Why Does a BPM Finder Say My Song Is Half or Double the Tempo?

Your BPM finder is probably not broken. A song's rhythm repeats at more than one speed, so a track you count as 140 can come back as 70, and the software has to guess which pulse you would tap. Neither number is a bug. Both pulses are really in the recording.

This matters well beyond the DJ booth. A fitness player, a rhythm game, a light show and a song that switches styles all need a tempo they can trust. Here is how the guess is made, how often it goes wrong, and a one-minute way to settle it yourself.

How does software find a tempo?

Most tempo estimators work in two steps. In a 2017 paper for the ISMIR music-research conference, Hendrik Schreiber and Meinard Müller describe them. First the software builds a signal that tracks how much the sound changes from moment to moment, which points to likely beats. Then it looks for patterns that repeat in that signal, often with a Fourier transform or autocorrelation, two standard ways to find repetition.

The result is a chart with peaks at the speeds where the music repeats. One song usually has several peaks, and the software has to pick one.

Why do half and double keep winning?

Music repeats at many speeds at once. A kick drum may land on every beat, a hi-hat on every half beat and a chord change on every fourth. Each layer is a candidate. Justin London, a music researcher at Carleton College, gives an example in a 2011 paper. At a metronome marking of 75 beats per minute, the eighth notes run twice as fast and the half notes at half the rate, and it is not clear whether a listener's pulse would be 75 or 150. His plain summary: "we may tap slowly to quick music, and vice-versa."

Software breaks the tie with a prior, a built-in taste for likely tempos. The librosa audio-analysis library, for example, starts from a guess of 120 beats per minute and weights its candidates so that tempos near 120 are favored over very slow or very fast ones. A DJ program wants something different. A project page on the Mixxx DJ software's wiki says that for mixing, "the correct BPM is the one which leads for the easiest beatmatching," and its approach keeps tempos "as close as possible to the most common 120 bpm."

How often does it go wrong?

Researchers score tempo software two ways. Accuracy 1 counts an answer as right only if it lands within 4 percent of the true tempo. Accuracy 2 also accepts half, double, three times and one third. Schreiber and Müller explain why the second score exists: many algorithms tend to under- or over-estimate the true value by a factor of 2 or 3. In a 2006 comparison of the entries to the ISMIR 2004 tempo contest, Fabien Gouyon and colleagues found that algorithms can reach over 80 percent accuracy on music with a constant tempo "if we do not insist on finding a specific metrical level."

Schreiber and Müller then put numbers on the gap. They ran a simple estimator over six research collections of music, combined, and reported these results:

• About 69 percent of its answers were within 4 percent of the true tempo.
• Nearly a quarter were off by a factor of two: 12.3 percent in one direction and 11.2 percent in the other.
• When answers off by a factor of two or three counted as right, the score rose to about 94 percent.
• The best result in the paper came from a correction step the authors added to their estimator. It got 77.4 percent of answers within 4 percent of the true tempo, which to their knowledge was the highest reported for the combined set at the time.

Style changes the odds. One ballroom collection holds 698 recordings but only 63 different tempos, so a method can look brilliant there: one published method scored 95 percent on ballroom music when trained on it, and 66.8 percent on a mixed-genre collection. In a collection of electronic dance tracks, 88.1 percent of the tempos fall between 91 and 182 beats per minute, which is why a system that knows the genre can fold its answer into the likely range.

The paper's method also assumes one steady tempo. The authors note that pop, rock and dance often have one, while some genres, such as Romantic-era classical music, change tempo locally.

A one-minute check you can do yourself

For picking a playlist, the difference rarely matters. It matters when something has to line up with the beat. You do not need software to settle it. Try this.

• Play the most danceable part of the song and tap along on a key or a phone screen for 15 to 20 seconds. Any tap-tempo tool will average your taps.
• Notice which speed your foot wants. That is the tempo that matters for your purpose. Write the double and the half beside it, for example 140 and 70.
• Tap again near the end of the song. If the two readings differ by more than a few beats per minute, the performance drifts and no single number describes it.
• Running or walking? Count steps per minute. A 170 BPM song matches every step, and an 85 BPM song matches every second step. Either can work.
• Using Ableton Live? Its manual says "Sometimes the estimation of the original tempo is incorrect," and the ×2 and ÷2 buttons double or halve the tempo in one click.
• When you hand a tempo to a collaborator or an app, say which level you mean, for example 140 with a half-time feel, so nobody matches the wrong pulse.

What this means for adaptive music

Anything that adapts to the beat depends on a tempo someone has checked. The D-Jogger running player at Ghent University kept each song's average tempo and beat times in a library. Its metadata came from an adaptation of BeatRoot, the winner of a 2006 beat-tracking evaluation, and the authors still say "the system supports manual verification and correction of the metadata." Ableton builds the fix into Live, as noted above, and its manual also covers the case where the tempo is right but the downbeat is wrong.

Games store tempo as written data. A StepMania chart lists tempos as "Beat=BPM" pairs and sets an offset, "the offset between the beginning of the song and the start of the note data in seconds." The osu! file format gives each section's beat length in milliseconds, and its own example turns a 333.33 ms beat into 180 BPM. Beat Saber's community map format has a BPM value that, in the wiki's words, "dictates how the grid will align with your audio file." All three treat tempo as something the author declares, not something the game guesses.

A number is also not a grid. The tempo needs a start point, so every beat lands where it should. That is why designing a song so it can adapt begins with a shared tempo map: when every version of a song keeps the same timeline, an app can switch between versions in the middle of a phrase. On Starchild, listeners can change a song's tempo live while it plays. See pitch, tempo and vocal controls for how those controls work from the listener's side.

Sources

• ISMIR 2017: A post-processing procedure for improving music tempo estimates using supervised learning (Schreiber and Müller)
• ISMIR 2004 tempo induction contest: accuracy measures
• Music Technology Group, Universitat Pompeu Fabra: An experimental comparison of audio tempo induction algorithms (Gouyon et al., 2006)
• Empirical Musicology Review: Tactus ≠ Tempo, some dissociations between attentional focus, motor behavior, and tempo judgment (London, 2011)
• librosa 0.10.2 documentation: librosa.feature.tempo
• librosa 0.10.2 documentation: librosa.beat.beat_track
• Mixxx wiki: Downbeats and phrase detection
• Ableton Live manual: Audio Clips, Tempo, and Warping
• PLOS ONE via PubMed Central: Encouraging Spontaneous Synchronisation with D-Jogger, an Adaptive Music Player That Aligns Movement and Music (Moens et al., 2014)
• StepMania wiki: The .sm file format
• osu! wiki: osu! file format
• BSMG Wiki: Beat Saber map format, Info