Music Information Retrieval - Fall 2010

Lecture Descriptions, Tests, Homework and Play

Week 1- Wednesday Sept 8

Week 2 - Monday Sept 13 and Wednesday Sept 15

  1. Mid-Point Smoothing Algorithm (play with JAVA aplet) http://cgm.cs.mcgill.ca/~godfried/teaching/projects97/ziad/project/frames_main.html
  2. Grids, Connectivity, and Contour Tracing.pdf
Lecture 3: 
  1. Detecting lines in noisy pictures (pdf)
  2. Smoothing (pdf)
  3. Moments as Feature Descriptors (pdf)

Week 3 - Monday Sept 20 and Wednesday Sept 22

  1. Rhythmic Oddity and Off-Beatness (pdf)
Lecture 5: 
  1. Eric Thul's Thesis on Rhythm Complexity (pdf)
  2. Mathematical Measures of Syncopation (pdf)
  3. Michael Keith's Dictionary of Exotic Rhythms
  1. Watch the five Programs on Rhythm in the series How Music Works by Howard Goodall on YouTube.
  2. Write a short (half page) critique on the programs to be handed in Monday, September 27. Make some connections between the material we covered in class and that covered by Howard Goodall.

Week 4 - Monday Sept 27 and Wednesday Sept 29

  1. Bayesian Decision Theory with Gaussian Distributions (HTML)
Lecture 7: 
  1. The Relative Neighborhood Graph of a Finite Planar Set (pdf)
  2. Editing Nearest Neighbor Decision Rules (pdf)

Week 5 - Monday Oct 4 and Wednesday Oct 6

  1. The Gabriel Graph Approach to Instance-Based-Learning (pdf)
  2. The Projection Method for Finding Nearest Neighbors (HTML)
Lecture 9: 
  1. Analysis of Clapping Music by Steve Reich (pdf)
  2. Rhythmic Similarity Measures (pdf)

Week 6 - Monday Oct 11 and Wednesday Oct 13

Lecture 10:
  1. Phylogenetic analysis of rhythms
    1. Afro-Cuban rhythms
    2. Flamenco Meters (compás)
  1. Classification-and-Phylogenetic-Analysis-of-African-Ternary-Rhythm-Timelines (pdf)
  2. El-Compas-Flamenco: A-Phylogenetic-Analysis (pdf)
  3. Measuring-Similarity-Between-Flamenco-Rhythms (pdf)
Lecture 11:
  1. First Midterm Test
  2. Classification-and-Phylogenetic-Analysis-of-African-Ternary-Rhythm-Timelines (pdf)

Week 7 - Monday Oct 18 and Wednesday Oct 20

Lecture 12:
  1. Nearest-neighbor decision rules
    1. Jensen's inequality
    2. Proof of Cover-Hart bound
  1. The Nearest Neighbor Decision Rule - Error Bounds
  1. Watch the performance by Seda Röder of the piece Ein Kinderspiel Part 3/3 by Helmut Lachenmann on YouTube.
  2. Write a short (half page) description of all the features of music that you hear in this piece. Make some connections between the material we covered in class and this piece. To be handed in Monday, October 25. Try to listen to it with good quality headphones at a loud volume.
Lecture 13:
  1. Comparison of Afro-Cuban timeline musicological categorization with that obtained with the edit distance and human perception
  2. Geometric proof of Jensen's inequality
  3. Automatic generation of "good" rhythms.
    1. Maximally even sets
    2. Euclidean rhythms
    3. Euclidean strings
    4. Leap year rules in calendar design
  1. Read the paper: "A Visual Explanation of Jensen's Inequality," by Tristan Needham, The American Mathematical Monthly, Vol. 100, No. 8, October 1993, pp. 768-771.
  2. Euclidean Rhythms (pdf)

Week 8 - Monday Oct 25 and Wednesday Oct 27

Lecture 14:
  1. Paper presentation by Garth Griffin
  2. Automatic generation of "good" rhythms continued...
    1. Toggle rhythms
    2. Paradiddle method
    3. Alternating hands method
  1. Rhythm Generation (pdf)
Lecture 15:
  1. Paper presentation by Andrew Winslow
  2. Bayesian decision theory for discrete-valued features
    1. Class-conditional and unconditional independence assumptions
  1. Bayes Decision Theory with Discrete-Valued Features (HTML)

Week 9 - Monday Nov 1 and Wednesday Nov 3

Lecture 16:
  1. Paper presentation by Barry Lai
  2. Methods for Estimating the Error Probability of a Decision Rule
  3. Error-correction learning in neural networks
    1. Introduction to Machine Learning by Nils J. Nilsson, Chapter 4: Neural Networks, pp. 35-42.
Lecture 17:
  1. Paper presentation by Samuel Li
  2. Nearest neighbor decision rules via neural networks
  3. Maximally even sets and balanced rhythms
  4. The snap heuristic
  5. Points with specified distance multiplicities
  6. Erdős-deep and Winograd-deep rhythms, scales, and chords
  7. Ilona Palasti's 8-point solution
  8. Graceful graph labelling
    1. Methods for Estimating the Error Probability of a Decision Rule (pdf)

Week 10 - Monday Nov 8 and Wednesday Nov 10

Lecture 18:

  1. Paper presentation by Cari Sisson
  2. The Two-Bracelets Theorem
  3. The Common Tone Theorem
  4. The Circle-of-Fifths Transform
  5. Generating deep sets
  1. Read the paper: "Prelude to Musical Geometry," by Brian J. McCartin, The College Mathematics Journal, Vol. 29, No. 5, November 1998, pp. 354-370.
Lecture 19:
  1. Paper presentation by Zach Abramson
  2. Universals in music
  3. Categorical perception of rhythm
  4. Auditory streaming (melodic fission)
    1. Read the paper: "Universals in Music: A Perspective from Cognitive Psychology," by Dane L. Harwood, Ethnomusicology, Vol. 20, No. 3, September 1976, pp. 531-533.

Week 11 - Monday Nov 15 and Wednesday Nov 17

Lecture 20:

  1. Paper presentation by Gordon Briggs
  2. More universals in music
  3. Eric Regener's proof of the Hexachordal Theorem
  1. Read the paper: "Prelude to Musical Geometry," by Brian J. McCartin, The College Mathematics Journal, Vol. 29, No. 5, November 1998, pp. 354-370.
Lecture 21:
  1. Paper presentation by John Mazella
  2. The memetics of rhythm
  3. Structural characterization of rhythms
  4. Almost maximally even sets
  5. Kasner polygons
  6. Shadow rhythms
  7. Rhythm-shadow contour isomorphism
  8. Spatial rhythmic resolution, metric dissonance, and Gestalt de-spatialization
    1. Read the paper: "A Spatial Theory of Rhythmic Resolution," by Neil McLachlan, Leonardo Music Journal, Vol. 10, 2000, pp. 61-67.
    2. Read the paper: The Rhythm that Conquered the World (pdf)

Week 12 - Monday Nov 22 and Wednesday Nov 24

Lecture 22:

  1. In-class Test #2
Lecture 23:
  1. Thanksgiving holiday - No-class

Week 13 - Monday Nov 29 and Wednesday Dec 1

Lecture 24:

  1. Feature selection methods
    1. Search methods
      1. Forward sequential selection
      2. Backward sequential selection
      3. Dual-space methods
    2. Evaluation criteria
      1. Error probability and Kolmogorov variational distance
      2. Information measures
        1. Discrimination information
          Relative entropy
          Kullback-Liebler numbers
          Divergence
      3. Distance measures
        1. Bhattacharya distance
        2. Affinity
      4. Dependence measures
        1. Mutual information
    3. Independence and uncorrelation
Lecture 25:
  1. Chords, scales and modes
  2. Maximal area sets
  3. Consonance and dissonance
  4. Voice leading
  5. The geometry of chords
  1. Read the paper: "Maximal Area Sets and Harmony," by David Rappaport, Graphs and Combinatorics, Vol. 23, 2007, pp. 321-329.
  2. Read the web page: The Geometry of Musical Chords (html)
  1. Watch the animation of the geometry of chords in a Chopin piece by Dmitri Tymoczko on YouTube.
  2. Watch the lecture on the geometry of chords by Dmitri Tymoczko on YouTube.

Week 14 - Monday Dec 6 and Wednesday Dec 8

Lecture 26:

  1. McLachlan's spatial theory of rhythmic resolution
    1. Gestalt perception, streaming, and trance-inducing rhythms
    2. Examples of Balinese rhythms
  2. Mutation mechanisms in the evolution of rhythms
  3. Binarization and ternarization of rhythms
    1. Examples of Afro-Cuban rhythms
    2. Examples of Afro-Peruvian rhythms
  4. Mathematical models for binarization and ternarization of rhythms
    1. Read the paper: Mathematical Models for Binarization and Ternarization of Musical Rhythms (pdf)
Lecture 27:
  1. The use of contextual information in sequence recognition
    1. Compound decision theory
    2. Dictionary look-up methods
    3. Markov methods
    4. The Viterbi algorithm
    5. Hybrid methods
  2. Modeling Common-Practice Rhythm - Temperley's Six Bayesian Models of Rhythm
    1. Uniform position model
    2. Zeroth-order duration model
    3. Metrical position model
    4. Fine-grained position model
    5. Hierarchical position model
    6. First-order metrical duration model
    1. Read the paper: The Use of Context in Pattern Recognition (pdf)
    2. Read the paper: Modeling Common-Practice Rhythm by David Temperley (pdf)