Source: https://guthlabs.ai/docs/instruments/delay-time-from-bpm-musical-note-divisions/mechanism/

instrument mechanism / verified-clean

# Delay Time from BPM (Musical Note Divisions) mechanism

The inspectable method record for Delay Time from BPM (Musical Note Divisions), kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The delay-time arithmetic is correct under the stated assumptions, but the instrument cannot receive PASS until the modulation-rate formula, exact note-division parsing rules, and BPM/input constraints are explicitly specified.

- The delay-time formulas are standard: quarter-note milliseconds = 60000/BPM, with note-length fractions, dotted multiplier 1.5, and triplet multiplier 2/3. However, the formula for the advertised corresponding modulation frequency is omitted; it should be explicitly defined as Hz = 1000/delay_ms.

- The accepted mapping from note-division labels such as 1/4, 1/8 dotted, and 1/8 triplet to numeric fractions is not specified precisely enough for implementation.

## Units and conventions

- BPM means beats per minute, with one quarter note representing one beat.

- 60000 converts minutes to milliseconds, so quarter-note duration is 60000/BPM ms.

- A division such as 1/8 means one-half of a quarter-note duration; 1/16 means one-quarter; 1/32 means one-eighth.

- Dotted means the base note duration multiplied by 1.5.

- Triplet means the base note duration multiplied by 2/3.

- Modulation frequency is assumed to be the reciprocal of delay duration after converting milliseconds to seconds: Hz = 1000/delay_ms.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "BPM": 120,
    "note_division": "1/4"
  },
  "expected_outputs": {
    "delay_ms": 500,
    "modulation_rate_hz": 2
  },
  "working": "Quarter note = 60000 / 120 = 500 ms. A 1/4 note is the quarter note, so delay = 500 ms. Convert to frequency: Hz = 1000 / 500 = 2 Hz."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

BPM=0 produces an undefined delay through division by zero and must be rejected. Negative BPM also exposes an unstated sign convention: direct arithmetic returns a physically invalid negative delay, while magnitude-based handling returns a positive delay.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/delay-time-from-bpm-musical-note-divisions/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/delay-time-from-bpm-musical-note-divisions/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/delay-time-from-bpm-musical-note-divisions/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche3/tranche3-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`