FA-81501 / MIDI event timing / Open access

Set Tempo meta event to BPM: BPM truncated instead of rounded · case 01

A tempo of 3840000 microseconds reports 15.62 BPM instead of 15.63.

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

ROOT CAUSE

The scaled BPM is floor-divided with no half adjustment.

VERIFIED REPAIR

Restore the BPM rounding step so that it reads `(12000000000 + us) // (2 * us)`.

Unsuccessful approach: Python round uses round-half-even, so exact halves like 1562.5 still round down.

Case contract

Input the bytes of a Set Tempo meta event: FF 51 03 followed by a 24-bit big-endian microseconds-per-quarter value (nonzero). Return [microseconds, bpm_x100] where bpm_x100 = 6000000000 / microseconds rounded half up. Anything else 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) != 6 or x[0] != 0xFF or x[1] != 0x51 or x[2] != 3:
        return None
    us = (x[3] << 16) | (x[4] << 8) | x[5]
    if us == 0:
        return None
    centi = 6000000000 // us
    return [us, centi]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([255, 81, 3, 7, 161, 32], [500000, 12000]), ([255, 81, 3, 9, 39, 192], [600000, 10000]), ([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 81, 3, 0, 0, 1], [1, 6000000000]), ([255, 81, 4, 7, 161, 32], None), ([255, 81, 2, 7, 161, 32], None), ([255, 81, 3, 0, 0, 0], None)], [([255, 81, 3, 11, 184, 0], [768000, 7813]), ([255, 81, 3, 255, 255, 255], [16777215, 358]), ([255, 81, 4, 7, 161, 32], None), ([255, 81, 2, 7, 161, 32], None), ([255, 81, 3, 0, 0, 0], None), ([255, 82, 3, 7, 161, 32], None), ([255, 81, 3, 7, 161], None), ([255, 81, 3, 6, 26, 128], [400000, 15000])], [([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 82, 3, 7, 161, 32], None), ([255, 81, 3, 7, 161], None), ([255, 81, 3, 6, 26, 128], [400000, 15000]), ([255, 81, 3, 3, 13, 64], [200000, 30000]), ([255, 81, 3, 0, 3, 232], [1000, 6000000]), ([255, 81, 3, 15, 66, 64], [1000000, 6000])], [([255, 81, 3, 7, 161, 32], [500000, 12000]), ([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 11, 184, 0], [768000, 7813]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 81, 3, 255, 255, 255], [16777215, 358]), ([255, 81, 3, 3, 13, 64], [200000, 30000]), ([255, 81, 3, 0, 3, 232], [1000, 6000000]), ([255, 81, 3, 15, 66, 64], [1000000, 6000])], [([255, 81, 3, 7, 161, 32], [500000, 12000]), ([255, 81, 3, 9, 39, 192], [600000, 10000]), ([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 11, 184, 0], [768000, 7813]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 81, 3, 0, 0, 1], [1, 6000000000]), ([255, 81, 3, 255, 255, 255], [16777215, 358]), ([255, 81, 4, 7, 161, 32], None)]]
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, 12000]`	`[500000, 12000]`	Passed
oracle 1	`[600000, 10000]`	`[600000, 10000]`	Passed
oracle 2	`[3840000, 1562]`	`[3840000, 1563]`	Failed
oracle 3	`[153600, 39062]`	`[153600, 39063]`	Failed
oracle 4	`[1, 6000000000]`	`[1, 6000000000]`	Passed
oracle 5	`None`	`None`	Passed
oracle 6	`None`	`None`	Passed
oracle 7	`None`	`None`	Passed

SHA-256 / 3c97905c03af2effccc36ca8191908b24f8f0c670c86d68fcdb1b136ba4a5c6b

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) != 6 or x[0] != 0xFF or x[1] != 0x51 or x[2] != 3:
        return None
    us = (x[3] << 16) | (x[4] << 8) | x[5]
    if us == 0:
        return None
    centi = round(6000000000 / us)
    return [us, centi]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([255, 81, 3, 7, 161, 32], [500000, 12000]), ([255, 81, 3, 9, 39, 192], [600000, 10000]), ([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 81, 3, 0, 0, 1], [1, 6000000000]), ([255, 81, 4, 7, 161, 32], None), ([255, 81, 2, 7, 161, 32], None), ([255, 81, 3, 0, 0, 0], None)], [([255, 81, 3, 11, 184, 0], [768000, 7813]), ([255, 81, 3, 255, 255, 255], [16777215, 358]), ([255, 81, 4, 7, 161, 32], None), ([255, 81, 2, 7, 161, 32], None), ([255, 81, 3, 0, 0, 0], None), ([255, 82, 3, 7, 161, 32], None), ([255, 81, 3, 7, 161], None), ([255, 81, 3, 6, 26, 128], [400000, 15000])], [([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 82, 3, 7, 161, 32], None), ([255, 81, 3, 7, 161], None), ([255, 81, 3, 6, 26, 128], [400000, 15000]), ([255, 81, 3, 3, 13, 64], [200000, 30000]), ([255, 81, 3, 0, 3, 232], [1000, 6000000]), ([255, 81, 3, 15, 66, 64], [1000000, 6000])], [([255, 81, 3, 7, 161, 32], [500000, 12000]), ([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 11, 184, 0], [768000, 7813]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 81, 3, 255, 255, 255], [16777215, 358]), ([255, 81, 3, 3, 13, 64], [200000, 30000]), ([255, 81, 3, 0, 3, 232], [1000, 6000000]), ([255, 81, 3, 15, 66, 64], [1000000, 6000])], [([255, 81, 3, 7, 161, 32], [500000, 12000]), ([255, 81, 3, 9, 39, 192], [600000, 10000]), ([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 11, 184, 0], [768000, 7813]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 81, 3, 0, 0, 1], [1, 6000000000]), ([255, 81, 3, 255, 255, 255], [16777215, 358]), ([255, 81, 4, 7, 161, 32], None)]]
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, 12000]`	`[500000, 12000]`	Passed
oracle 1	`[600000, 10000]`	`[600000, 10000]`	Passed
oracle 2	`[3840000, 1562]`	`[3840000, 1563]`	Failed
oracle 3	`[153600, 39062]`	`[153600, 39063]`	Failed
oracle 4	`[1, 6000000000]`	`[1, 6000000000]`	Passed
oracle 5	`None`	`None`	Passed
oracle 6	`None`	`None`	Passed
oracle 7	`None`	`None`	Passed

SHA-256 / 3e3e9013323d98c0cc844b82097c2a2226ec16e86b82901383b95727e9ce4d60

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) != 6 or x[0] != 0xFF or x[1] != 0x51 or x[2] != 3:
        return None
    us = (x[3] << 16) | (x[4] << 8) | x[5]
    if us == 0:
        return None
    centi = (12000000000 + us) // (2 * us)
    return [us, centi]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([255, 81, 3, 7, 161, 32], [500000, 12000]), ([255, 81, 3, 9, 39, 192], [600000, 10000]), ([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 81, 3, 0, 0, 1], [1, 6000000000]), ([255, 81, 4, 7, 161, 32], None), ([255, 81, 2, 7, 161, 32], None), ([255, 81, 3, 0, 0, 0], None)], [([255, 81, 3, 11, 184, 0], [768000, 7813]), ([255, 81, 3, 255, 255, 255], [16777215, 358]), ([255, 81, 4, 7, 161, 32], None), ([255, 81, 2, 7, 161, 32], None), ([255, 81, 3, 0, 0, 0], None), ([255, 82, 3, 7, 161, 32], None), ([255, 81, 3, 7, 161], None), ([255, 81, 3, 6, 26, 128], [400000, 15000])], [([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 82, 3, 7, 161, 32], None), ([255, 81, 3, 7, 161], None), ([255, 81, 3, 6, 26, 128], [400000, 15000]), ([255, 81, 3, 3, 13, 64], [200000, 30000]), ([255, 81, 3, 0, 3, 232], [1000, 6000000]), ([255, 81, 3, 15, 66, 64], [1000000, 6000])], [([255, 81, 3, 7, 161, 32], [500000, 12000]), ([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 11, 184, 0], [768000, 7813]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 81, 3, 255, 255, 255], [16777215, 358]), ([255, 81, 3, 3, 13, 64], [200000, 30000]), ([255, 81, 3, 0, 3, 232], [1000, 6000000]), ([255, 81, 3, 15, 66, 64], [1000000, 6000])], [([255, 81, 3, 7, 161, 32], [500000, 12000]), ([255, 81, 3, 9, 39, 192], [600000, 10000]), ([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 11, 184, 0], [768000, 7813]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 81, 3, 0, 0, 1], [1, 6000000000]), ([255, 81, 3, 255, 255, 255], [16777215, 358]), ([255, 81, 4, 7, 161, 32], None)]]
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, 12000]`	`[500000, 12000]`	Passed
oracle 1	`[600000, 10000]`	`[600000, 10000]`	Passed
oracle 2	`[3840000, 1563]`	`[3840000, 1563]`	Passed
oracle 3	`[153600, 39063]`	`[153600, 39063]`	Passed
oracle 4	`[1, 6000000000]`	`[1, 6000000000]`	Passed
oracle 5	`None`	`None`	Passed
oracle 6	`None`	`None`	Passed
oracle 7	`None`	`None`	Passed

SHA-256 / 02d8de02aed83c046e812b7176345c2232a226d542bbb08a29c07efb5d700745

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 2026-09-29T14:50:03.709797+00:00.

Case digest / bc221b6fa58ea402433d73fd095c20602a960980cb8ff1f7697436c6a817a8b2