The latest articles on DEV Community by Conkormedia (@conkormedia). https://dev.to/conkormedia https://media2.dev.to/dynamic/image/width=90,height=90,fit=cover,gravity=auto,format=auto/https:%2F%2Fdev-to-uploads.s3.us-east-2.amazonaws.com%2Fuploads%2Fuser%2Fprofile_image%2F4029277%2Fcf59ae00-4cc3-4b97-b66b-2284fc275ead.png https://dev.to/conkormedia en Conkormedia Tue, 14 Jul 2026 21:36:50 +0000 https://dev.to/conkormedia/detecting-musical-key-and-tempo-on-device-the-dsp-behind-beatscope-31me https://dev.to/conkormedia/detecting-musical-key-and-tempo-on-device-the-dsp-behind-beatscope-31me <p>I needed to read a track's <strong>BPM</strong> and <strong>musical key</strong> in seconds, offline, on a<br> phone. No ML black box, no server. Here's the signal-processing pipeline I ended<br> up with — hand-rolled, since the usual packages weren't an option.</p> <h2> Tempo </h2> <p>Tempo is periodicity in the track's energy. The steps:</p> <ol> <li> <strong>Spectral flux → onsets.</strong> Sum the positive frame-to-frame magnitude increases of the STFT. Peaks are onsets (kick, snare, synth attacks). That's the onset envelope. </li> </ol> <div class="highlight js-code-highlight"> <pre class="highlight plaintext"><code> flux[n] = Σ_k max(0, |X[n,k]| - |X[n-1,k]|) </code></pre> </div> <ol> <li> <strong>Autocorrelation.</strong> The lag where the onset envelope best matches itself is the beat period.</li> <li> <strong>Comb over multiples.</strong> Weight candidate periods by their multiples (½, 2×) so tempo isn't confused with its harmonics.</li> <li> <strong>Octave folding + prior.</strong> Fold candidates into 60–180 BPM and softly prefer typical dance tempos — kills the "174 vs 87" error.</li> <li> <strong>Median smoothing</strong> for stability.</li> </ol> <p>For the beat <strong>grid</strong>, I use dynamic programming (Ellis-style): reward beats that<br> land on onsets, penalize deviation from a steady interval. The DP gives a grid<br> that doesn't drift.</p> <h2> Key </h2> <ol> <li> <strong>Chromagram.</strong> Fold the spectrum (~55–2000 Hz) into 12 pitch classes, accumulated with a leaky integrator (~8 s memory) → an averaged chroma vector.</li> <li> <strong>Krumhansl–Schmuckler correlation.</strong> Correlate against 24 reference key profiles (12 major + 12 minor); best match wins. </li> </ol> <div class="highlight js-code-highlight"> <pre class="highlight plaintext"><code> key = argmax_i corr(rotate(chroma, i), profile) </code></pre> </div> <ol> <li> <strong>Map to Camelot</strong> for harmonic mixing. This lineage goes back to libKeyFinder.</li> </ol> <h2> Honest limits </h2> <ul> <li>Atonal/dense harmony blurs the chroma vector → less certain key.</li> <li>Mid-track modulation → it reports the dominant key.</li> <li>Weak percussion/rubato → fewer onsets, shakier BPM.</li> </ul> <h2> Sources </h2> <ul> <li>Krumhansl, <em>Cognitive Foundations of Musical Pitch</em> (1990)</li> <li>Sha'ath, <em>Estimation of Key in Digital Music Recordings</em> (2011)</li> <li>Ellis, <em>Beat Tracking by Dynamic Programming</em> (2007)</li> </ul> <p>The pipeline ships in <strong>BeatScope</strong>, a free offline analyzer for macOS/iPhone:<br> <a href="https://beatscope.pro" rel="noopener noreferrer">https://beatscope.pro</a> — happy to answer DSP questions in the comments.</p> algorithms mobile music showdev