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

FMP Notebooks

• Part 6: Tempo and Beat Tracking
• Onset Detection
• Energy-Based Novelty
• Spectral-Based Novelty
• Tempo and Beat
• Fourier Tempogram
• Autocorrelation Tempogram
• Predominant Local Pulse (PLP)

Slides

• Tempo and Beat Tracking: Slides (PDF), Handouts (6 slides per page) (PDF)

Videos

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