EFFECTS OF MUSICALLY MEANINGFUL OPERATORS IN
EVOLUTIONARY COMPOSITION
John Huddleston Jianna Zhang
Western Washington University
Computer Science
516 High St.
Bellingham, WA 98225
ABSTRACT
Musically meaningful genetic operators have become an
accepted aspect of evolutionary composition despite a
lack of objective evidence to support their use. This
research investigates the impact of four musically
meaningful mutation operators from previous research
on population fitness relative to a standard mutation
operator. Two-dimensional rhythmic patterns are
evolved using user-defined fitness trajectories. Although
none of the meaningful operators has led to drastic
improvements, the Invert-All operator has been
consistently successful. These experimental results
suggest that the combination of the Invert and Rotate
mutation operators will lead to the best improvement
over the standard mutation.
1. INTRODUCTION
Musically meaningful genetic operators have been a part
of evolutionary composition for over a decade despite a
dearth of experimental data to justify their use. We
investigate the effects of four musically meaningful
mutation operators (MMMOs) on populations of simple
rhythmic patterns. The goal of this project is to
determine the individual effects of these MMMOs on
population fitness and provide a numerical basis for
justifying their use in evolutionary composition of
rhythms. The performance of each MMMO is judged in
relation to a standard mutation operator.
The remainder of this paper is organized into five
sections: a background on MMMOs, the approaches
used in this research, the results of these approaches, and
a discussion of the results. The discussion of results is
followed by our conclusions and a summary of future
work.
2. BACKGROUND
The introduction of MMMOs to the field of evolutionary
composition was first made in Biles' "GenJam" [1],
although that research did not conclusively state the
impact of this new breed of mutations on population
fitness. The theory behind meaningful genetic operators
extends back to the original research on reordering
operators summarized in [4]. Most of the research from
this time manifested as mutation-inspired crossover
operators rather than standalone mutation operators. In
relation to music, operators are considered "meaningful"
when their algorithms take into account the musical
semantics of the input representation as well as principles
of music theory. The purpose of these knowledge-based
operators is to evolve better individuals faster than
"dumb" classic operators [1].
Biles defines mutation operators for populations of
measures including reverse, rotate right, invert, sort
notes ascending, sort notes descending, and transpose
notes. At a second level composed of measure-based
phrases, he implements mutators such as genetic repair,
super phrase, lick thinner, and orphan phrase. These
operators attempt to maintain diversity and quality in the
phrase populations by weeding out poor or frequently
used measures and building new phrases from the best or
infrequently used measures. The two most successful
mutators replace existing measures with the least
frequently occurring measures in the entire population
[1].
Papadopoulos and Wiggins [6] describe significant
improvement in the evolution of melodic patterns using a
restricted copy mutation which copies melodic fragments
of a constant size to metrically logical locations
elsewhere in the piece. The impact of this mutation is
limited by the number of valid locations to which a
fragment can be copied. Thus, the copy mutation could
potentially reduce the population diversity by creating
many similar mutants.
Tokui and Iba [7] describe a MMMO, Timbre
Exchange, which exchanges timbres amongst instruments
within an individual. The same research also uses the
rotate and reverse operators inspired by [1]. The impact
of these mutators on population fitness or diversity is not
addressed.
Dostail's [3] four MMMOs accentuate quiet notes that
match strong rhythms in a piece of source music,
syncopate strong beats, randomly change the type of
notes played in a given measure, and even rewrite
rhythms to match the source music. The operators are
the sole basis of recombination and mutation and without
their influence a population of rhythms cannot achieve
successful results.
3. METHODS
Throughout this paper the term "gene" is used to
describe a boolean value indicating the presence or
absence of a musical beat. The terms "mutator" and
"MMMO" refer to a "musically meaningful mutation
operator.
To isolate the effectiveness of the different operators
from potential problems caused by an exponentially
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