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Evolutionary Generation of Music with Geometry*
1st Justus Huebotter
MSc Artificial Intelligence
Vrije Universiteit
Amsterdam, Netherlands
huebotter@outlook.com
2nd Thomas Maaiveld
MSc Artificial Intelligence
Vrije Universiteit
Amsterdam, Netherlands
tmaaiveld@gmail.com
3rd Stefan Wijtsma
MSc Artificial Intelligence
Vrije Universiteit
Amsterdam, Netherlands
stefanwijtsma@gmail.com
Abstract—The aim of this paper is to explore methods of gener-
ating interesting music using evolutionary computing techniques.
Multiple populations of rotating geometric shapes are evolved and
selected from to create live music. Our implemented framework
visualizes the selected shapes and uses them as a trigger for sound
generation. An adapted evolutionary programming strategy is
used allow the system to evolve and create constantly changing,
interesting and aesthetically pleasing music in real time. We
describe our setup and further elaborate on how the standard
evolutionary strategies are adapted to generating music from
geometry. The aim of this exploratory paper is to serve as a
proof of concept for evolving music with structure and novelty
derived from geometric shapes. We describe the performed
experiments using a multi-population representation, various
selection mechanisms, and multi-objective fitness evaluation that
is based on a moving optimum.
Index Terms—evolutionary computing, evolutionary art, evo-
lutionary strategies, music generation
I. INTRODUCTION
Evolutionary algorithms (EAs) — computer programs in-
spired by Darwinian evolution — have drawn the attention
for various artistic and musical projects [1]–[3]. The field of
evolutionary art applies computational methods from evolu-
tionary computing to create interesting and beautiful artistic
expressions, that come in the form of images, video, audio,
text, animations or complete performances. Several researchers
as well as artists have recombined, modified, and extended
these techniques, beginning the exploration of possible appli-
cations of evolution to aesthetic design [2]. Central to EAs
is the concept of fitness, used e.g. for survivor selection
mechanisms. Therefore, the field of evolutionary art is invested
in translating aesthetics into well-defined measurements that
could be used for fitness evaluation. In other words, a key
aspect of this field is finding ways of converting ”what is
beautiful” into a mathematical function that describes what is
aesthetically pleasant to the human. Modelling this function
may be achieved by having a ”human in the loop”, such
as learning optimal aesthetic parameters by estimating fitness
through feedback from a user or system designer. Evolving
aesthetically pleasing art without a human in the loop presents
unique challenges when combined with a sufficiently large
search space to allow for creativity and when applied in a
domain where aesthetic measures of quality are abstract and
poorly defined. Moreover, in a setting of continuous music
generation, the optimal fitness (what is considered pleasant)
might even change over time.
One way of avoiding having a human in the loop in
harmonic music generation is by exploiting the concept of
”Sacred Geometry” [4], [5], describing the similarities of
mathematical relations in geometry and harmonics in music.
The key idea is to let the relations between different geo-
metric shapes form a basis for musical tonality and rhythm.
This paper proposes a framework for applying evolutionary
programming techniques to combine music and geometry into
an evolving art installation. The research is focused towards
creating a system able to generate and evolve music using
fixed aesthetic measures of fitness inspired by geometrical pro-
portions. The goal is to explore methods of music generation
and fitness estimation without human interference in order to
take a step towards completely autonomous, continuous music
generation. The experiments conducted are aimed at answering
the following research questions:
1) What properties of geometry are translatable into the
domain of music creation?
2) How can evolutionary methods help to generate har-
monic and dynamic music?
3) Can an evolutionary algorithm generate musical novelty,
interest and structure through a predefined set of geo-
metrical rules?
This paper presents related work in the domain of evolution-
ary art, gives a complete description of our implementation and
the adapted evolutionary programming strategy, and presents
experiments with different parameter settings. Finally, the find-
ings are discussed to formulate a conclusion and interesting
directions for future research.
II. RE LATE D WORK
Evolutionary programming has proven to be fruitful tech-
nique to simulate evolution computationally [6]. A summary
review by Johnson et al. provides an overview of previous
research and existing implementations concerning the formu-
lation and measurement of aesthetic fitness in evolutionary art
[7]. The review outlines a variety of theoretical approaches
to measuring aesthetic fitness. Theory of form within evolu-
tionary art, focused on ”use of symmetry, and the balance
between order and complexity”, functioned as a theoretical
resource for the implementation described in this paper. Both
the algorithmic encoding of form, as well as the usage of
measures for form as drivers for evolution were considered key
to answering the research questions. McCormack [8] specified
five open questions in evolutionary music and art, of which the
second and third questions, designing a representative aesthetic
fitness function and producing recognizably artistic works by
evolutionary means, are directly relevant to this research.
Johnson’s taxonomy classifies the body of literature describ-
ing previous evolutionary art publications by fitness scope and
fitness measure [3]. Situating our design within the ”Aesthetic
Measure” category of this taxonomy allowed for the inves-
tigation of similar existing implementations. Some previous
evolutionary music implementations applied abstracted statis-
tical measures to quantify the aesthetic value of the produced
music, which could be derived either by using human response
[9]–[11] or by examining properties inherent to the music
[12], [13]. Others were focused on directly evaluating musical
attributes. A multitude of melodic and rhythmic features found
in the literature are listed in [14]. Bilotta et al. implemented a
distribution-based musical sequence generator with qualitative
fitness measures by devising a scoring scheme to examine
consonance between different notes of the Western chromatic
scale [15]. Browne and Fox used a pre-trained, undirected
neural network to measure tension and release in evolved
compositions [16], [17]. In these implementations, fitness
evaluation is often focused around the elimination of bad
results, relying on rich representation and a broad search space
to generate musical interest.
Previous work concerning implementation of rhythmic aes-
thetic is sparse. The aforementioned implementations omitted
rhythmic information as part of an aesthetic measure and
focused on consonance. Horowitz utilized an interactive ge-
netic algorithm to model and parameterize user preference
of rhythm [18], but lack of previous examples of formal
fitness estimation necessitated a novel approach to estimating
the fitness of rhythmic combinations. Nonetheless, geometric
proportions and their relationship to musical rhythm have been
explored in the domain of computer science [4] and provided
a useful basis for constructing music through a representation
that may be evolved. The other approaches provided general
inspiration for some of the attributes of the evolutionary
algorithm and fitness measure. Challenges specific to the rep-
resentation, implementation and research objectives specified
in this paper necessitated adaptation and exploration of novel
approaches to evolution and fitness measurement. The style of
implementation and using a graphical interface with rotating
polygons and UI control surface was inspired by the work of
musician and sound artist Rui Gato1.
III. SYS TE M DESCRIPTION
The system architecture consists of several elements, visu-
alised in Figure 1. The system code was written in Python
3, while music generation was performed using Sonic Pi2,
an open source music tool that allows users to generate
music through live coding. Music is generated by triggering
of real-time music events through internal OSC commands
1For more information please see his website or this workshop and live
demonstration of his work.
2For more information please see The Sonic Pi website.
from Python to Sonic Pi. Apart from some Python library
dependencies, the system runs on a standard Python distri-
bution on Windows and MacOS using the default Sonic Pi
synthesizers. Sonic Pi also plays custom samples, some of
which are included in the project repository. Please note that
the samples provided are limited to avoid licensing problems,
but can easily be expanded upon.
This section gives an overview of the system implementa-
tion and describes the procedure for producing sound from
evolved geometric shapes, followed by a specification of the
genotypic and phenotypic representations of the individuals
and a description of the population structure. The algorithmic
procedure and equations utilized to perform variation and
selection are described to give an overview of the evolutionary
algorithm. Lastly, the implementation of presets containing
initialization parameters and a sequential parameter control
system (’autopilot’) will be described, which enable the system
to create continuous, dynamically evolving music.
Rotating polygons are visualized on a screen and shown
to the user. A musical note is triggered whenever one of
their vertices crosses a vertical line through the middle of the
upper half of the display. To determine what polygons should
be played, the system reads from an array containing the
phenotypes of genes selected to be played by the evolutionary
algorithm. The process is initialized using a set of initial
parameters retrieved from the configuration file of the active
preset. The presets and parameters can be set using a GUI and
can be written to by the autopilot.
A. From Shape to Sound
The display system visualizes individuals as polygonal
shapes with vertex counts (hereafter referred to as the ’or-
der’) ranging from 3 to 12. Each polygon may have several
replicated polygons circumscribing it, meaning the angles of
the inner polygon are tangent to the sides of the outer polygon.
The properties of the shapes are derived from the phenotype
representation of corresponding individuals currently being
played. Apart from the order, some important geometric qual-
ities encoded in the phenotype are the radius, rotation speed,
(relative) offset and number of copies to be produced. The
radius of the polygon is related to the frequency of the played
tone. The radius of a shape is set to correspond with a note of
the chromatic scale; a larger radius results in a higher tone
played. Any shape may assume a radius corresponding to
any note. When a vertex of a shape touches the line at the
0°orientation on the display, a sample corresponding to that
shape is played.
The phenotype of an individual may also encode a mapping
for a series of circumscribed shapes of the same order. The
amount of circumscribed shapes is encoded as the number of
copies to be produced (hereafter referred to as the ’number’).
For instance, a phenotype could encode a series of hexagons,
which will result in a tonal pattern of notes increasing by a
fixed interval. The width of the interval depends on the order
of the shape; the higher the order, the smaller the increment in
the radius of the circumscribed copies. The ratio between the
2
radius of a polygon and and the radius of its circumscribed
polygon is equivalent to the ratio between the apothem and
radius of the circumscribed polygon (since its apothem is
equivalent to the radius of the inscribed polygon). This ratio
depends on the order of the shape and is given by cos (180°
o),
where orepresents the shapes order. The obtained ratio cor-
responds with a tonal interval, which differs for polygons of
varying orders. Thus, a different order produces a different
repeating harmonic pattern of intervals (the note corresponding
to the innermost shape). Furthermore, the angular orientation
of the shapes’ vertices relative to the innermost shape is also
rationally divided for circumscribed shapes (by ratios of 2,
3 or 4), resulting in a regular rhythm. Lastly, the beats per
minute (BPM) attribute functions as an integer multiplier for
the rotation rate of a shape, and thus for the playback speed
of the samples it plays. Thus, the rhythm of the music is
determined by the order, number, rotation rate (BPM) and
offset parameters of the playing polygons; higher values result
in a more densely populated rhythmic axis. By combining
multiple polygons with different amounts of vertices, and
creating multiple copies of the same shape with an increasing
size, a wide spectrum of tonality, harmony and rhythm can be
represented.
Certain non-geometric properties evolved by the system and
encoded in the phenotype are not encoded in the graphical
representation and relate solely to the music, such as the
instrument type and panning. For forming longer musical
compositions, the structural aspect of what elements to repeat
and what to take away or change is the main challenge. Crucial
to producing aesthetically pleasing music is combining the
right instruments, and evolving the set of playing instruments
in a dynamic manner. This is handled by a combination of the
representation, evolutionary process, the selected preset and
the autopilot. These will be explained in the remainder of this
section.
B. Representation
An individual may be represented by its genotype and
corresponding phenotype mapping, which in turn provide the
information necessary to represent it visually and musically.
To create the desired mix of different polygons with pleasing
musical properties, 17 different parameters were encoded in
the genotype, shown in Table I. The genotypes are a real-
numbered vector of 17 values in [0.0, 1.0). These contain
information on both the geometric shape as well as its musical
properties. Since some instruments have very different ranges
of pleasant musical properties and may require restriction to a
certain range, genotypes are converted into phenotypes using
a custom mapping function for each instrument. Phenotypes
are represented as a vector of 22 values, extending the 17
values of the genotype with the type of instrument (’nature’)
defined by the population the individual is a member of,
and pitch of the sound, dependent on the note properties
of the genotype. Multiple populations are evolved separately,
one for each instrument set; a separate population is defined
for kicks, snares, hats, percussion, bass, guitar and synths.
TABLE I: Overview of the parameters represented in each individuals
genotype and parameters added to the phenotype. Not all parameters
are expressed as for each instrument category and the color values
are mapped to different musical properties per population.
Genotype & Phenotype Phenotype
amplitude attack bpm cutoff nature
initial offset instrument echo reverb pitch
mod phase mod range number order red
pan release rootnote rootoctave green
total offset blue
TABLE II: Summary of the applied evolutionary scheme.
Evolution Scheme
Populations 7
Population Size 10 (n)
Representation Real-Valued Vectors
Initialisation Random [0.0, 1.0)
Parent Selection Probabilistic (pm)
Recombination None
Mutation Polynomial Bounded (η)
Fitness Multi-objective (weighted sum)
Specialty Moving Optimum
Survivor Selection Select Best n(µ+λ)
Playing Selection Select Best k
Termination Condition Manual (none)
Genotypes are equivalent across all populations to ensure that
they evolve in a similar fashion, while different phenotypes
are produced by the mapping function variant associated with
each population.
C. Evolutionary Process
The populations are randomly initialized with a size µ.
Individuals are selected with a probability pmto be mutated
by bounded polynomial mutation with a step size of η. The
fitness values of the original population of length µand
mutated offspring of length λare calculated, of which the
best µindividuals are selected. These steps are equivalent
to a standard implementation of a (µ+λ)strategy genetic
algorithm.
Once all populations have evolved and a new generation
is prepared, the next step is to select kpopulation members
to be played. kis defined as the sum of the amount of
members drawn from each population, which is controlled by
the preset and the autopilot. The selected population members’
phenotypes are compiled and used to generate the visuals
and audio. Since the algorithm has no predefined termination
condition, evolution continues until the user terminates the
process. A summary of this scheme is shown in Table II.
D. Fitness Evaluation
The aesthetic fitness of an individual iis measured by
computing the weighted sum of metrics of fitness as shown
in Equation 1. The formulations of these three metrics are
explained below in this section. The fitness function objective
is to minimize this weighted sum.
f(i) = wdist ·fdist(i) + wsym ·fsym(i) + wage ·fage(i)(1)
3
The distance metric fdist represents the distance between
the order of a given shape and a defined optimal shape.
Rather than being fixed, the optimum value changes over
time to generate varying musical patterns. The optimum is
computed by taking the average order of all playing shapes.
Also, the system allows to set a manual optimum. For any
given individual i, its fdist is defined as the absolute difference
between its shape order oi, which is encoded in its phenotype
representation, and the optimal order o(t)at a given time
point. A higher distance from the optimum incurs a large
penalty to the individual’s fitness, reducing the likelihood of
being selected for the next generation. Several optima may be
configured, in which case fdist represents the distance to the
nearest optimum:
fdist(i) = min
k(oi−ok(t)) (2)
In order to formulate an aesthetic estimation of rhythmic
fitness of shapes, a custom encoding scheme was devised
to evaluate the rhythmic purity of two encoded ratios. The
encoding penalizes rhythms that feature conflicting rhythmic
intervals. As two shapes rotate, their order (a shape’s number
of angles) determines the temporal intervals at which samples
are played. Certain polyrhythmic combinations may produce
interesting combinations explored in virtually all musical
cultures worldwide, such as 6 on 4 or 12 on 8. Others may
produce rhythmic patterns that are rarely used, highly irrational
and would be difficult to impossible for a human listener to
interpret, such as 5 on 11, 11 on 12, or 3 on 7. The assigned
value from the encoding scheme is retrieved to find the penalty
for a specific pair of rhythmic subdivisions, and the sum is
normalized to average over the encoding value for all shapes
currently playing:
fsym(i) = 1
n
n
X
j=1
enc(pi, pj)(3)
Ratio Whole Half Third/Quarter Eighth/Tenth Other
Encoding 0 1 2 5 10
Lastly, the age metric fage is defined as a parabolic function
that represents how many subsequent generations an individual
has been selected to be played. The age is initialized at 0 for
all individuals and only increased if for individuals selected for
playing. Using a parabolic function and setting its minimum as
a parameter crepresenting the expected age of an individual,
an age curve can be defined. This metric ensures individuals
selected for playing stay active for a short while, but are
eventually phased out, even if they are considered highly fit in
terms of distance and symmetry. In our experiments, we have
set the constant c= 4.
fage(i) = (age −c)2
−c2
c2(4)
Fig. 1: Overview of system architecture explained in this paper.
E. Presets
Presets contain all information needed for a run, such as
parameters for the evolutionary process, the instruments used
and the maximum number of instruments from each category.
They also contain all earlier mentioned hyperparameters such
as the weights for the fitness objectives. By summarizing
all configuration parameters into this single preset file, the
parameter settings can be modulated in a real-time through a
GUI. Furthermore, this allows the system to switch between
presets, alternating between different parameter sets.
F. Autopilot
Although the evolution takes care of mutation and selection
of playing instruments, the system needed a way of creating
higher level musical structure. This is mostly done through
changing the nature of instruments playing, i.e. changing the
number of maximum active instruments for each category. This
is handled by the autopilot, being an automated semi random
sequence generator, able to set parameters such as the number
of currently active instruments. The autopilot probabilistically
adds or removes an instrument in every evolutionary cycle,
which effectively allows the system to creates buildups and
breaks by changing the number of instruments playing.
IV. EXP ER IM EN TAL SETUP
In order to address the research questions we set out to
answer, the system’s ability to generate a sequence of music
from an initial set of genes and parameters was tested. The
challenging aspect of this task is to maintain musical diversity,
while keeping some elements constant. Notably, this could
be achieved with a predefined control sequence (autopilot).
However, in order to demonstrate the evolutionary process by
which novel musical ideas can be generated, we aim to show
how the proposed architecture can achieve this through pure
evolution, making use of the three fitness objectives.
An experiment was set up to test the system’s capacity
to balance the abstractly defined objectives of novelty and
structural cohesion in the music. Our main goal is to show
how the three weighted fitness objectives can steer the evo-
lutionary process to produce aesthetically structured music
4
with novel ideas generated by the evolutionary process. In
this experiment, different evolution parameter settings were
applied sequentially in a continuous run to showcase the effect
on the populations, as well as on the set of individuals that are
currently playing. We used 7 populations with 10 individuals
each, and evolved them for 240 generations while changing the
parameters every 30 generations to demonstrate their influence
on the behaviour. From each population, the fittest individual
was selected for the playing subset, resulting in 7 playing
individuals at any given time (as the autopilot sequence gener-
ation was inactive). The population size, independent mutation
probability of an attribute and mutation eta were set to 10, 0.5
and 0.5 respectively. To showcase the evolutionary response to
different evolution parameters, the weight for symmetry, age,
and distance to optimum fitness objectives were modulated, as
well as the optimum itself (playing mean to manual) and the
mutation rate. Parameter c, the age at which fage is optimal,
was set to 4.
To quantify the system behaviour, the total fitness, partial
fitness scores for symmetry, age, and distance, the age, and
the order were measured over generations. By starting the
experiment without any fitness evaluation (i.e. all weights set
to zero) and initializing the populations randomly, the output
is completely random at first, as selections over equal fitness
values are resolved using random selection. Parameter mod-
ulations were applied every 30 generations, and the resulting
outcome measures. Please note that the generation length was
set to only two seconds for this experiment for demonstration
purposes, but ideally, each generation should be allowed to
play a bit longer. The resulting video and music were recorded
and uploaded here. Since there was no ’human in the loop’
assessing the musicality of the output, we discuss an analysis
of the system behaviour under different parameter settings in
the next section.
V. EX PE RI ME NTAL RESULTS
The parameter modulations over generations and a descrip-
tion of the effect on the evolution metrics and the music are
given in Table III. The results for the different quantitative
evaluation metrics are given in Figure 2 and Figure 3 for
the individuals selected to play and the full populations
respectively. In both plots, the black line represents the mean
value across all populations for each metric. The colored
lines indicate means (for the population plots) or values (for
the playing plots, as only one individual was selected from
each instrument) for each instrument category. Figure 4 in the
Appendix gives a visualization of the modulation trajectory of
the experiment parameters.
Results show that that the properties described by the fitness
function are all affected by modulation of the evolution-
ary parameters. Other musical properties (effects, root note)
remain random during evolution. Introducing the symmetry
objective leads to convergence to a more rhythmically aligned
subset of order, most commonly 3-6-12 during the experiment.
Introducing the age objective improves the odds of survival
for young genes, and phases out individuals as they age past
TABLE III: Description of the control sequence used for the evolution
parameters and the observed effects on the metrics and music during
the performed experiment.
Generation Modulation Observed Effects
1 - 30 Initialization:
Fitness weights
set to 0.0
mutation rate
set to 0.5
no target order
set
Fitness stays at 0 as expected, age
shows that playing instruments con-
stantly change at random. Random
rhythmic variations and combinations
occur with no discernible pattern.
31 - 60 Symmetry
weight set to
1.0
The effect of the selective pressure on
order is visible in population plot. Fit-
ness quickly converges, Initially, musi-
cal patterns evolve with a strong simi-
larity to the patterns present last varia-
tion generated by the random mutation
phase (generation 30). The shapes grad-
ually collapse into triangles, hexagons
and dodecahedrons, as their propor-
tional vertex counts accrue them a
strong symmetry fitness.
61 - 90 Age weight set
to 1.0
Impact on mean population fitness is
small, because only playing individuals
are affected. This leads to wavy patterns
visible in the playing only plot. As
musical patterns with a low symmetry
score are culled by the selective pres-
sure of the age weight, rhythms and
instruments are preserved for longer,
especially those with a high similarity
score.
91 - 120 Distance
weight set to
1.0
Impact on fitness visible as initial spike
with convergence over multiple gen-
erations (∼30). Order of playing and
population is reduced to small bound
around the previous mean. Rhythms be-
come sparser as the system gradually
regresses to a central optimum of 6,
producing mostly hexagonal shapes.
121 - 150 Target order set
to 11
Fitness goes up, but fails to escape a
local minimum. Rhythmic activity in
the music gradually increases as higher-
order shapes are selected. The failure
to converge to the target optimum is
reflected by a dominance of medium-
order shapes such as hexagons, with oc-
casional octagons that step sufficiently
towards the target to survive, but are
eventually phased out by their weight
penalty and their lack of symmetry to
the hexagons.
151 - 180 Target order set
to 3
Fitness goes up initially and population
order changes within ∼15 generations
to the desired optimum. During the
transition, many polyrhythms are heard
in the music, which produce the noise
visible in the fitness plots during these
transitions as different interactions are
expected to produce varying symmetry
scores as the population diversifies dur-
ing transition.
181 - 210 Target order set
to 11, mutation
rate set to 1.0
Fitness goes up, but this time manages
to break out from the local minimum
position. Takeover time is not heav-
ily affected. The resulting music has a
higher rhythmic density, and introduces
some melodic lines in the tonal instru-
ment samples.
211 - 240 Target order set
to 3
Fitness spikes again, then converges
within ∼15 generations. Significant re-
duction in rhythmic density.
5
Fig. 2: Individual (color) and average (black) values of total fitness,
separate fitness objectives, age and order for currently playing indi-
viduals only.
the threshold. The distance objective further constrains the set
of orders present in the playing group, but can drive novelty
during transitions to new optima. Moreover, modulating the
optimum affects musical properties such as dynamic and
rhythmic density, offering a means of introducing long-term
structure in the music. By modulating evolution parameters,
transitions can progress differently and produce a different
musical effect, depending on the success of the convergence
or rate of change.
As the fitness objectives are introduced, their selective
pressure seems to induce the expected musical effect in
the populations and playing group. The proposed parameters
allow for controlling the musical output in different temporal
magnitudes. The small population size allows for relatively
high homogeneity within the populations, preserving a sense
of musical order. On the other hand, novelty can be achieved
through order sequence configuration and adaptation of muta-
Fig. 3: Population average (color) and overall average (black) values
of total fitness, separate fitness objectives, age and order.
tion parameters, and is encouraged by the age curve that allows
new individuals to thrive and older members to be phased out.
The results show that the system is able to generate and select
a varying, gradually changing set of individuals that together
produce a pleasant and cohesive piece of music.
VI. DISCUSSION
The interplay of our parameters makes it possible to gen-
erate changing and interesting music, with variation in dy-
namic, diversity and rhythmic density. However, because of the
relatively quick convergence with this small population size,
some automation is needed for longer-term change of prop-
erties such as rhythmic and harmonic density. The proposed
autopilot can be used as a moving optimum generator, with
random or sinusoidal dynamic optima. Further modulating
parameters by sequence could provide dynamic transitions
between optima on fitness landscapes. The described related
works give additional suggestions to explore for other musical
6
or aesthetic fitness objectives that could be modulated by
the control infrastructure proposed in this paper. Additionally,
fine-tuning parameters beyond the basic configuration used to
highlight the effects in this paper could produce more variant
or desirable combinations and evolutionary effects for a live
performance.
Since the rotation speed of a shape was affected by both
order and BPM, this attribute also affects the rhythmic density,
symmetry and convergence in the music, but is not accounted
for in the fitness metrics. This introduces an element of ran-
domness to the playing speed, which contributed to rhythmic
diversity but may have an unexpected effect on rhythmic
convergence and symmetry. The BPM and order could be
more strictly separated in order to allow for more interesting
changes in dynamic, density and tempo. Higher-order shapes
may function differently in lower-tempo configurations and
vice versa.
This study was limited in that it was heavily focused at
cutting the ’human out of the loop’, focusing on implementing
aesthetic measures over user-centred evaluation of the resulting
music. As such, no questionnaires or listening experiments
were performed and psychological perceptions or reactions
to the music were measured. Limiting the focus of the re-
search to generating musical structure and novelty through our
infrastructure allowed us to focus on the proposed research
questions, which were addressed via an empirical experiment
setup and measurements instead.
Lastly, while fitness measures of rhythmic properties of
the music were strongly represented in this study, the system
lacks a means by which to generate meaningful or intelligent
harmonic combinations. The current implementations offer
largely a random or unplanned selection of specific tones
to be played. Further exploration of such metrics using a
fitness landscape exploration technique to drive novelty and
optimization may prove fruitful in the context of harmonic
evaluation as well.
VII. CONCLUSION & FU RTH ER WORK
We proposed and implemented an infrastructure for gen-
erating music with structure and novelty by means of ge-
ometrically represented sound sequences, evolved using an
evolutionary computing process. The order property of the
shapes proved an effective evolutionary tool to create rhyth-
mically diverse music containing procedural melodic patterns.
The plots from our experiment show that our system is able
to generate musical novelty, interest and structure through a
predefined set of geometric rules. The proposed three-objective
fitness function was able to balance the evolutionary forces.
The system parameters can be tweaked through hardware or
other user input, or can be subject to sinusoidal functions
for gradual change, allowing the user to generate music by
a controlled evolutionary process. We hope that the described
research and implementation offer some insight or inspiration
with respect to automatic music generation using evolutionary
computing techniques.
Fig. 4: Overview of the parameter changes applied over time during
the experiment, as well as a plot of the root note means per population
(bottom row).
PLACEHOLDER FORMATTING TEXT
7
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