, slash, tail = x.partition('/')
    r, quality = root(head)
    if r is None or quality not in shapes:
        return None
    tones = [(r + i) % 12 for i in shapes[quality]]
    if slash:
        b, rest = root(tail)
        if b is None or rest:
            return None
        if b in tones:
            tones.remove(b)
        tones.insert(0, b)
    return tones
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('C', [0, 4, 7]), ('Cm', [0, 3, 7]), ('Bb', [10, 2, 5]), ('Bb7', [10, 2, 5, 8]), ('F#m7b5', [6, 9, 0, 4]), ('Gdim7', [7, 10, 1, 4]), ('Aaug', [9, 1, 5]), ('Cb', [11, 3, 6])], [('Bbm7', [10, 1, 5, 8]), ('Ebmaj7', [3, 7, 10, 2]), ('Gdim7', [7, 10, 1, 4]), ('Aaug', [9, 1, 5]), ('Dsus4', [2, 7, 9]), ('C/E', [4, 0, 7]), ('C/Bb', [10, 0, 4, 7]), ('E#', [5, 9, 0])], [('Bb7', [10, 2, 5, 8]), ('C/E', [4, 0, 7]), ('C/G', [7, 0, 4]), ('C/Bb', [10, 0, 4, 7]), ('Am/G', [7, 9, 0, 4]), ('F/A', [9, 5, 0]), ('Bb/D', [2, 10, 5]), ('Bb/Ab', [8, 10, 2, 5])], [('Ebmaj7', [3, 7, 10, 2]), ('F/A', [9, 5, 0]), ('Bb/D', [2, 10, 5]), ('G7/F', [5, 7, 11, 2]), ('Cmaj7/B', [11, 0, 4, 7]), ('Cb', [11, 3, 6]), ('A6', [9, 1, 4, 6]), ('D/F#', [6, 2, 9])], [('C/Bb', [10, 0, 4, 7]), ('Cb', [11, 3, 6]), ('E#', [5, 9, 0]), ('A6', [9, 1, 4, 6]), ('AmMaj7', [9, 0, 4, 8]), ('C/E/G', None), ('C/Ebm', None), ('F#', [6, 10, 1])]]
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	`[0, 4, 7]`	`[0, 4, 7]`	Passed
oracle 1	`[0, 3, 7]`	`[0, 3, 7]`	Passed
oracle 2	`None`	`[10, 2, 5]`	Failed
oracle 3	`[10, 2, 5, 8]`	`[10, 2, 5, 8]`	Passed
oracle 4	`[6, 9, 0, 4]`	`[6, 9, 0, 4]`	Passed
oracle 5	`[7, 10, 1, 4]`	`[7, 10, 1, 4]`	Passed
oracle 6	`[9, 1, 5]`	`[9, 1, 5]`	Passed
oracle 7	`None`	`[11, 3, 6]`	Failed

SHA-256 / 7d86b96b8c9f60ad09ff5b028a18c433015eb3e3c48469cf6333954c4a3372e7

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:50:00.553798+00:00.

Case digest / 79efa5201fc45c3758e30a099dc4167c8aef6e6e9854237a11a3e0b58dd68c1c