# Lecture Descriptions, Tests, Homework and Play

### Week 1- Wednesday Sept 8

##### Lecture 1:
1. Introduce course
2. Definition of terms
3. Music notation systems
1. Rhythm and Transforms by William Sethares: http://books.google.com/books?id=l3X9dqBz9jIC&dq=rhythm+and+transforms&printsec=frontcover&source=bn&hl=en&ei=BRuGTMbJLYKClAenn8C4Dw&sa=X&oi=book_result&ct=result&resnum=5&ved=0CCcQ6AEwBA#v=onepage&q&f=false
2. Chapter 1: What is Rhythm
3. Chapter 2: Visualizing and Conceptualizing Rhythm
4. Introduction to Pattern Recognition.pdf

### Week 2 - Monday Sept 13 and Wednesday Sept 15

##### Lecture 2:
1. More music notation systems
2. Introduction to optical music information retrieval
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. More on optical music information retrieval
1. Music score sheet segmentation
2. Staff-line removal via Hough transform
3. Hysteresis smoothing of time functions
4. Topological features of music notes
2. Auditory (pitch and rhythm) and visual illusions
3. Moments as Descriptors of Shape

### Week 3 - Monday Sept 20 and Wednesday Sept 22

##### Lecture 4:
1. Features of Rhythm:
1. Mathematical measures of rhythm complexity
2. Rhythmic oddity
3. Off-Beatness
4. Measures of irregularity
5. Syncopation
6. Metrical hierarchy of Lerdahl and Jackendoff
7. Metrical complexity
8. Flatness of inter-onset-interval histograms
9. Homometric sets
##### Lecture 5:
1. Features of Rhythm continued:
1. Weighted note-to-beat distance
2. Keith's measure of syncopation
3. Pressing's measure of cognitive complexity
4. Lempel-Ziv complexity
5. The Hexachordal Theorem and Z-related sets
6. Proof of Hexachordal Theorem by Juan Iglesias
• ##### Video Watching Assignment
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

##### Lecture 6:
1. Bayesian Decision Theory:
1. Maximum a posteriori probability decision rule
2. Bayes' rule
3. Probability of misclassification
4. Discriminant functions and neural networks
5. Gaussian probability density functions
6. Covariance matrices
7. Decision regions
8. Correlation and independence
##### Lecture 7:
1. Nonparametric Decision Theory via Proximity Graphs
1. K-nearest neighbor decision rules
2. Cover-Hart bounds
3. Hart's condensed nearest neighbor rule
4. Wilson's edited nearest neighbor rule
5. Voronoi condensing
6. Delaunay triangulation
7. Gabriel graph
8. Relative neighbor graph

### Week 5 - Monday Oct 4 and Wednesday Oct 6

##### Lecture 8:
1. Nonparametric Decision Theory via Proximity Graphs continued...
1. Voronoi diagrams
2. Delaunay triangulation editing
3. Gabriel graph editing
4. Relative neighbor graph editing
5. Searching nearest neighbors
1. Voronoi diagram method
2. Projection method
2. Psychological Measures of Rhythm Complexity
1. Perceptual complexity
2. Performance complexity
3. Meter complexity
3. Applications of rhythm complexity
1. Analysis of Clapping Music by Steve Reich
##### Lecture 9:
1. Proximity graph decision rules
2. Searching Gabriel neighbors.
3. Application of complexity measures to ethnomusicology (West African timelines and Indian talas)
4. Measuring Rhythm Similarity
1. Feature-based methods versus transformation methods
2. Hamming distance
3. Minkowski metrics (Euclidean, City-Block, etc.)
4. Directed swap distance (restriction scaffold assignment)
5. One-to-one assignment
6. Fuzzy Hamming distance
7. Extended edit distances
8. Chronotonic distance

### Week 6 - Monday Oct 11 and Wednesday Oct 13

##### Lecture 10:
1. Phylogenetic analysis of rhythms
1. Afro-Cuban rhythms
2. Flamenco Meters (compás)

### 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
• ##### Video Watching Assignment
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
3. Alternating hands method
##### Lecture 15:
1. Paper presentation by Andrew Winslow
2. Bayesian decision theory for discrete-valued features
1. Class-conditional and unconditional independence assumptions

### 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
##### 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

### 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.

### 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
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)

### Lecture 22:

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

### 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
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)
• ##### Video Watching Assignment
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.

### 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
##### 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