PCP Teaser

Lecture: Chord Recognition

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

  • What is a musical interval? What is a musical chord?
  • What are the intervals of the twelve-tone equal-tempered scale?
  • What is the relation between intervals and the harmonic series?
  • How do the chroma patterns of the major and minor chords look like?
  • What is the basic procedure of a template-based chord recognizer?
  • Which information does a time–chord representation visualize?
  • For what purpose are hidden Markov models used in the context of chord recognition?
  • What is a Markov chain? What are the states correspond to in the chord recognition application? What do the state transition probabilities express?
  • What is a hidden Markov model (HMM)? What is the difference between an HMM and a Markov chain? (See Figure 5.26.)
  • What are the observations in the chord recognition context?
  • What is the uncovering problem?
  • What is the purpose of the Viterbi algorithm? How does it work? (See Figure 5.27 and Table 5.2.)
  • What are the number of operations and the memory requirements required by the Viterbi algorithm?

Reading Assignments

  • Chapter 5, Müller, FMP, Springer 2021
    • Introduction to Chapter 5
  • Section 5.1: Basic Theory of Harmony
    • Section 5.1.1: Intervals
    • Section Triads
    • Section Major and Minor Chords
  • Section 5.2: Template-Based Chord Recognition
    • 5.2.1: Basic Approach
  • Section 5.3: HMM-Based Chord Recognition
    • Section 5.3.1: Markov Chains and Transition Probabilities
    • Section 5.3.2: Hidden Markov Models
    • Section Uncovering Problem


There are a many videos on chord recognition, harmonic analysis, and ear training. Here is a selection.

Question & Answer Session

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