Why delay times are calculated rather than dialled by ear
A delay unit measures in milliseconds and music measures in note values, so something has to translate. The translation is exact: there are 60,000 milliseconds in a minute, and tempo is stated in quarter notes per minute, so one quarter note lasts 60,000 divided by the tempo. At 120 BPM that is 500 ms. Everything else follows by halving and doubling.
Getting it exactly right matters more than it looks. A delay set 5% away from the note value drifts by a quarter of a beat over five repeats, which is audible as a smear rather than as a rhythm. Set it exactly and the repeats land on subdivisions the listener is already counting, so they read as part of the arrangement rather than as an effect. That is why almost every modern delay plugin offers tempo sync - but you still need the number when you are using a hardware unit, printing a delay to tape, working out an LFO rate in hertz, or checking whether a session's tempo map matches what was played.
The same arithmetic drives reverb. Pre-delay - the gap between the dry sound and the onset of the reverb tail - is a small note value, and a tail set to end just before the next downbeat clears the mix instead of muddying it. Both are the bar length and its fractions, so both come out of the same division.
The formula and the three feels
Start with the quarter note: tquarter = 60,000 / BPM milliseconds. Then scale by the note value. A note whose denominator is d lasts 4/d quarter notes, so an eighth note is 4/8 = half a quarter, a sixteenth is a quarter of a quarter, and a whole note is four of them. Putting those together gives delay = (60,000 / BPM) x (4 / d).
Then apply the feel. A dot adds half the note's own length, so a dotted note is 1.5 times the straight value. A triplet fits three notes into the space of two, so each is 2/3 of the straight value. Both factors are exact, not approximations.
The dotted eighth deserves its own paragraph, because it is the single most-used delay setting in popular music. A dotted eighth is 1.5 eighth notes, which is three sixteenths. Against a straight sixteenth pattern the repeats fall on the first, fourth, seventh and tenth sixteenths - offset from the pulse but repeating every three, so they weave against the beat and realign every three beats. That is the sound on countless guitar parts, and it comes purely from the 3:4 relationship between the delay and the bar.
The repetition rate in hertz is the reciprocal: 1000 divided by the delay in milliseconds. At 120 BPM a quarter-note delay of 500 ms is 2 Hz, and an eighth is 4 Hz. Use those figures when a modulation source is set by frequency rather than by note value - a tremolo, an auto-pan, or a filter LFO you want moving with the track.
Worked example: a delay and reverb set for a 128 BPM track in 4/4
Take a track at 128 BPM in 4/4. You want an eighth-note delay on a vocal throw, a dotted-eighth delay on a guitar, and a reverb that clears before the next bar.
- Quarter note. 60,000 / 128 = 468.75 ms.
- Eighth note. 468.75 x (4/8) = 468.75 x 0.5 = 234.375 ms. Round to 234 ms on a unit that only takes whole milliseconds; the 0.375 ms error accumulates to 1.5 ms after four repeats, which nothing will hear.
- Dotted eighth. 234.375 x 1.5 = 351.5625 ms. Check it against the sixteenth: a sixteenth is 468.75 / 4 = 117.1875 ms, and three of those is 351.5625 ms. The two routes agree, which is the check worth doing.
- Eighth triplet. 234.375 x (2/3) = 156.25 ms. Three of them fill 468.75 ms, one quarter note, as they must.
- Bar length. 468.75 x 4 beats x (4/4) = 1875 ms, or 1.875 s.
- Pre-delay at a 1/64 note. 468.75 x (4/64) = 468.75 / 16 = 29.30 ms. That sits just under the fusion window, so it adds a sense of size without opening an audible gap.
- Reverb tail of one bar. 1875 ms, so set the decay time to about 1.9 s. The tail then falls to inaudibility roughly as the next downbeat arrives.
- Rates in hertz. The eighth delay repeats at 1000 / 234.375 = 4.267 Hz, and the quarter at 1000 / 468.75 = 2.133 Hz. Those are the numbers to type into a free-running LFO.
Choosing a division, and what each one does
Short divisions thicken; long ones create space. Below about 30 ms a single repeat does not register as a separate event at all - the precedence effect fuses it with the direct sound, and you hear a change in width and tone rather than an echo. That region is where slapback thickening, doubling and comb-filter effects such as flanging and chorus live. From roughly 30 to 100 ms the repeat is heard as a distinct slap, the classic rockabilly guitar and vocal sound.
Above 100 ms the delay becomes rhythmic and the note value dominates the perception. A sixteenth is busy and works on sparse material; an eighth is the default rhythmic delay; a dotted eighth adds the cross-rhythm described above; a quarter or a dotted quarter creates a call-and-response wide enough to hear as a separate phrase. Longer than a bar and the repeats start arriving over a different chord, which is a compositional decision rather than a mix one.
Reverb pre-delay works on the same perceptual boundary from the opposite direction. A short pre-delay of 10 to 30 ms keeps the reverb fused with the source and reads as room size. Longer values separate the tail from the source, which preserves the clarity of a lead vocal but starts to be heard as an effect above roughly 100 ms. Setting the pre-delay to a 1/64 or 1/32 note keeps it in the useful region at most tempos while staying locked to the track: at 128 BPM a 1/64 gives 29 ms and a 1/32 gives 59 ms.
For tail length, the useful rule is that the reverb should be gone before the next musical event that matters. One bar is a safe default for a dense arrangement, two bars for something sparse. The song length and bar count calculator converts between bars, beats and seconds when you need to think in whole sections rather than single hits.
Delay times at common tempos
| Tempo | Whole | 1/2 | 1/4 | 1/8 | 1/16 | Dotted 1/8 |
|---|---|---|---|---|---|---|
| 70 BPM | 3428.6 | 1714.3 | 857.1 | 428.6 | 214.3 | 642.9 |
| 85 BPM | 2823.5 | 1411.8 | 705.9 | 352.9 | 176.5 | 529.4 |
| 100 BPM | 2400.0 | 1200.0 | 600.0 | 300.0 | 150.0 | 450.0 |
| 110 BPM | 2181.8 | 1090.9 | 545.5 | 272.7 | 136.4 | 409.1 |
| 120 BPM | 2000.0 | 1000.0 | 500.0 | 250.0 | 125.0 | 375.0 |
| 128 BPM | 1875.0 | 937.5 | 468.8 | 234.4 | 117.2 | 351.6 |
| 140 BPM | 1714.3 | 857.1 | 428.6 | 214.3 | 107.1 | 321.4 |
| 174 BPM | 1379.3 | 689.7 | 344.8 | 172.4 | 86.2 | 258.6 |
Rounded to one decimal place. Note the doubling relationship: 70 BPM and 140 BPM share the same numbers one column apart, so a half note at 140 equals a quarter at 70.
Pitfalls
- Tempo is quarter notes per minute, whatever the time signature says. In 6/8 at 120 BPM a bar is three quarter notes and lasts 1.5 s, not 3 s. Getting this wrong doubles or halves every reverb tail.
- A tempo-synced plugin still needs the right host tempo. If the project tempo does not match the recording, sync locks the delay to the wrong grid, and the error is invisible on screen.
- Rounding to whole milliseconds is usually harmless, but check the repeat count. A 0.4 ms error is nothing after four repeats and audible as drift after forty.
- Analogue and tape delays drift on purpose. Their time varies with voltage, temperature and tape wear, so a calculated number is a starting point rather than a setting.
- Delay time and modulation interact. Any chorus or modulation applied to a delay line varies its time, so a modulated delay is not exactly at the value you dialled - which is usually the point.
- The reverb tail figure is a working convention, not a measurement. Decay time in a plugin is normally RT60, the time to fall by 60 dB, and how audible the last part of that tail is depends entirely on how loud the rest of the mix is.
Where the millisecond numbers come from perceptually
The 30 ms figure that separates thickening from echo is the precedence or Haas effect: when two versions of the same sound arrive within roughly the first 30 to 40 milliseconds, the auditory system localises to the first and treats the second as part of it, raising the perceived loudness and width instead of producing a second event. Beyond that window the second arrival is heard as an echo. The exact boundary depends on the material - clicks separate at shorter delays than sustained sounds - so treat 30 ms as a region rather than a line.
Below about 20 ms, a delayed copy summed with the original produces comb filtering: cancellation at frequencies where the delay equals half a period, reinforcement where it equals a whole one. The first notch sits at 1/(2t), so a 1 ms delay notches at 500 Hz and every odd multiple. This is the mechanism behind flanging, and it is also what goes wrong when two microphones on one source are not time-aligned. The decibel addition calculator shows what happens to level when sources sum, which is the other half of that picture.
At the long end, room acoustics take over. A physical room's reverberation time is set by its volume and the absorption of its surfaces, and it does not care about your tempo. Tempo-synced reverb is therefore a production convention rather than a physical one - a way of making an artificial tail behave like part of the arrangement. The note to frequency calculator gives the wavelengths that determine how a real room behaves at each pitch, which is a different and complementary question.
One last connection worth making: a delay time short enough becomes a pitch. A repeat every 5 ms is 200 Hz, and with enough feedback a very short delay line resonates at that frequency - the basis of Karplus-Strong string synthesis. The boundary between rhythm and pitch is around 20 Hz, or 50 ms, which is exactly where the delay stops sounding like repeats and starts sounding like a tone.