How BeatTiming verifies every calculation.
Each tool shows its formula and states its limits. Before a release goes live, automated tests check the answers. The same tests can be run again to check the result.
Our calculation checks and limits
Last verified September 5, 2026. The test seed is 0x18acc0de. This fixed starting value lets us run the same set of random test cases again.
What those numbers mean
The total counts automated checks, not human reviews. Each check tests one condition in a fixed set of cases. Some checks compare an answer with a known value. Others run a calculation in reverse or compare it with a separate whole-number method. Tests also cover input limits. A failed check stops the release.
Calculator formulas and verification
| Calculator group | Core relationship | How it is checked |
|---|---|---|
| Tap tempo | BPM = 60,000 ÷ estimated tap interval in milliseconds | Exact-tempo sweeps from 15–500 BPM, jitter trials at both endpoints, outlier handling and reset boundaries. |
| Note, delay, reverb and LFO timing | note ms = 60,000 ÷ BPM × division; Hz = 1,000 ÷ duration ms | Reciprocal timing and frequency invariants across straight, dotted, triplet and extended note values. |
| Bars and loop BPM | quarter-note equivalents = bars × numerator × 4 ÷ denominator | Independent checks across 2/4 through 12/8, including compound meters, half-time, double-time and target-duration results. |
| Pitch, varispeed and beatmatching | speed ratio = 2^(semitones ÷ 12); deck change = target ÷ source − 1 | Forward/reverse round trips, microscopic nonzero changes, deck-range boundaries and pitch-change direction. |
| Sample frames and PCM size | frames = duration × sample rate; bytes = frames × channels × stored bytes | Integer results are checked against decimal-rational BigInt references, including exact half-frame rounding and maximum inputs. |
| DJ set planning | set time = tracks × play time − (tracks − 1) × overlap | The selected whole-track count must cover the set while one fewer track must fall short; spare tracks always round upward. |
| Harmonic mixing | same, relative and adjacent-circle relationships across 24 major/minor keys | Every key pair is checked in both directions, and each conservative shortlist must contain exactly four defined choices. |
Documented formulas for every calculator
Precision and rounding policy
Tempo, pitch and frequency use JavaScript’s IEEE 754 double-precision numbers. These can have tiny rounding errors, so we do not call every answer exact. Tests allow only a small error close to the limits of that number format. The display adds decimal places when rounding would hide a real change or make a value outside a limit look valid.
Whole sample-frame counts, PCM file payload sizes, clock milliseconds and some other counts need stricter rounding. Where this matters, decimal inputs become exact fractions handled with BigInt whole-number math. A result exactly halfway between two sample frames rounds up. The tool rejects whole-number results that are too large to store safely.
Four layers of release testing
- Known answers.Checks use familiar values such as 120 BPM, one-octave shifts and common sample rates.
- Boundaries.Checks cover the smallest and largest inputs, invalid values, half-frame ties, deck limits, signed zero and nearby floating-point values.
- Stress invariants.A fixed-seed test set checks rules that should hold across note, bar, pitch, beatmatch, sample, loop, set, tap-tempo and key calculations.
- Published output.Checks inspect the finished pages. They cover default answers, formulas, metadata, canonical URLs, links, structured data and 404 pages that cannot be indexed.
Important limitations
- Tap tempo depends on how steadily you tap. It does not listen to or analyze an audio file.
- Tempo-based delay and reverb values are starting points. Listen to the source and full mix, and check how your plugin responds.
- The sample-size tool reports packed PCM audio data only. It excludes file headers, metadata, padding and compression.
- A key match cannot fix a wrong key label. It also cannot guarantee that two melodies, vocals or arrangements will blend.
- The time covered by a sample buffer is not the same as the measured round-trip delay of a whole audio system.
Corrections and release policy
Changes to an equation must include matching tests and updated assumptions. Releases that change only page content still run the full calculation test suite. If we find an error, we correct the formula or text and add a test for it. We update this record before the change goes live.