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?

- Chapter 6, MÃ¼ller, 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

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

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 (BurgmÃ¼ller 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