Scatology

Scatology Study of output Study of output Also called coprology Also called coprology From what comes out you get a pretty good idea of what when in!!!!! From what comes out you get a pretty good idea of what when in!!!!!

Allusion in Music

Beethoven and Mozart

Weber and Beethoven

Stravinsky and Lithuania

Stravinsky and Lithuania II

Bruckner and Schubert

Beethoven, Schumann, Liszt, Spohr, and Wagner

Beethoven and Mozart II

Mahler and Handel

Beethoven and Handel

Various composers over time

Ur-motive over 200 years

Berlioz and Haydn

Interesting tune

Source

Chopin’s variation technique

Algorithmic composition

Beethoven

Mozart sources for algo. ex.

Sorcerer output example

What can allusions mean?

Bach’s fugue 4

Bach’s hidden motive

Mendelssohn/Wagner/Mahler

Haydn/Beethoven/Mahler

Finding musical allusions

Intervals work best

Incremental works best

Rhythm matching

Finding allusions Locating repeating patterns Locating repeating patterns Pattern matching a staple of artificial intelligence Pattern matching a staple of artificial intelligence Often called pattern recognition Often called pattern recognition Origins in set theory in mathematics Origins in set theory in mathematics Finding patterns in math can be quite different than finding them in music. Finding patterns in math can be quite different than finding them in music.

Pattern Matching code No user-given pattern No user-given pattern Segmentation (incremental) Segmentation (incremental) Controllers (variables) Controllers (variables) Too wide: noise Too wide: noise Types of variations? Types of variations? Too narrow: no patterns Too narrow: no patterns Self-adjusting?? Self-adjusting??

Types of variations Transposition Transposition Inversion Inversion Retrograde Retrograde Inversion-retrograde Inversion-retrograde Interpolated notes Interpolated notes Excised notes Excised notes Equivalent sets Equivalent sets

Set Theory Pattern matching for contemporary music. Note that many musical/math set processes do not have corresponding counterparts!

Mathematical set theory Set: {45,15,17} Set: {45,15,17} Curly brackets Curly brackets Typically unordered Typically unordered

Mathematical set theory  is an element of  is not an element of  is a proper subset of  is a subset of  is not a subset of  the empty set; a set with no elements  union  intersection

Mathematics and Sets Example of a set proof: A C)C) A  C)  C)

Venn Diagrams help!

Musical set theory Set: [9,3,5] Set: [9,3,5] Brackets Brackets Ordered or unordered Ordered or unordered Modulo 12 (pitch classes) Modulo 12 (pitch classes) Ordered version of above: [9,3,5] Ordered version of above: [9,3,5] Normal (unordered/smallest) version of above [3,5,9] Normal (unordered/smallest) version of above [3,5,9] Prime version (unordered/invertible) of above [0,2,6] Prime version (unordered/invertible) of above [0,2,6]

Music and Sets The same set The same set [0,3,7] [0,3,7] [0,3,7] [0,3,7] [0,3,7] [0,3,7]

The same set

Cellular automata

An example rule set An example rule set 8 possible ways to set upper patterns (2 3 ) 8 possible ways to set upper patterns (2 3 ) 256 possible rule sets (2 8 ) 256 possible rule sets (2 8 ) Follows Steven Wolfram’s model in a New Kind of Science (NKS) Follows Steven Wolfram’s model in a New Kind of Science (NKS)

Sequence of steps Time downward (one dimensional?) Time downward (one dimensional?)

Rule 30

Rule 90

Rule 110

In color Rule 30 Rule 30 Rule 110 Rule 110

More about A New Kind of Science

Conway’s Game of Life

Conway’s Life Rules 1.Any live cell with fewer than two live neighbors dies, as if by loneliness. 1.Any live cell with fewer than two live neighbors dies, as if by loneliness. 2.Any live cell with more than three live neighbors dies, as if by overcrowding. 2.Any live cell with more than three live neighbors dies, as if by overcrowding. 3.Any live cell with two or three live neighbors lives, unchanged, to the next generation. 3.Any live cell with two or three live neighbors lives, unchanged, to the next generation. 4.Any dead cell with exactly three live neighbors comes to life. 4.Any dead cell with exactly three live neighbors comes to life.

Many different patterns Gosper Glider Gun Gosper Glider Gun Diehard Acorn Diehard Acorn

Game of Life Many available programs Many available programs Both on site and downloadable Both on site and downloadable Thousands of named figures Thousands of named figures Many that refigure infinitely Many that refigure infinitely Called two dimensional Called two dimensional

Growth and Diminishment

Genetic Algorithms

Definition computer simulation a computer simulation in which a population of abstract representations (called chromosomes, genotype, or genome) of candidate solutions (called individuals, creatures, or phenotypes) to an optimization problem evolves toward better solutions. Basics A genetic representation of the solution domain, A fitness function to evaluate the solution domain. Along the way crossover and mutation Until a solution is found that satisfies minimum criteria

Genotype and Phenotype

Karl Sims Evolved Virtual Creatures Evolved Virtual Creatures Not an animation Not an animation Evolved objects in motion Evolved objects in motion Encased in various media (water, air, etc.) Encased in various media (water, air, etc.) With gravity With gravity

Evolved Virtual Creatures

Object Oriented Programming Called OOP Called OOP Paradigm change from FP (functional programming) Paradigm change from FP (functional programming) Classes Classes Instances Instances Methods Methods Inheritance Inheritance Encapsulation Encapsulation Abstraction Abstraction Polymorphism Polymorphism

GoF Gang of Four Gang of Four Erich GammaRichard HelmRalph JohnsonJohn Vlissides Erich Gamma, Richard Helm, Ralph Johnson, and John Vlissides Erich GammaRichard HelmRalph JohnsonJohn Vlissides Erich Gamma Richard Helm Ralph Johnson John Vlissides Design Patterns: Elements of Reusable Object-Oriented Software Design Patterns: Elements of Reusable Object-Oriented Software Now in its 36th printing Now in its 36th printing 23 classic software design patterns 23 classic software design patterns

CLOS Common Lisp Object System Common Lisp Object System (defclass “name” (inheritance [superclasses]) (defclass “name” (inheritance [superclasses]) (defmethod (defmethod GUI (menus, windows, buttons, etc.) GUI (menus, windows, buttons, etc.) Platform and program dependent Platform and program dependent

Bits and Pieces mapcar mapcar (mapcar #'first '((a 1)(b 2))) = (A B) Loop Loop (loop for event in ‘(( )( )) (loop for event in ‘(( )( )) collect (second event)) collect (second event)) = (60 62) = (60 62) setf (simple object system) setf (simple object system) ? (setq x 'b) B ? (setf (get 'color x) 'blue) BLUE ? (get 'color x) BLUE

Assignment Read Chapter 4 of CMMC Read Chapter 4 of CMMC Begin work in earnest on your final project Begin work in earnest on your final project Get all past homework in or else!! Get all past homework in or else!! Enjoy life, you only get so much time. Enjoy life, you only get so much time.