PCP Teaser

Lecture: Tempo and Beat Tracking

After working through the material of this lecture, you should be able to answer the following questions:

  • What is the relation between beat and tempo?
  • What is the goal of onset detection? What are important signal characteristics exploited for onset detection? What are main challenges in onset detection?
  • What is the main idea of energy-based novelty detection? What is a novelty function? What is the role of half-wave rectification?
  • What is the main idea of spectral-based novelty detection? (See Eq. 6.6, Eq. 6.7, and Eq. 6.8.)
  • Why is the role of logarithmic compression? (See Eq. 6.5.)
  • What is the unit of a beat or pulse rate? What do measure, tactus, and tatum refer to?
  • What does a tempogram representation encode?
  • How can one compute a tempogram using Fourier analysis? (See Eq. 6.25 and Eq. 2.26.)
  • How can one compute a tempogram using Autocorrelation analysis? What is the relation between lag and tempo? (See See Eq. 6.29, Eq. 6.30, and Eq. 6.31).
  • What are tempo harmonics and tempo subharmonics? What is the main difference between Fourier and autocorrelation tempograms? (See Table 6.2.)
  • How can one compute the predominant local pulse (PLP) information from a Fourier tempogram and its phase? (See Eq. 6.36 to Eq. 6.39.)
  • What does the amplitude of a PLP function encode?

Reading Assignments

  • Chapter 6, Müller, FMP, Springer 2021
    • Introduction to Chapter 6
  • Section 6.1: Onset Detection
    • Section 6.1.1: Energy-Based Novelty
    • Section 6.1.2: Spectral-Based Novelty
  • Section 6.2: Tempo Analysis
    • 6.2.1: Tempogram Representation
    • 6.2.2: Fourier Tempogram
    • 6.2.3: Autocorrelation Tempogram
  • Section 6.3: Beat and Pulse Tracking
    • Section 6.3.1: Predominant Local Pulse



Here is a selection of videos related to tempo and beat.

  • Tempo and Beat Tracking (24:34)
    Foot tapping; onset positions ("Another One Bites The Dust" example); pulse levels ("Happy Birth Day" example ); tempo change (Chopin example); spectral-based onset detection; novelty function; Fourier tempogram; predominant local pulse (PLP); pulse levels (Burgmüller example); tempo changes (Brahms example); prior knowledge (Borodin example); tempogram toolbox
  • Beat and Rhythm in Music Explained (7:08)
    Beat; measures; bar lines; time signature; tempo; beats per minute (BPM); tapping; rhythm; full note; quarter note; eighth note; sixteens note; kick drum; bass sound; snare drum
  • Beat Tracking (1:07:40)
    Lecture by Dan Ellis; rhythm perception; onset extraction; beat tracking; dynamic programming approach

Question & Answer Session

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