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Conkormedia

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

#algorithms #mobile #music #showdev

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]|)
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  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)
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  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.

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