RoBach

1. RoBach A Case Study in the Use of Genetic Algorithms for Automatic Music Composition

2. Introduction to Music Generation • First attempt: 1956, Hiller and Isaacson, Illiac Suite • Many failed attempts since • Unsolved problem: balancing structure and novelty More Novel More Structured Optimal Solutions

3. Music Generation Strategies • Rule-based • Learning by example corpus • Evolutionary

4. Genetic Algorithms • Purpose: robust, efficient optimization • Other optimization algorithms • Calculus-based: needs continuity and derivatives; local search scope (which hill to climb?) • Enumerative: inefficient • Random: more inefficient • GAs need no auxiliary information • GAs search from many places at once • GAs constantly seek improvement

5. Genetic Algorithms • GAs work with codings of parameters, not the parameters themselves • Codings are strings in some applicable alphabet • Implementation-specific requirements • Routine to interpret strings • Routine to judge the fitness of strings

6. Genetic Algorithms • Generate population of random strings • Three step generational loop: • Every iteration yields ‘current best’ solution M x = + x = + x = + Initial Population Reproduction Crossover & Mutation New Population

7. The Corpus - Bach’s Chorales • A corpus of works provides the basis for statistical data • Almost 300 Bach chorales were analyzed for histograms • Frequency of intervals, chord changes, and phrases were collected • Reasons for using chorales as models: • Highly Structural • Large existing corpus

8. The Composition Object • The Composition object was designed to match the structure of a chorale • 4 voices • Sequential chords • Serves as the interface between composers and critics Composition Voice 1 Voice 2 Voice 3 Voice 4 Chord List

9. Introduction to Haskore • Haskore is a programming environment designed for music composition • It is implemented in the functional language Haskell, which is useful for list processing • Haskore defines lists of music objects that can be generated and manipulated recursively • Our “Composition” object contains a list of notes for each voice, making it favorable for this environment

10. Music Composer Building Blocks • Each composer consists of several “building blocks” • Building blocks determine the various characteristics of each composer • There are two basic types of building blocks: • Generators • Chords • Modifiers • Rhythm

11. a b c d e f g More on Building Blocks • Sample composer: • {a, b, c, d, e, f, g, h} • Each letter represents a different building block, layered onto the composer h • There are an infinite number of combinations of building blocks: {a, b, c, g, e, d, a, a, a, g, e, d, …} • This means an infinite number of composers, generating an infinite amount of music!

12. {e, c, d, d, e, b, a, b} {a, d, e, a, b} {c, b, a} {d, e, b, c, e, a, b} More on Building Blocks • There is an infinite number of composers! • Composer blocks are not commutative: {a, b} is different from {b, a} • Each composer can have an unlimited number of blocks: {a, b, c, d, e, f, g, h, a, b, c, d, e, f, g, h, a, b, ... } Unfortunately, not all of them are good...

13. Defined by a “genetic sequence” Chromosome --> Word32 (32-bit binary string) 32 string can be divided any way we choose Contains code for composer’s traits Traits controlled include: Harmony Melody Rhythm Order tweaker {d, d, b, a, e} {a, g, h} {e, a, h, h, h, h, h, h} {f, g, a, b, c} {c, h, g, a, a, b} Inside a Composer [ 0 1 1 0 0 1 0 1 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 0 1 1 0 0 ]

14. Composer blocks are called by genes within the traits Each gene (binary combination) represents a composer block The number of composer blocks available -> number of bits per gene Ex. 3 bits -> 8 combinations -> 7 composer blocks Translator calls the blocks represented each combination To mix things up, tweaker mixes rhythm genes with melody genes The blocks then modify the composition 000 tells the translator to call nothing Can call multiples of the same block A Composer’s Genes Gene Melody (trait) z x z f • z • b • c • x • d • a • z • a f b c d a a [ 0 1 1 0 0 1 0 1 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 0 1 1 0 0 ] Trait 2 calls

15. Critic Building Blocks Mathematical analysis of music • Histogram comparison • The degree of feature similarity is analyzed with a method similar to chi-square • Intervals • Chord Progression • Melodic • Rhythms • Similarities, Differences • Phrasing • Patterns in rhythm and intervals

16. In Critic Functions Implementation of CriticsSurvival of the Fittest Composers The Good The Bad Rating

17. {156, 129, …, 61} {31, 165, …, 142} {5, 2, …, 1} {19, 189, …, 54} {16, 91, …, 122} Genetic Structure of the Critics: Part 1 • Different critics evaluate the same music differently, much like many people like different genres of music • Having many critics will yield a variety of music, instead of allowing one type of composer to dominate • Critics define weighting vectors for the critic functions, that is, how strongly they value each one in their analysis • The 32-bit chromosome must define the 14 weights to create a critic • The best critics are the ones that give the largest score difference between “bad” (current) music and the selected corpus

18. Genetic Structure of the Critics: Part 2 • Each ci is associated with a particular critic function, while d and e apply to all critic functions • d is the index to the array a, containing possible values for the scaling factor ad • e defines whether the scale will be power or exponential • The weight of the ith critic function is given by: • wi = ad^ci, if e=0 • wi = ci^ad, if e=1

19. Experiment Setup • Using our definitions for composer and critic blocks and chromosomes, we created an environment of 20 composers and 20 critics • Each epoch consisted of: • Evolve the composers for 100 generations • Define the current music as the bad corpus • Evolve the critics for 100 generations • After many epochs had passed, we listened to the results

20. Good Music 1 Experiment Results 10111000011101010100001000000110

21. Analysis of Results • Every epoch converged proving a successful genetic algorithm • Music that scored poorly was worse than music that scored better • Ratings improved after each epoch Bad music Good Music 2 Good Music 3 Good Music 4 Real BachMusic

22. Future Improvements • More composer/critic blocks (longer string) • Composer blocks implement histograms • Composer blocks correspond with critic blocks • Next experiment • Larger population, more generation • Add brand new melody modifier block

23. 1337 pR353N70r5 Adam Aaron Adam Bildersee Rebecca Cooper Malamo Countouris Carlin Eng Melissa Fritz Tim Heath Kyle Leiby Yunxue Xu Luke Zarko Special Thanks to Joel Donovan and Peter Lee!