Detecting musical key and tempo on-device: the DSP behind BeatScope

I needed to read a track's BPM and musical key in seconds, offline, on a

phone. No ML black box, no server. Here's the signal-processing pipeline I ended

up with — hand-rolled, since the usual packages weren't an option.

Tempo

Tempo is periodicity in the track's energy. The steps:

1. 
   Spectral flux → onsets. Sum the positive frame-to-frame magnitude increases
   of the STFT. Peaks are onsets (kick, snare, synth attacks). That's the onset
   envelope.
   

   flux[n] = Σ_k max(0, |X[n,k]| - |X[n-1,k]|)

1. 
   Autocorrelation. The lag where the onset envelope best matches itself is the
   beat period.


2. 
   Comb over multiples. Weight candidate periods by their multiples (½, 2×) so
   tempo isn't confused with its harmonics.


3. 
   Octave folding + prior. Fold candidates into 60–180 BPM and softly prefer
   typical dance tempos — kills the "174 vs 87" error.


4. 
   Median smoothing for stability.

For the beat grid, I use dynamic programming (Ellis-style): reward beats that

land on onsets, penalize deviation from a steady interval. The DP gives a grid

that doesn't drift.

Key

1. 
   Chromagram. Fold the spectrum (~55–2000 Hz) into 12 pitch classes,
   accumulated with a leaky integrator (~8 s memory) → an averaged chroma vector.


2. 
   Krumhansl–Schmuckler correlation. Correlate against 24 reference key
   profiles (12 major + 12 minor); best match wins.
   

   key = argmax_i corr(rotate(chroma, i), profile)

1. 
   Map to Camelot for harmonic mixing. This lineage goes back to libKeyFinder.

Honest limits

• Atonal/dense harmony blurs the chroma vector → less certain key.


• Mid-track modulation → it reports the dominant key.


• Weak percussion/rubato → fewer onsets, shakier BPM.

Sources

• Krumhansl, Cognitive Foundations of Musical Pitch (1990)


• Sha'ath, Estimation of Key in Digital Music Recordings (2011)


• Ellis, Beat Tracking by Dynamic Programming (2007)

The pipeline ships in BeatScope, a free offline analyzer for macOS/iPhone:

https://beatscope.pro — happy to answer DSP questions in the comments.