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How tempo sets the length of a bar
Every timing decision in electronic music, from a delay time to a visual cut, comes from one piece of arithmetic: how long a beat lasts. Here is how to get from a tempo to a bar, a sixteenth note and a delay.
Beats per minute to seconds
Tempo is counted in beats per minute, shortened to bpm. There are 60 seconds in a minute, so seconds per beat is 60 divided by the bpm.
At 120 bpm a beat lasts 0.5 seconds. At 129.2 bpm it lasts 60 divided by 129.2, which is 0.4644 seconds.
From a beat to a bar
Most dance music is in four beats to a bar, written 4/4. A bar is four beats, so seconds per bar is 240 divided by the bpm.
- 120 bpm: 2.000 seconds per bar.
- 128 bpm: 1.875 seconds per bar.
- 129.2 bpm: 1.858 seconds per bar, which rounds to 1.86.
The last line is the tempo given for the released track CONTROL YOUR BODY, which is described as 129.2 bpm. One bar of it lasts about 1.86 seconds. A change of 1.2 bpm moves the bar length by less than 0.02 seconds, so a plan made for 128 bpm still fits.
Smaller divisions
Divide the beat to get the grid the drums sit on.
| Note | Fraction of a beat | Length at 128 bpm |
|---|---|---|
| Quarter | 1 | 0.469 s |
| Eighth | 1/2 | 0.234 s |
| Sixteenth | 1/4 | 0.117 s |
| Dotted eighth | 3/4 | 0.352 s |
The dotted eighth matters for delay effects. A delay set to a dotted eighth against a straight sixteenth hi-hat pattern makes interlocking repeats, a sound common in techno and house.
From a time to a frequency
A repeating event has a rate in hertz, which is repeats per second. Divide 1 by the period.
- A kick on every beat at 128 bpm repeats 2.13 times a second, so 2.13 Hz.
- A sixteenth note pattern repeats at 8.53 Hz.
Slow movements in a synthesizer, such as a filter sweep that follows the tempo, are low frequency oscillators set to these rates. Many instruments can lock the rate to the host tempo, so you do not type the number yourself, but knowing it helps you check that the lock is doing what you meant.
Why this matters for visuals
A visual that responds to a kick does not need to know the tempo, because it reads the sound. Planning a cut does. If you want a change to land on bar 17, the time is 16 bars times the bar length. At 129.2 bpm that is 16 times 1.858, about 29.7 seconds after the start of bar 1, provided the track starts on the grid. Check the first kick by ear, and slide the number if it sits slightly off.
Triplets and swing
A triplet divides a beat into three instead of two. A quarter note triplet at 128 bpm lasts 0.469 times two thirds, which is 0.3125 seconds. Swing delays every second sixteenth or eighth. Where the delay is a fixed fraction of the note, the arithmetic still works from the beat length above.
Common mistakes
- Using 60 divided by bpm for a bar. That gives one beat. A bar in 4/4 is four of them.
- Rounding the tempo too early. A tempo of 129.2 rounded to 129 drifts by about 0.09 seconds over a minute of music, which can be enough to put a tight cut visibly off.
- Assuming a track starts at time zero on the grid. Many files have a few milliseconds of silence first.
Keep going
- What a bar of electronic music looks like on a score
- Why a kick can drive a visual
- How to make a live visual for a DJ set
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