FA-81646 / MIDI event timing / Open access

14-bit pitch bend to cents: maximum bend falls short of the range · case 01

Full upward bend (127, 127) on a 48-semitone MPE range reports 4799 cents instead of exactly 4800.

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

ROOT CAUSE

Positive offsets are divided by 8192 although only 8191 steps exist above the centre.

THE FAILURE

Positive offsets are divided by 8192 although only 8191 steps exist above the centre.

Unsuccessful approach: Dividing negative offsets by 8191 makes full downward bend overshoot the range.

Case contract

Input [lsb, msb, range_semitones] with 7-bit data bytes. value = msb*128 + lsb, offset = value - 8192. Positive offsets scale to +range by dividing by 8191, negative ones by 8192. cents = offset * range * 100 / divisor, rounded half away from zero. Invalid bytes or negative range 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
    lsb, msb, rng = x
    if not all(isinstance(v, int) and 0 <= v <= 127 for v in (lsb, msb)) or rng < 0:
        return None
    value = (msb << 7) | lsb
    offset = value - 8192
    den = 8192
    c = Fraction(abs(offset) * rng * 100, den)
    cents = int(c + Fraction(1, 2))
    return cents if offset >= 0 else -cents
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([0, 64, 2], 0), ([127, 127, 2], 200), ([0, 0, 2], -200), ([0, 96, 2], 100), ([0, 32, 2], -100), ([0, 56, 1], -13), ([127, 127, 48], 4800), ([0, 0, 48], -4800)], [([0, 96, 2], 100), ([0, 32, 2], -100), ([0, 56, 1], -13), ([0, 24, 1], -63), ([0, 40, 1], -38), ([1, 64, 2], 0), ([127, 127, 48], 4800), ([0, 0, 48], -4800)], [([0, 24, 1], -63), ([0, 40, 1], -38), ([1, 64, 2], 0), ([127, 63, 2], 0), ([0, 72, 12], 150), ([0, 56, 3], -38), ([127, 127, 48], 4800), ([0, 0, 48], -4800)], [([127, 63, 2], 0), ([0, 72, 12], 150), ([0, 56, 3], -38), ([0, 128, 2], None), ([128, 64, 2], None), ([0, 64, -1], None), ([127, 127, 48], 4800), ([0, 0, 48], -4800)], [([0, 128, 2], None), ([128, 64, 2], None), ([0, 64, -1], None), ([127, 127, 12], 1200), ([0, 0, 12], -1200), ([64, 100, 2], 114), ([127, 127, 48], 4800), ([0, 0, 48], -4800)]]
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`	`0`	Passed
oracle 1	`200`	`200`	Passed
oracle 2	`-200`	`-200`	Passed
oracle 3	`100`	`100`	Passed
oracle 4	`-100`	`-100`	Passed
oracle 5	`-13`	`-13`	Passed
oracle 6	`4799`	`4800`	Failed
oracle 7	`-4800`	`-4800`	Passed

SHA-256 / 7ca004f52803f2a779e726bfbf33d6deeef69095d35f450154909c19a9849d19

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
    lsb, msb, rng = x
    if not all(isinstance(v, int) and 0 <= v <= 127 for v in (lsb, msb)) or rng < 0:
        return None
    value = (msb << 7) | lsb
    offset = value - 8192
    den = 8191
    c = Fraction(abs(offset) * rng * 100, den)
    cents = int(c + Fraction(1, 2))
    return cents if offset >= 0 else -cents
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([0, 64, 2], 0), ([127, 127, 2], 200), ([0, 0, 2], -200), ([0, 96, 2], 100), ([0, 32, 2], -100), ([0, 56, 1], -13), ([127, 127, 48], 4800), ([0, 0, 48], -4800)], [([0, 96, 2], 100), ([0, 32, 2], -100), ([0, 56, 1], -13), ([0, 24, 1], -63), ([0, 40, 1], -38), ([1, 64, 2], 0), ([127, 127, 48], 4800), ([0, 0, 48], -4800)], [([0, 24, 1], -63), ([0, 40, 1], -38), ([1, 64, 2], 0), ([127, 63, 2], 0), ([0, 72, 12], 150), ([0, 56, 3], -38), ([127, 127, 48], 4800), ([0, 0, 48], -4800)], [([127, 63, 2], 0), ([0, 72, 12], 150), ([0, 56, 3], -38), ([0, 128, 2], None), ([128, 64, 2], None), ([0, 64, -1], None), ([127, 127, 48], 4800), ([0, 0, 48], -4800)], [([0, 128, 2], None), ([128, 64, 2], None), ([0, 64, -1], None), ([127, 127, 12], 1200), ([0, 0, 12], -1200), ([64, 100, 2], 114), ([127, 127, 48], 4800), ([0, 0, 48], -4800)]]
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`	`0`	Passed
oracle 1	`200`	`200`	Passed
oracle 2	`-200`	`-200`	Passed
oracle 3	`100`	`100`	Passed
oracle 4	`-100`	`-100`	Passed
oracle 5	`-13`	`-13`	Passed
oracle 6	`4800`	`4800`	Passed
oracle 7	`-4801`	`-4800`	Failed

SHA-256 / 510afda3f261a6c8cce22b5f9f9bd77a89278bcf0ecbf62736a5f9235c35e23d

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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 2026-09-29T14:50:05.029182+00:00.

Case digest / 0be8fe46622a0630035763656ca42e9262610df84fda5bd704146de34525e12c