This research was funded by a generous gift from the Xerox Corporation. Beat-Detection: Keeping Tabs on Tempo Using Auto-Correlation David J. Heid Research Mentor: Mark Bocko July 29 th, 2011 Abstract: The goal of this project is to develop a “smart” metronome that can track a musician’s tempo in real-time by using beat- detection. Using a normal metronome, a musician will try to maintain a steady tempo by listening to evenly spaced “ticks” set at a rate given by the player. Our device listens to the user, providing a tempo reading, and tracks tempo changes as you play, even after metric modulation. This project combines the methods of auto-correlation and dynamic programming to achieve the functionality described. Eventually, we would like to implement this tempo-tracking method as a special feature included in a regular digital metronome. Procedure: Record Audio Data (Fig. 1) Rectify the audio data (Fig. 2) Take the Envelope (Fig. 3) Perform Auto-Correlation (Fig. 5) Dynamic Programming. & Error Detection Evaluate for a Tempo Change Display Tempo Taking the Envelope: Using a 2Hz low-pass (LP) filter on the rectified waveform, we find the envelope of the waveform (Fig. 3). Taking the envelope allows us to determine the note onsets in a given audio signal. Auto-Correlation: Auto-correlation can be used to determine the inter- onset-intervals (IOIs) between successive notes. inaccurate tempo reading. A simple algorithm checks to see if the tempo lies within the context of past tempo readings. If an extreme value is read, it is normalized based on previous tempo calculations but a warning flag is set off, indicating a possible tempo change. Metric Modulation: Additional programming allows our design to follow tempo changes. Unlike a traditional metronome, if an intentional tempo change occurs for musical effect and/or metric modulation, our design will update itself based on the auto- correlation and programming algorithms built-in. Results: Notable progress has been made towards implementing a real-time device that tracks tempo and metric modulation. It appears that a combination of strategies are required to accurately track tempo. Several quantized songs have been used to test our tempo tracking method in Matlab (Figs. 8 & 9). Tempo-analysis is currently based on the user giving an accurate initial tempo to track, but it exceeds the limitations of current tap-metronomes that would misinterpret smaller note durations as a change in the overall tempo. Further research is needed to track syncopated and more complex rhythms. Fig. 1 Fig. 2 Fig. 3 A maximum peak is observed when the signal is perfectly aligned with itself, while smaller peaks represent partial overlapping (Figs. 4 & 5) The auto-correlation is most accurate at 0 time lag, where the peaks are the strongest. By finding the distance between the maximum peak and either neighbor peak, we know the period (T), and can then find the tempo of the musician’s playing in beats per minute (bpm) Dynamic Programming: Auto-correlation is accurate in determining the most frequently occurring note duration. However, auto- correlation gets confused when the notes do not have the same IOI and duration. Most real-life compositions contain a combination of note values (quarter notes, eighth notes, sixteenth notes, etc). Several programming algorithms have been implemented to allow for these changes without affecting the tempo reading (Figs. 6 & 7). Error Detection: Occasionally, the auto-correlation will get confused by the varying note durations within a frame, and will give an Fig. 4 Fig. 5 Fig. 8 Fig. 9 Fig. 6 Fig. 7