FA-81556 / MIDI event timing / Open access

Eighth-note swing time remapping: offbeat half stretched by the downbeat factor · case 01

With 66% swing a note late in the beat (tick 479 of a 480-tick beat) lands after the next downbeat.

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

ROOT CAUSE

The second half of the beat is scaled by the first-half factor split/half instead of (ppq-split)/half.

VERIFIED REPAIR

Restore the second half scale step so that it reads `(ppq - split) / half`.

Unsuccessful approach: Using an unscaled second half shifts it by the swing offset without compressing it, overrunning the beat.

Case contract

Input [ticks, ppq, swing] with even ppq > 0 and swing 50..75 percent. Within each beat, positions in the first half [0, ppq/2) scale linearly onto [0, split) and positions in the second half onto [split, ppq), where split = ppq*swing/100. The remapped position is floored. Invalid parameters return 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
from fractions import Fraction
N = 1
observations = []
def solve(x):
    if not isinstance(x, list) or len(x) != 3:
        return None
    ticks, ppq, swing = x
    if ppq <= 0 or ppq % 2 or not 50 <= swing <= 75:
        return None
    half = ppq // 2
    split = Fraction(ppq * swing, 100)
    out = []
    for t in ticks:
        beat, pos = divmod(t, ppq)
        if pos < half:
            new = pos * split / half
        else:
            new = split + (pos - half) * split / half
        out.append(beat * ppq + int(new))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([[0, 240, 480, 720], 480, 50], [0, 240, 480, 720]), ([[0, 240, 480, 720], 480, 66], [0, 316, 480, 796]), ([[240, 300, 479], 480, 66], [316, 357, 479]), ([[960, 1200, 1320], 480, 75], [960, 1320, 1380]), ([[1, 239, 241], 480, 70], [1, 334, 336]), ([[0, 60], 120, 58], [0, 69]), ([[0, 240], 480, 49], None), ([[0, 240], 480, 76], None)], [([[240, 300, 479], 480, 66], [316, 357, 479]), ([[120, 360], 480, 60], [144, 384]), ([[1, 239, 241], 480, 70], [1, 334, 336]), ([[0, 240], 480, 49], None), ([[0, 240], 480, 76], None), ([[0, 240], 481, 60], None), ([[100, 300], 480, 55], [110, 318]), ([[250, 470], 480, 50], [250, 470])], [([[240, 300, 479], 480, 66], [316, 357, 479]), ([[120, 360], 480, 60], [144, 384]), ([[960, 1200, 1320], 480, 75], [960, 1320, 1380]), ([[1, 239, 241], 480, 70], [1, 334, 336]), ([[100, 300], 480, 55], [110, 318]), ([[90], 120, 62], [97]), ([[5, 55], 100, 64], [6, 67]), ([[250, 470], 480, 50], [250, 470])], [([[0, 240, 480, 720], 480, 50], [0, 240, 480, 720]), ([[0, 240, 480, 720], 480, 66], [0, 316, 480, 796]), ([[960, 1200, 1320], 480, 75], [960, 1320, 1380]), ([[1, 239, 241], 480, 70], [1, 334, 336]), ([[100, 300], 480, 55], [110, 318]), ([[90], 120, 62], [97]), ([[5, 55], 100, 64], [6, 67]), ([[30, 100], 120, 67], [40, 106])], [([[0, 240, 480, 720], 480, 50], [0, 240, 480, 720]), ([[0, 240, 480, 720], 480, 66], [0, 316, 480, 796]), ([[0, 60], 120, 58], [0, 69]), ([[0, 240], 480, 49], None), ([[100, 300], 480, 55], [110, 318]), ([[90], 120, 62], [97]), ([[5, 55], 100, 64], [6, 67]), ([[30, 100], 120, 67], [40, 106])]]
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, 240, 480, 720]`	`[0, 240, 480, 720]`	Passed
oracle 1	`[0, 316, 480, 796]`	`[0, 316, 480, 796]`	Passed
oracle 2	`[316, 396, 632]`	`[316, 357, 479]`	Failed
oracle 3	`[960, 1320, 1500]`	`[960, 1320, 1380]`	Failed
oracle 4	`[1, 334, 337]`	`[1, 334, 336]`	Failed
oracle 5	`[0, 69]`	`[0, 69]`	Passed
oracle 6	`None`	`None`	Passed
oracle 7	`None`	`None`	Passed

SHA-256 / 9429660f5867870e0f68ab85279bca4ae2eea517e1976f79d655725c02e4237d

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(x):
    if not isinstance(x, list) or len(x) != 3:
        return None
    ticks, ppq, swing = x
    if ppq <= 0 or ppq % 2 or not 50 <= swing <= 75:
        return None
    half = ppq // 2
    split = Fraction(ppq * swing, 100)
    out = []
    for t in ticks:
        beat, pos = divmod(t, ppq)
        if pos < half:
            new = pos * split / half
        else:
            new = split + (pos - half) * (ppq - half) / half
        out.append(beat * ppq + int(new))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([[0, 240, 480, 720], 480, 50], [0, 240, 480, 720]), ([[0, 240, 480, 720], 480, 66], [0, 316, 480, 796]), ([[240, 300, 479], 480, 66], [316, 357, 479]), ([[960, 1200, 1320], 480, 75], [960, 1320, 1380]), ([[1, 239, 241], 480, 70], [1, 334, 336]), ([[0, 60], 120, 58], [0, 69]), ([[0, 240], 480, 49], None), ([[0, 240], 480, 76], None)], [([[240, 300, 479], 480, 66], [316, 357, 479]), ([[120, 360], 480, 60], [144, 384]), ([[1, 239, 241], 480, 70], [1, 334, 336]), ([[0, 240], 480, 49], None), ([[0, 240], 480, 76], None), ([[0, 240], 481, 60], None), ([[100, 300], 480, 55], [110, 318]), ([[250, 470], 480, 50], [250, 470])], [([[240, 300, 479], 480, 66], [316, 357, 479]), ([[120, 360], 480, 60], [144, 384]), ([[960, 1200, 1320], 480, 75], [960, 1320, 1380]), ([[1, 239, 241], 480, 70], [1, 334, 336]), ([[100, 300], 480, 55], [110, 318]), ([[90], 120, 62], [97]), ([[5, 55], 100, 64], [6, 67]), ([[250, 470], 480, 50], [250, 470])], [([[0, 240, 480, 720], 480, 50], [0, 240, 480, 720]), ([[0, 240, 480, 720], 480, 66], [0, 316, 480, 796]), ([[960, 1200, 1320], 480, 75], [960, 1320, 1380]), ([[1, 239, 241], 480, 70], [1, 334, 336]), ([[100, 300], 480, 55], [110, 318]), ([[90], 120, 62], [97]), ([[5, 55], 100, 64], [6, 67]), ([[30, 100], 120, 67], [40, 106])], [([[0, 240, 480, 720], 480, 50], [0, 240, 480, 720]), ([[0, 240, 480, 720], 480, 66], [0, 316, 480, 796]), ([[0, 60], 120, 58], [0, 69]), ([[0, 240], 480, 49], None), ([[100, 300], 480, 55], [110, 318]), ([[90], 120, 62], [97]), ([[5, 55], 100, 64], [6, 67]), ([[30, 100], 120, 67], [40, 106])]]
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, 240, 480, 720]`	`[0, 240, 480, 720]`	Passed
oracle 1	`[0, 316, 480, 796]`	`[0, 316, 480, 796]`	Passed
oracle 2	`[316, 376, 555]`	`[316, 357, 479]`	Failed
oracle 3	`[960, 1320, 1440]`	`[960, 1320, 1380]`	Failed
oracle 4	`[1, 334, 337]`	`[1, 334, 336]`	Failed
oracle 5	`[0, 69]`	`[0, 69]`	Passed
oracle 6	`None`	`None`	Passed
oracle 7	`None`	`None`	Passed

SHA-256 / 772afb3888b83081f836b89d2797d1c2eaa93e23d500c77982fc7a3b1776daa7

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(x):
    if not isinstance(x, list) or len(x) != 3:
        return None
    ticks, ppq, swing = x
    if ppq <= 0 or ppq % 2 or not 50 <= swing <= 75:
        return None
    half = ppq // 2
    split = Fraction(ppq * swing, 100)
    out = []
    for t in ticks:
        beat, pos = divmod(t, ppq)
        if pos < half:
            new = pos * split / half
        else:
            new = split + (pos - half) * (ppq - split) / half
        out.append(beat * ppq + int(new))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([[0, 240, 480, 720], 480, 50], [0, 240, 480, 720]), ([[0, 240, 480, 720], 480, 66], [0, 316, 480, 796]), ([[240, 300, 479], 480, 66], [316, 357, 479]), ([[960, 1200, 1320], 480, 75], [960, 1320, 1380]), ([[1, 239, 241], 480, 70], [1, 334, 336]), ([[0, 60], 120, 58], [0, 69]), ([[0, 240], 480, 49], None), ([[0, 240], 480, 76], None)], [([[240, 300, 479], 480, 66], [316, 357, 479]), ([[120, 360], 480, 60], [144, 384]), ([[1, 239, 241], 480, 70], [1, 334, 336]), ([[0, 240], 480, 49], None), ([[0, 240], 480, 76], None), ([[0, 240], 481, 60], None), ([[100, 300], 480, 55], [110, 318]), ([[250, 470], 480, 50], [250, 470])], [([[240, 300, 479], 480, 66], [316, 357, 479]), ([[120, 360], 480, 60], [144, 384]), ([[960, 1200, 1320], 480, 75], [960, 1320, 1380]), ([[1, 239, 241], 480, 70], [1, 334, 336]), ([[100, 300], 480, 55], [110, 318]), ([[90], 120, 62], [97]), ([[5, 55], 100, 64], [6, 67]), ([[250, 470], 480, 50], [250, 470])], [([[0, 240, 480, 720], 480, 50], [0, 240, 480, 720]), ([[0, 240, 480, 720], 480, 66], [0, 316, 480, 796]), ([[960, 1200, 1320], 480, 75], [960, 1320, 1380]), ([[1, 239, 241], 480, 70], [1, 334, 336]), ([[100, 300], 480, 55], [110, 318]), ([[90], 120, 62], [97]), ([[5, 55], 100, 64], [6, 67]), ([[30, 100], 120, 67], [40, 106])], [([[0, 240, 480, 720], 480, 50], [0, 240, 480, 720]), ([[0, 240, 480, 720], 480, 66], [0, 316, 480, 796]), ([[0, 60], 120, 58], [0, 69]), ([[0, 240], 480, 49], None), ([[100, 300], 480, 55], [110, 318]), ([[90], 120, 62], [97]), ([[5, 55], 100, 64], [6, 67]), ([[30, 100], 120, 67], [40, 106])]]
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, 240, 480, 720]`	`[0, 240, 480, 720]`	Passed
oracle 1	`[0, 316, 480, 796]`	`[0, 316, 480, 796]`	Passed
oracle 2	`[316, 357, 479]`	`[316, 357, 479]`	Passed
oracle 3	`[960, 1320, 1380]`	`[960, 1320, 1380]`	Passed
oracle 4	`[1, 334, 336]`	`[1, 334, 336]`	Passed
oracle 5	`[0, 69]`	`[0, 69]`	Passed
oracle 6	`None`	`None`	Passed
oracle 7	`None`	`None`	Passed

SHA-256 / 2d1bbbfb48c68b12b8c9286a896b5caa275c9f43d6980f6c1f5e0a0dac222d26

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 2026-09-29T14:50:04.082891+00:00.

Case digest / 174dced850b17f78953e70c80ef9bda9985c830016cebbb741ab7bff4dd99f37