FA-81756 / MIDI event timing / Open access

Time Signature meta event decoding: denominator byte used as the denominator · case 01

4/4 decodes as 4/2 and 6/8 as 6/3, because the stored power of two is not expanded.

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

ROOT CAUSE

The dd byte is taken as the denominator itself instead of its base-2 exponent.

VERIFIED REPAIR

Restore the denominator exponent step so that it reads `den = 2 ** dd`.

Unsuccessful approach: Doubling the exponent happens to match 4/4 and 2/2 but gives 6/6 for 6/8.

Case contract

Input [bytes, ppq]. bytes must be FF 58 04 nn dd cc bb with nn > 0, dd <= 6 and bb > 0. The denominator is 2**dd; the metronome click is cc MIDI clocks (24 per quarter) converted to ticks as ppq*cc//24; the bar length in ticks is ppq*4*nn//denominator. Return [nn, denominator, click_ticks, bar_ticks] or None.

Why this case matters

MIDI sequencers, file readers and synth drivers depend on exact event ordering and tick/time arithmetic.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(x):
    if not isinstance(x, list) or len(x) != 2:
        return None
    data, ppq = x
    if len(data) != 7 or data[0] != 0xFF or data[1] != 0x58 or data[2] != 4:
        return None
    nn, dd, cc, bb = data[3:7]
    if nn == 0 or dd > 6 or bb == 0 or ppq <= 0:
        return None
    den = dd
    click = ppq * cc // 24
    bar = ppq * 4 * nn // den
    return [nn, den, click, bar]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([[255, 88, 4, 4, 2, 24, 8], 480], [4, 4, 480, 1920]), ([[255, 88, 4, 6, 3, 36, 8], 480], [6, 8, 720, 1440]), ([[255, 88, 4, 3, 2, 24, 8], 100], [3, 4, 100, 300]), ([[255, 88, 4, 3, 4, 6, 8], 90], [3, 16, 22, 67]), ([[255, 88, 4, 4, 2, 24, 8], 0], None), ([[255, 88, 4, 0, 2, 24, 8], 480], None), ([[255, 88, 4, 4, 7, 24, 8], 480], None), ([[255, 88, 5, 4, 2, 24, 8], 480], None)], [([[255, 88, 4, 4, 2, 24, 8], 480], [4, 4, 480, 1920]), ([[255, 88, 4, 6, 3, 36, 8], 480], [6, 8, 720, 1440]), ([[255, 88, 4, 7, 3, 12, 8], 90], [7, 8, 45, 315]), ([[255, 88, 5, 4, 2, 24, 8], 480], None), ([[255, 88, 3, 4, 2, 24, 8], 480], None), ([[255, 89, 4, 4, 2, 24, 8], 480], None), ([[255, 88, 4, 4, 2, 24, 0], 480], None), ([[255, 88, 4, 9, 3, 18, 8], 100], [9, 8, 75, 450])], [([[255, 88, 4, 4, 2, 24, 8], 480], [4, 4, 480, 1920]), ([[255, 88, 4, 6, 3, 36, 8], 480], [6, 8, 720, 1440]), ([[255, 88, 4, 3, 2, 24, 8], 100], [3, 4, 100, 300]), ([[255, 88, 4, 7, 3, 12, 8], 90], [7, 8, 45, 315]), ([[255, 88, 4, 5, 4, 6, 8], 90], [5, 16, 22, 112]), ([[255, 88, 4, 2, 1, 48, 8], 96], [2, 2, 192, 384]), ([[255, 88, 4, 3, 4, 6, 8], 90], [3, 16, 22, 67]), ([[255, 88, 4, 4, 2, 24, 0], 480], None)], [([[255, 88, 4, 3, 2, 24, 8], 100], [3, 4, 100, 300]), ([[255, 88, 4, 7, 3, 12, 8], 90], [7, 8, 45, 315]), ([[255, 88, 4, 5, 4, 6, 8], 90], [5, 16, 22, 112]), ([[255, 88, 4, 2, 1, 48, 8], 96], [2, 2, 192, 384]), ([[255, 88, 4, 3, 4, 6, 8], 90], [3, 16, 22, 67]), ([[255, 88, 4, 4, 2, 24, 8], 0], None), ([[255, 88, 4, 0, 2, 24, 8], 480], None), ([[255, 88, 4, 9, 3, 18, 8], 100], [9, 8, 75, 450])], [([[255, 88, 4, 5, 4, 6, 8], 90], [5, 16, 22, 112]), ([[255, 88, 4, 2, 1, 48, 8], 96], [2, 2, 192, 384]), ([[255, 88, 4, 3, 4, 6, 8], 90], [3, 16, 22, 67]), ([[255, 88, 4, 4, 2, 24, 8], 0], None), ([[255, 88, 4, 0, 2, 24, 8], 480], None), ([[255, 88, 4, 4, 7, 24, 8], 480], None), ([[255, 88, 5, 4, 2, 24, 8], 480], None), ([[255, 88, 4, 9, 3, 18, 8], 100], [9, 8, 75, 450])]]
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	`[4, 2, 480, 3840]`	`[4, 4, 480, 1920]`	Failed
oracle 1	`[6, 3, 720, 3840]`	`[6, 8, 720, 1440]`	Failed
oracle 2	`[3, 2, 100, 600]`	`[3, 4, 100, 300]`	Failed
oracle 3	`[3, 4, 22, 270]`	`[3, 16, 22, 67]`	Failed
oracle 4	`None`	`None`	Passed
oracle 5	`None`	`None`	Passed
oracle 6	`None`	`None`	Passed
oracle 7	`None`	`None`	Passed

SHA-256 / 4bcfce9760dd1f8befdc16bc010956d7dc9d24164d40a5caccfa9c67107ee079

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(x):
    if not isinstance(x, list) or len(x) != 2:
        return None
    data, ppq = x
    if len(data) != 7 or data[0] != 0xFF or data[1] != 0x58 or data[2] != 4:
        return None
    nn, dd, cc, bb = data[3:7]
    if nn == 0 or dd > 6 or bb == 0 or ppq <= 0:
        return None
    den = 2 * dd
    click = ppq * cc // 24
    bar = ppq * 4 * nn // den
    return [nn, den, click, bar]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([[255, 88, 4, 4, 2, 24, 8], 480], [4, 4, 480, 1920]), ([[255, 88, 4, 6, 3, 36, 8], 480], [6, 8, 720, 1440]), ([[255, 88, 4, 3, 2, 24, 8], 100], [3, 4, 100, 300]), ([[255, 88, 4, 3, 4, 6, 8], 90], [3, 16, 22, 67]), ([[255, 88, 4, 4, 2, 24, 8], 0], None), ([[255, 88, 4, 0, 2, 24, 8], 480], None), ([[255, 88, 4, 4, 7, 24, 8], 480], None), ([[255, 88, 5, 4, 2, 24, 8], 480], None)], [([[255, 88, 4, 4, 2, 24, 8], 480], [4, 4, 480, 1920]), ([[255, 88, 4, 6, 3, 36, 8], 480], [6, 8, 720, 1440]), ([[255, 88, 4, 7, 3, 12, 8], 90], [7, 8, 45, 315]), ([[255, 88, 5, 4, 2, 24, 8], 480], None), ([[255, 88, 3, 4, 2, 24, 8], 480], None), ([[255, 89, 4, 4, 2, 24, 8], 480], None), ([[255, 88, 4, 4, 2, 24, 0], 480], None), ([[255, 88, 4, 9, 3, 18, 8], 100], [9, 8, 75, 450])], [([[255, 88, 4, 4, 2, 24, 8], 480], [4, 4, 480, 1920]), ([[255, 88, 4, 6, 3, 36, 8], 480], [6, 8, 720, 1440]), ([[255, 88, 4, 3, 2, 24, 8], 100], [3, 4, 100, 300]), ([[255, 88, 4, 7, 3, 12, 8], 90], [7, 8, 45, 315]), ([[255, 88, 4, 5, 4, 6, 8], 90], [5, 16, 22, 112]), ([[255, 88, 4, 2, 1, 48, 8], 96], [2, 2, 192, 384]), ([[255, 88, 4, 3, 4, 6, 8], 90], [3, 16, 22, 67]), ([[255, 88, 4, 4, 2, 24, 0], 480], None)], [([[255, 88, 4, 3, 2, 24, 8], 100], [3, 4, 100, 300]), ([[255, 88, 4, 7, 3, 12, 8], 90], [7, 8, 45, 315]), ([[255, 88, 4, 5, 4, 6, 8], 90], [5, 16, 22, 112]), ([[255, 88, 4, 2, 1, 48, 8], 96], [2, 2, 192, 384]), ([[255, 88, 4, 3, 4, 6, 8], 90], [3, 16, 22, 67]), ([[255, 88, 4, 4, 2, 24, 8], 0], None), ([[255, 88, 4, 0, 2, 24, 8], 480], None), ([[255, 88, 4, 9, 3, 18, 8], 100], [9, 8, 75, 450])], [([[255, 88, 4, 5, 4, 6, 8], 90], [5, 16, 22, 112]), ([[255, 88, 4, 2, 1, 48, 8], 96], [2, 2, 192, 384]), ([[255, 88, 4, 3, 4, 6, 8], 90], [3, 16, 22, 67]), ([[255, 88, 4, 4, 2, 24, 8], 0], None), ([[255, 88, 4, 0, 2, 24, 8], 480], None), ([[255, 88, 4, 4, 7, 24, 8], 480], None), ([[255, 88, 5, 4, 2, 24, 8], 480], None), ([[255, 88, 4, 9, 3, 18, 8], 100], [9, 8, 75, 450])]]
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	`[4, 4, 480, 1920]`	`[4, 4, 480, 1920]`	Passed
oracle 1	`[6, 6, 720, 1920]`	`[6, 8, 720, 1440]`	Failed
oracle 2	`[3, 4, 100, 300]`	`[3, 4, 100, 300]`	Passed
oracle 3	`[3, 8, 22, 135]`	`[3, 16, 22, 67]`	Failed
oracle 4	`None`	`None`	Passed
oracle 5	`None`	`None`	Passed
oracle 6	`None`	`None`	Passed
oracle 7	`None`	`None`	Passed

SHA-256 / a69d562b08865c7b41c528b3263e12b00dc502fbfb18fdd3a5a7b3f9fdc1ccc4

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(x):
    if not isinstance(x, list) or len(x) != 2:
        return None
    data, ppq = x
    if len(data) != 7 or data[0] != 0xFF or data[1] != 0x58 or data[2] != 4:
        return None
    nn, dd, cc, bb = data[3:7]
    if nn == 0 or dd > 6 or bb == 0 or ppq <= 0:
        return None
    den = 2 ** dd
    click = ppq * cc // 24
    bar = ppq * 4 * nn // den
    return [nn, den, click, bar]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([[255, 88, 4, 4, 2, 24, 8], 480], [4, 4, 480, 1920]), ([[255, 88, 4, 6, 3, 36, 8], 480], [6, 8, 720, 1440]), ([[255, 88, 4, 3, 2, 24, 8], 100], [3, 4, 100, 300]), ([[255, 88, 4, 3, 4, 6, 8], 90], [3, 16, 22, 67]), ([[255, 88, 4, 4, 2, 24, 8], 0], None), ([[255, 88, 4, 0, 2, 24, 8], 480], None), ([[255, 88, 4, 4, 7, 24, 8], 480], None), ([[255, 88, 5, 4, 2, 24, 8], 480], None)], [([[255, 88, 4, 4, 2, 24, 8], 480], [4, 4, 480, 1920]), ([[255, 88, 4, 6, 3, 36, 8], 480], [6, 8, 720, 1440]), ([[255, 88, 4, 7, 3, 12, 8], 90], [7, 8, 45, 315]), ([[255, 88, 5, 4, 2, 24, 8], 480], None), ([[255, 88, 3, 4, 2, 24, 8], 480], None), ([[255, 89, 4, 4, 2, 24, 8], 480], None), ([[255, 88, 4, 4, 2, 24, 0], 480], None), ([[255, 88, 4, 9, 3, 18, 8], 100], [9, 8, 75, 450])], [([[255, 88, 4, 4, 2, 24, 8], 480], [4, 4, 480, 1920]), ([[255, 88, 4, 6, 3, 36, 8], 480], [6, 8, 720, 1440]), ([[255, 88, 4, 3, 2, 24, 8], 100], [3, 4, 100, 300]), ([[255, 88, 4, 7, 3, 12, 8], 90], [7, 8, 45, 315]), ([[255, 88, 4, 5, 4, 6, 8], 90], [5, 16, 22, 112]), ([[255, 88, 4, 2, 1, 48, 8], 96], [2, 2, 192, 384]), ([[255, 88, 4, 3, 4, 6, 8], 90], [3, 16, 22, 67]), ([[255, 88, 4, 4, 2, 24, 0], 480], None)], [([[255, 88, 4, 3, 2, 24, 8], 100], [3, 4, 100, 300]), ([[255, 88, 4, 7, 3, 12, 8], 90], [7, 8, 45, 315]), ([[255, 88, 4, 5, 4, 6, 8], 90], [5, 16, 22, 112]), ([[255, 88, 4, 2, 1, 48, 8], 96], [2, 2, 192, 384]), ([[255, 88, 4, 3, 4, 6, 8], 90], [3, 16, 22, 67]), ([[255, 88, 4, 4, 2, 24, 8], 0], None), ([[255, 88, 4, 0, 2, 24, 8], 480], None), ([[255, 88, 4, 9, 3, 18, 8], 100], [9, 8, 75, 450])], [([[255, 88, 4, 5, 4, 6, 8], 90], [5, 16, 22, 112]), ([[255, 88, 4, 2, 1, 48, 8], 96], [2, 2, 192, 384]), ([[255, 88, 4, 3, 4, 6, 8], 90], [3, 16, 22, 67]), ([[255, 88, 4, 4, 2, 24, 8], 0], None), ([[255, 88, 4, 0, 2, 24, 8], 480], None), ([[255, 88, 4, 4, 7, 24, 8], 480], None), ([[255, 88, 5, 4, 2, 24, 8], 480], None), ([[255, 88, 4, 9, 3, 18, 8], 100], [9, 8, 75, 450])]]
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	`[4, 4, 480, 1920]`	`[4, 4, 480, 1920]`	Passed
oracle 1	`[6, 8, 720, 1440]`	`[6, 8, 720, 1440]`	Passed
oracle 2	`[3, 4, 100, 300]`	`[3, 4, 100, 300]`	Passed
oracle 3	`[3, 16, 22, 67]`	`[3, 16, 22, 67]`	Passed
oracle 4	`None`	`None`	Passed
oracle 5	`None`	`None`	Passed
oracle 6	`None`	`None`	Passed
oracle 7	`None`	`None`	Passed

SHA-256 / b6280b043ee1139b2fd43153f3b8ba2b91f2cc5c4482d8b6e65d64e2e0f8a841

Verification & scope

A deterministic bounded teaching model with a stipulated toy contract; it is not a complete Standard MIDI File or MIDI 1.0/2.0 implementation. 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 2026-09-29T14:50:05.759322+00:00.

Case digest / 029ffbd743ea237ce998c5ff981300a16a671089c3ca7bd7daff924ec7a39564