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FA-81531 / MIDI event timing / Open access

Bar, beat and tick position with meter changes: beat count not reset each bar · case 01

The first beat of bar 2 in 4/4 is reported as beat 5.

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

ROOT CAUSE

The beat index is computed from the offset since the segment start without reducing to the current bar.

VERIFIED REPAIR

Restore the beat within bar step so that it reads `offset % bar_len // beat + 1`.

Unsuccessful approach: Reducing to the bar but dropping the +1 reports zero-based beats.

Case contract

Input [ppq, signatures, tick]. signatures is a list of [bar_index, numerator, denominator] sorted by bar, the first at bar 0; each takes effect at the start of its bar. A beat lasts ppq*4/denominator ticks. Return [bar (1-based), beat (1-based), tick within beat]; invalid input returns 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) != 3:
        return None
    ppq, sigs, tick = x
    if tick < 0 or not sigs or sigs[0][0] != 0:
        return None
    start = 0
    for k, (b, num, den) in enumerate(sigs):
        beat = ppq * 4 // den
        bar_len = beat * num
        next_bar = sigs[k + 1][0] if k + 1 < len(sigs) else None
        if next_bar is not None:
            span = (next_bar - b) * bar_len
            if tick >= start + span:
                start += span
                continue
        offset = tick - start
        return [b + offset // bar_len + 1, offset // beat + 1, offset % beat]
    return None
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([480, [[0, 4, 4]], 0], [1, 1, 0]), ([480, [[0, 4, 4]], 1920], [2, 1, 0]), ([480, [[0, 4, 4]], 2400], [2, 2, 0]), ([480, [[0, 6, 8]], 720], [1, 4, 0]), ([480, [[0, 6, 8]], 1440], [2, 1, 0]), ([480, [[0, 3, 4]], 1450], [2, 1, 10]), ([480, [[1, 4, 4]], 0], None), ([480, [[0, 4, 4]], -5], None)], [([480, [[0, 4, 4]], 1920], [2, 1, 0]), ([480, [[0, 4, 4]], 2400], [2, 2, 0]), ([480, [[0, 6, 8]], 720], [1, 4, 0]), ([480, [[0, 6, 8]], 1440], [2, 1, 0]), ([480, [[0, 3, 4]], 1450], [2, 1, 10]), ([480, [[0, 4, 4], [2, 3, 4]], 3840], [3, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5280], [4, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5300], [4, 1, 20])], [([480, [[0, 4, 4]], 2400], [2, 2, 0]), ([480, [[0, 6, 8]], 1440], [2, 1, 0]), ([480, [[0, 3, 4]], 1450], [2, 1, 10]), ([480, [[0, 4, 4], [2, 3, 4]], 3840], [3, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5280], [4, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5300], [4, 1, 20]), ([480, [[0, 2, 2]], 1000], [1, 2, 40]), ([96, [[0, 7, 8], [1, 4, 4]], 336], [2, 1, 0])], [([480, [[0, 6, 8]], 720], [1, 4, 0]), ([480, [[0, 3, 4]], 1450], [2, 1, 10]), ([480, [[0, 4, 4], [2, 3, 4]], 3840], [3, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5280], [4, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5300], [4, 1, 20]), ([480, [[0, 2, 2]], 1000], [1, 2, 40]), ([96, [[0, 7, 8], [1, 4, 4]], 336], [2, 1, 0]), ([96, [[0, 7, 8], [1, 4, 4]], 400], [2, 1, 64])], [([480, [[0, 6, 8]], 1440], [2, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5280], [4, 1, 0]), ([96, [[0, 7, 8], [1, 4, 4]], 336], [2, 1, 0]), ([96, [[0, 7, 8], [1, 4, 4]], 400], [2, 1, 64]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 1920], [2, 1, 0]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 4320], [4, 1, 0]), ([480, [[0, 3, 16]], 700], [2, 3, 100]), ([120, [[0, 4, 4], [4, 6, 8], [6, 4, 4]], 2000], [5, 2, 20])]]
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 0[1, 1, 0][1, 1, 0]Passed
oracle 1[2, 5, 0][2, 1, 0]Failed
oracle 2[2, 6, 0][2, 2, 0]Failed
oracle 3[1, 4, 0][1, 4, 0]Passed
oracle 4[2, 7, 0][2, 1, 0]Failed
oracle 5[2, 4, 10][2, 1, 10]Failed
oracle 6NoneNonePassed
oracle 7NoneNonePassed

SHA-256 / ae042bfc585eb8e47f8737cd425e882add056162370106125458e35466f1824a

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) != 3:
        return None
    ppq, sigs, tick = x
    if tick < 0 or not sigs or sigs[0][0] != 0:
        return None
    start = 0
    for k, (b, num, den) in enumerate(sigs):
        beat = ppq * 4 // den
        bar_len = beat * num
        next_bar = sigs[k + 1][0] if k + 1 < len(sigs) else None
        if next_bar is not None:
            span = (next_bar - b) * bar_len
            if tick >= start + span:
                start += span
                continue
        offset = tick - start
        return [b + offset // bar_len + 1, offset % bar_len // beat, offset % beat]
    return None
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([480, [[0, 4, 4]], 0], [1, 1, 0]), ([480, [[0, 4, 4]], 1920], [2, 1, 0]), ([480, [[0, 4, 4]], 2400], [2, 2, 0]), ([480, [[0, 6, 8]], 720], [1, 4, 0]), ([480, [[0, 6, 8]], 1440], [2, 1, 0]), ([480, [[0, 3, 4]], 1450], [2, 1, 10]), ([480, [[1, 4, 4]], 0], None), ([480, [[0, 4, 4]], -5], None)], [([480, [[0, 4, 4]], 1920], [2, 1, 0]), ([480, [[0, 4, 4]], 2400], [2, 2, 0]), ([480, [[0, 6, 8]], 720], [1, 4, 0]), ([480, [[0, 6, 8]], 1440], [2, 1, 0]), ([480, [[0, 3, 4]], 1450], [2, 1, 10]), ([480, [[0, 4, 4], [2, 3, 4]], 3840], [3, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5280], [4, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5300], [4, 1, 20])], [([480, [[0, 4, 4]], 2400], [2, 2, 0]), ([480, [[0, 6, 8]], 1440], [2, 1, 0]), ([480, [[0, 3, 4]], 1450], [2, 1, 10]), ([480, [[0, 4, 4], [2, 3, 4]], 3840], [3, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5280], [4, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5300], [4, 1, 20]), ([480, [[0, 2, 2]], 1000], [1, 2, 40]), ([96, [[0, 7, 8], [1, 4, 4]], 336], [2, 1, 0])], [([480, [[0, 6, 8]], 720], [1, 4, 0]), ([480, [[0, 3, 4]], 1450], [2, 1, 10]), ([480, [[0, 4, 4], [2, 3, 4]], 3840], [3, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5280], [4, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5300], [4, 1, 20]), ([480, [[0, 2, 2]], 1000], [1, 2, 40]), ([96, [[0, 7, 8], [1, 4, 4]], 336], [2, 1, 0]), ([96, [[0, 7, 8], [1, 4, 4]], 400], [2, 1, 64])], [([480, [[0, 6, 8]], 1440], [2, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5280], [4, 1, 0]), ([96, [[0, 7, 8], [1, 4, 4]], 336], [2, 1, 0]), ([96, [[0, 7, 8], [1, 4, 4]], 400], [2, 1, 64]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 1920], [2, 1, 0]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 4320], [4, 1, 0]), ([480, [[0, 3, 16]], 700], [2, 3, 100]), ([120, [[0, 4, 4], [4, 6, 8], [6, 4, 4]], 2000], [5, 2, 20])]]
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 0[1, 0, 0][1, 1, 0]Failed
oracle 1[2, 0, 0][2, 1, 0]Failed
oracle 2[2, 1, 0][2, 2, 0]Failed
oracle 3[1, 3, 0][1, 4, 0]Failed
oracle 4[2, 0, 0][2, 1, 0]Failed
oracle 5[2, 0, 10][2, 1, 10]Failed
oracle 6NoneNonePassed
oracle 7NoneNonePassed

SHA-256 / 5bd2320ad7f6aa81517365120e980d111c0a2cc8f202f9bc2e08b74cadce2e0f

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) != 3:
        return None
    ppq, sigs, tick = x
    if tick < 0 or not sigs or sigs[0][0] != 0:
        return None
    start = 0
    for k, (b, num, den) in enumerate(sigs):
        beat = ppq * 4 // den
        bar_len = beat * num
        next_bar = sigs[k + 1][0] if k + 1 < len(sigs) else None
        if next_bar is not None:
            span = (next_bar - b) * bar_len
            if tick >= start + span:
                start += span
                continue
        offset = tick - start
        return [b + offset // bar_len + 1, offset % bar_len // beat + 1, offset % beat]
    return None
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([480, [[0, 4, 4]], 0], [1, 1, 0]), ([480, [[0, 4, 4]], 1920], [2, 1, 0]), ([480, [[0, 4, 4]], 2400], [2, 2, 0]), ([480, [[0, 6, 8]], 720], [1, 4, 0]), ([480, [[0, 6, 8]], 1440], [2, 1, 0]), ([480, [[0, 3, 4]], 1450], [2, 1, 10]), ([480, [[1, 4, 4]], 0], None), ([480, [[0, 4, 4]], -5], None)], [([480, [[0, 4, 4]], 1920], [2, 1, 0]), ([480, [[0, 4, 4]], 2400], [2, 2, 0]), ([480, [[0, 6, 8]], 720], [1, 4, 0]), ([480, [[0, 6, 8]], 1440], [2, 1, 0]), ([480, [[0, 3, 4]], 1450], [2, 1, 10]), ([480, [[0, 4, 4], [2, 3, 4]], 3840], [3, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5280], [4, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5300], [4, 1, 20])], [([480, [[0, 4, 4]], 2400], [2, 2, 0]), ([480, [[0, 6, 8]], 1440], [2, 1, 0]), ([480, [[0, 3, 4]], 1450], [2, 1, 10]), ([480, [[0, 4, 4], [2, 3, 4]], 3840], [3, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5280], [4, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5300], [4, 1, 20]), ([480, [[0, 2, 2]], 1000], [1, 2, 40]), ([96, [[0, 7, 8], [1, 4, 4]], 336], [2, 1, 0])], [([480, [[0, 6, 8]], 720], [1, 4, 0]), ([480, [[0, 3, 4]], 1450], [2, 1, 10]), ([480, [[0, 4, 4], [2, 3, 4]], 3840], [3, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5280], [4, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5300], [4, 1, 20]), ([480, [[0, 2, 2]], 1000], [1, 2, 40]), ([96, [[0, 7, 8], [1, 4, 4]], 336], [2, 1, 0]), ([96, [[0, 7, 8], [1, 4, 4]], 400], [2, 1, 64])], [([480, [[0, 6, 8]], 1440], [2, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5280], [4, 1, 0]), ([96, [[0, 7, 8], [1, 4, 4]], 336], [2, 1, 0]), ([96, [[0, 7, 8], [1, 4, 4]], 400], [2, 1, 64]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 1920], [2, 1, 0]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 4320], [4, 1, 0]), ([480, [[0, 3, 16]], 700], [2, 3, 100]), ([120, [[0, 4, 4], [4, 6, 8], [6, 4, 4]], 2000], [5, 2, 20])]]
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 0[1, 1, 0][1, 1, 0]Passed
oracle 1[2, 1, 0][2, 1, 0]Passed
oracle 2[2, 2, 0][2, 2, 0]Passed
oracle 3[1, 4, 0][1, 4, 0]Passed
oracle 4[2, 1, 0][2, 1, 0]Passed
oracle 5[2, 1, 10][2, 1, 10]Passed
oracle 6NoneNonePassed
oracle 7NoneNonePassed

SHA-256 / 1420ebdba5df6efd24e3602f1a776ae5cf992cdc067401df281c5841f0f72f67

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 2026-09-29T14:50:03.794253+00:00.

Case digest / 83cfb8153bcfca31d8edcf9b6968a8b3fd0c3dc1ff360350938b625eb716220c