FA-81476 / MIDI event timing / Open access

Tick to microsecond conversion through a tempo map: first tempo applied from tick zero · case 01

Material before the first tempo event is timed at that later tempo instead of the default 120 BPM.

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

ROOT CAUSE

The starting tempo is taken from the earliest tempo change rather than the default.

VERIFIED REPAIR

Restore the initial tempo step so that it reads `tempo = 500000`.

Unsuccessful approach: Using the first listed change instead is the same mistake and also depends on input order.

Case contract

Input [ppq, changes, tick] where changes are [tick, microseconds_per_quarter] in any order (a later entry at the same tick overrides an earlier one). Before the first change the tempo is 500000. Each tempo applies from its tick onward. Sum the exact time of each segment and floor once at the end. Invalid ppq or negative tick 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
from fractions import Fraction
N = 1
observations = []
def solve(x):
    if not isinstance(x, list) or len(x) != 3:
        return None
    ppq, changes, target = x
    if ppq <= 0 or target < 0:
        return None
    tempo_at = {}
    for t, us in changes:
        tempo_at[t] = us
    points = sorted(tempo_at.items())
    total = Fraction(0)
    tick = 0
    tempo = points[0][1] if points else 500000
    for t, us in points:
        if t >= target:
            break
        total += Fraction((t - tick) * tempo, ppq)
        tick = t
        tempo = us
    total += Fraction((target - tick) * tempo, ppq)
    return int(total)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([480, [], 480], 500000), ([480, [], 1], 1041), ([96, [[0, 600000]], 96], 600000), ([480, [[480, 250000]], 960], 750000), ([7, [[3, 333333]], 10], 547618), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[0, 400000], [0, 300000]], 480], 300000), ([0, [], 10], None)], [([480, [[960, 1000000], [480, 250000]], 1440], 1750000), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[0, 400000], [0, 300000]], 480], 300000), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([0, [], 10], None), ([480, [], -1], None), ([480, [[0, 1000000], [480, 500000]], 720], 1250000), ([480, [[0, 300000], [0, 400000]], 480], 400000)], [([480, [[480, 250000]], 960], 750000), ([480, [[960, 1000000], [480, 250000]], 1440], 1750000), ([7, [[3, 333333]], 10], 547618), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000), ([480, [[0, 1000000], [480, 500000]], 720], 1250000), ([480, [[0, 300000], [0, 400000]], 480], 400000)], [([480, [[960, 1000000], [480, 250000]], 1440], 1750000), ([7, [[3, 333333]], 10], 547618), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000), ([480, [[480, 250000]], 480], 500000), ([480, [[100, 100000]], 50], 52083), ([11, [[5, 777777], [9, 123457]], 13], 554994)], [([480, [], 480], 500000), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000), ([480, [[480, 250000]], 480], 500000), ([480, [[100, 100000]], 50], 52083), ([11, [[5, 777777], [9, 123457]], 13], 554994), ([7, [[2, 300001], [2, 400003]], 6], 371430), ([13, [[4, 499999], [8, 333337]], 12], 410257)]]
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	`500000`	`500000`	Passed
oracle 1	`1041`	`1041`	Passed
oracle 2	`600000`	`600000`	Passed
oracle 3	`500000`	`750000`	Failed
oracle 4	`476190`	`547618`	Failed
oracle 5	`114287`	`171430`	Failed
oracle 6	`300000`	`300000`	Passed
oracle 7	`None`	`None`	Passed

SHA-256 / 1dcc9d028e7c58740da2026c1819498132b1ca19964708ed10dd5340f0a2f070

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
    ppq, changes, target = x
    if ppq <= 0 or target < 0:
        return None
    tempo_at = {}
    for t, us in changes:
        tempo_at[t] = us
    points = sorted(tempo_at.items())
    total = Fraction(0)
    tick = 0
    tempo = changes[0][1] if changes else 500000
    for t, us in points:
        if t >= target:
            break
        total += Fraction((t - tick) * tempo, ppq)
        tick = t
        tempo = us
    total += Fraction((target - tick) * tempo, ppq)
    return int(total)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([480, [], 480], 500000), ([480, [], 1], 1041), ([96, [[0, 600000]], 96], 600000), ([480, [[480, 250000]], 960], 750000), ([7, [[3, 333333]], 10], 547618), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[0, 400000], [0, 300000]], 480], 300000), ([0, [], 10], None)], [([480, [[960, 1000000], [480, 250000]], 1440], 1750000), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[0, 400000], [0, 300000]], 480], 300000), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([0, [], 10], None), ([480, [], -1], None), ([480, [[0, 1000000], [480, 500000]], 720], 1250000), ([480, [[0, 300000], [0, 400000]], 480], 400000)], [([480, [[480, 250000]], 960], 750000), ([480, [[960, 1000000], [480, 250000]], 1440], 1750000), ([7, [[3, 333333]], 10], 547618), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000), ([480, [[0, 1000000], [480, 500000]], 720], 1250000), ([480, [[0, 300000], [0, 400000]], 480], 400000)], [([480, [[960, 1000000], [480, 250000]], 1440], 1750000), ([7, [[3, 333333]], 10], 547618), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000), ([480, [[480, 250000]], 480], 500000), ([480, [[100, 100000]], 50], 52083), ([11, [[5, 777777], [9, 123457]], 13], 554994)], [([480, [], 480], 500000), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000), ([480, [[480, 250000]], 480], 500000), ([480, [[100, 100000]], 50], 52083), ([11, [[5, 777777], [9, 123457]], 13], 554994), ([7, [[2, 300001], [2, 400003]], 6], 371430), ([13, [[4, 499999], [8, 333337]], 12], 410257)]]
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	`500000`	`500000`	Passed
oracle 1	`1041`	`1041`	Passed
oracle 2	`600000`	`600000`	Passed
oracle 3	`500000`	`750000`	Failed
oracle 4	`476190`	`547618`	Failed
oracle 5	`114287`	`171430`	Failed
oracle 6	`300000`	`300000`	Passed
oracle 7	`None`	`None`	Passed

SHA-256 / 1ef4085bfbebb6129f81ed3183e11a3c5c4d35f90e979361768b9fdf90ee505d

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
    ppq, changes, target = x
    if ppq <= 0 or target < 0:
        return None
    tempo_at = {}
    for t, us in changes:
        tempo_at[t] = us
    points = sorted(tempo_at.items())
    total = Fraction(0)
    tick = 0
    tempo = 500000
    for t, us in points:
        if t >= target:
            break
        total += Fraction((t - tick) * tempo, ppq)
        tick = t
        tempo = us
    total += Fraction((target - tick) * tempo, ppq)
    return int(total)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([480, [], 480], 500000), ([480, [], 1], 1041), ([96, [[0, 600000]], 96], 600000), ([480, [[480, 250000]], 960], 750000), ([7, [[3, 333333]], 10], 547618), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[0, 400000], [0, 300000]], 480], 300000), ([0, [], 10], None)], [([480, [[960, 1000000], [480, 250000]], 1440], 1750000), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[0, 400000], [0, 300000]], 480], 300000), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([0, [], 10], None), ([480, [], -1], None), ([480, [[0, 1000000], [480, 500000]], 720], 1250000), ([480, [[0, 300000], [0, 400000]], 480], 400000)], [([480, [[480, 250000]], 960], 750000), ([480, [[960, 1000000], [480, 250000]], 1440], 1750000), ([7, [[3, 333333]], 10], 547618), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000), ([480, [[0, 1000000], [480, 500000]], 720], 1250000), ([480, [[0, 300000], [0, 400000]], 480], 400000)], [([480, [[960, 1000000], [480, 250000]], 1440], 1750000), ([7, [[3, 333333]], 10], 547618), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000), ([480, [[480, 250000]], 480], 500000), ([480, [[100, 100000]], 50], 52083), ([11, [[5, 777777], [9, 123457]], 13], 554994)], [([480, [], 480], 500000), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000), ([480, [[480, 250000]], 480], 500000), ([480, [[100, 100000]], 50], 52083), ([11, [[5, 777777], [9, 123457]], 13], 554994), ([7, [[2, 300001], [2, 400003]], 6], 371430), ([13, [[4, 499999], [8, 333337]], 12], 410257)]]
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	`500000`	`500000`	Passed
oracle 1	`1041`	`1041`	Passed
oracle 2	`600000`	`600000`	Passed
oracle 3	`750000`	`750000`	Passed
oracle 4	`547618`	`547618`	Passed
oracle 5	`171430`	`171430`	Passed
oracle 6	`300000`	`300000`	Passed
oracle 7	`None`	`None`	Passed

SHA-256 / 5176afe559e2f98e8418bff941fbd63673b178e4ce77a6908c3eaf98540ff3bd

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 2026-09-29T14:50:03.196444+00:00.

Case digest / af9a32ff9a054ed366609be6a9b981ed69a786c3f2258022fb4aba20e26f8448