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

A developer built BeatScope, a free offline music analyzer for macOS/iPhone that detects BPM and musical key using a hand-rolled signal-processing pipeline. The tempo detection uses spectral flux, autocorrelation, and dynamic programming, while key detection relies on chromagram and Krumhansl–Schmuckler correlation. The approach avoids machine learning and cloud dependencies, achieving fast, on-device analysis.

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: - 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. - Autocorrelation. The lag where the onset envelope best matches itself is the beat period. - Comb over multiples. Weight candidate periods by their multiples ½, 2× so tempo isn't confused with its harmonics. - Octave folding + prior. Fold candidates into 60–180 BPM and softly prefer typical dance tempos — kills the "174 vs 87" error. - 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 - Chromagram. Fold the spectrum ~55–2000 Hz into 12 pitch classes, accumulated with a leaky integrator ~8 s memory → an averaged chroma vector. - Krumhansl–Schmuckler correlation. Correlate against 24 reference key profiles 12 major + 12 minor ; best match wins. - 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 https://beatscope.pro — happy to answer DSP questions in the comments.