Transcript Computerized Arrangement of Vocal Music

Melody Generation with
Evolutionary Computation
By Matt Johnson
November 14, 2003
Main Topics
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Goal of Research
Why use an EA?
Problem Solving Approach
Representation
Fitness, Mutation, Reproduction
The Next Step
Goal of Research
• Write a computer program that will generate
a beautiful melody.
• Melody should be a traditional soprano part
in the style of church hymnody.
• This melody will then be processed by
CAVM so it may be heard in a harmonic
context.
Why use an EA?
• EAs can handle complex problems.
• Complexity of this problem:
– An average soprano can sing notes in the range
from D1 to G2, or 18 different pitches. (see pic
on next slide)
– There are 8 note durations typically found in
this style of music: sixteenth, eighth, quarter,
half, whole, dotted eighth, dotted quarter,
dotted half.
Vocal ranges
Why use an EA? (cont)
• The number of notes found in a typical
hymn can range from roughly 20 to 60.
Let’s use 40 for our calculation.
• Pitches * Durations = 18 * 8 = 144 =
Number of possible notes. (omitting rests)
• Think of a melody as a string of notes.
• Number of potential melodies: 144^40 = 2 *
10^86 melodies to chose from.
Problem Solving Thoughts
• Reduce the search space by constraining the
melody to notes within a key.
• Will use as much domain knowledge as
possible.
• Will initialize randomly so that no known
melodies are produced. – Uniqueness is
required.
Problem Solving Approach
• Find an appropriate representation.
• Make observations about melodies and
come up with a fitness function.
• Will use a basic evolutionary type algorithm
and tweak it as needed.
Representation
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The building block of music is the note.
A note is made up of a pitch and a duration.
A melody is a string of notes.
An individual in the population will be one
melody.
About Notes...
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Scale Degree
Name
Note Length
Octave
Representation (cont)
• A melody is a string of notes.
• Every individual represents one melody.
Melody Observations
• Melodies tend to move by step.
• Jumps of an interval larger than one fifth are
uncommon.
• Melodies frequently contain repeating
patterns.
Note Movement
Melody Example
Fitness
• Reward one step changes (interval of a
second)
• Reward jumps of a third, but not quite as
much as stepwise changes.
• Reward jumps of a fourth and a fifth, but
not quite as much as a third.
Fitness (cont)
• Penalize for jumps larger than a fifth.
• Penalize harshly for jumps larger than one
octave.
• Penalize for melodies with a high
percentage of sixteenth notes – they are
hard to sing.
Fitness - advanced
• Search for and reward naturally occurring
repetition of four or more notes.
• Search for and reward ascending and / or
descending runs.
Reproduction
• Melodies will be ranked based on their
fitness.
• A number of parents will be selected using
rank based selection.
• Interesting phrases from each melody will
be selected and combined to form a new
melody.
Genetic Operators
• Play Two – concatenate two different
melodies [2]
• Add Space – insert a rest into a melody [2]
• Play Twice – concatenate a melody onto
itself [2]
• Shift Up – Shift every note in the string up
to the next highest note [2]
Genetic Operators (cont)
• Phrase Start – mutate the beginning of each
phrase so that it starts with the tonic note on
a down beat [1]
• Perturb – mutate one note by moving it up
or down one step [1]
Competition
• Will periodically remove the worst
individuals from the population.
The Next Step
• Run the generated melody through CAVM.
• Evolve four parts at once.
Questions?
Related Work
• Peter Todd Gregory – “Frankensteinian
Methods for Evolutionary Music
Composition”
• Co-evolve hopeful singers and music critics
• The female individual represents the
evolving environment and chooses the
males.
• Males represent the singers.
Related Work (cont)
• The female maintains a note transition table.
• Table is used to select the males – the table
itself evolves.
• The males evolve their songs in order to be
selected.
References
1. G. Wiggins and G. Papadopoulos and S. PhonAmnuaisuk and A. Tuson. "Evolutionary
methods for musical composition“
2. Brad Johanson and Riccardo Poli. "GP-Music:
An Interactive Genetic Programming System for
Music Generation with Automated Fitness
Raters"