Valerio Velardo,∗ Mauro Vallati,†
and Steven Jan∗
∗School of Music, Humanities and Media
†School of Computing and Engineering
∗†University of Huddersfield
Queensgate, Huddersfield, HD1 3DH, Reino Unido
velardovalerio@gmail.com
{m.vallati, s.b.jan}@hud.ac.uk
Symbolic Melodic Similarity:
State of the Art and Future
Challenges
Abstracto: Fostered by the introduction of the Music Information Retrieval Evaluation Exchange (MIREX) competition,
the number of systems that calculate symbolic melodic similarity has recently increased considerably. To understand
the state of the art, we provide a comparative analysis of existing algorithms. The analysis is based on eight criteria that
help to characterize the systems, highlighting strengths and weaknesses. We also propose a taxonomy that classifies
algorithms based on their approach. Both taxonomy and criteria are fruitfully exploited to provide input for new,
forthcoming research in the area.
The advent of the Internet has made a large quantity
of audio and symbolic musical data freely available.
The analysis of these data can provide useful
insights into several aspects of music. By comparing
many musical pieces, it is possible to abstract
relevant rules and processes that characterize a
particular style. También, the analysis of large databases
can improve our understanding of the generative
proceso, shedding light on the evolutionary path
undergone by music over time. To capitalize upon
the significant body of knowledge currently stored
within online music data sets, a number of reliable
and efficient automatic tools have been developed
over the last decades. Melodic similarity-detection
algorithms are an instance of such tools. Cuando
used on online musical data sets, they can provide
valuable information on intra- and interwork
melodic relationships and on the underlying melodic
structures of the pieces analyzed.
Given two or more sequences of notes, symbolic
melodic similarity (SMS) aims to evaluate their
degree of likeness, as human listeners are able
to do. This task has relevance both within the
academy and in industry. Por ejemplo, beyond the
purely academic benefits of identifying the degree
of likeness between musical pieces and composer
practices afforded by melodic similarity systems,
the detection of plagiarism constitutes an example
of a practical application of this task with clear legal
and commercial implications. Many algorithms for
judging melodic similarity have been introduced
Computer Music Journal, 40:2, páginas. 70–83, Verano 2016
doi:10.1162/COMJ a 00359
C(cid:2) 2016 Instituto de Tecnología de Massachusetts.
over the years. Even though such tools perform
essentially the same task, they may be based on
theories and methods that belong to radically
different disciplines. Por ejemplo, there are some
algorithms based on principles from music theory,
others based on cognitive constraints, y otros
that implement notions from pure mathematics.
Thanks to the “Symbolic Melodic Similarity”
track of the Music Information Retrieval Evaluation
Exchange (MIREX) competition (Downie 2008),
introduced in 2005, the number of tools in this
field has increased dramatically. The last published
surveys on SMS, sin embargo, only consider algorithms
developed up to 2004 (M ¨ullensiefen and Frieler
2006; Hofmann-Engl 2010). This lack of review
of the state of the art is the first motivation for
this article. Accessibility is a second motivation.
The literature on SMS is distributed across many
different sources, which cover numerous topics
from computer science to music theory. This survey
brings together recent studies on SMS, describing
them in a concise way so that researchers can form
an initial overview of the approaches used by other
eruditos. Our article proposes a highly modular
taxonomy that allows the effective categorization of
techniques according to the approach they exploit.
We identify eight criteria, which summarize the
most relevant aspects of each melodic similarity
algoritmo. By analyzing the state of the art, we are
also able to provide guidelines and recommendations
for a further development of the field. Además, el
aforementioned taxonomy and the criteria facilitate
the classification and comparison of future systems.
The article is structured as follows. Primero, nosotros
outline relevant background information and related
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obras. Segundo, we outline the identified criteria.
Próximo, the taxonomy is presented and the considered
systems are briefly described and categorized. Entonces,
algorithms are compared with regard to the eight
criteria. Finalmente, by synthesizing the knowledge
gained with the analysis, we propose new directions
for research and offer conclusions.
Fondo
Stephen Downie defined music information retrieval
(MIR) as a “multidisciplinary research endeavor
that strives to develop innovative content-based
searching schemes, novel interfaces, and evolving
networked delivery mechanisms in an effort to
make the world’s vast store of music accessible
to all” (Downie 2004, pag. 12). The interdisciplinary
environment of MIR encompasses many fields, semejante
as computer science, psicología, musicology, música
cognition, and signal processing. Music information
retrieval combines these disciplines to create real-
world applications that are capable of extracting
relevant information from music. Its techniques
have been applied to solve a large number of tasks,
such as music recommendation, automatic music
transcription, and track separation. There are two
ways MIR systems can represent music: audio and
symbolic. Systems that adopt audio representation
directly encode musical information through digital
audio formats such as WAV and MP3. Aplicaciones
that use symbolic representation are usually based
on MIDI and MusicXML formats. Symbolic en-
coding allows the system to manipulate musical
elementos (such as notes that each have a specified
pitch and duration) without recourse to signal pro-
cesando, while having a clear representation of the
composition.
Symbolic melodic similarity is a central issue of
MIR. Many applications exploit musical similarity
to retrieve pieces from a database, to perform musi-
análisis calórico, and to categorize music. Esencialmente, todo
systems that are based on melodic similarity try to
find musical utterances that match the information
needed by the user, expressed in a query. Appli-
cations that evaluate melodic similarity improve
the accessibility of musical databases, permitiendo
users to efficiently retrieve the musical information
they need. Además, such systems can enhance
the understanding of the structure of music itself.
En efecto, musicologists can exploit applications to
track stylistic traits of musical pieces and to trace
the occurrences of musical patterns both within and
between musical works. This can deepen our under-
standing of musical style, while actively promoting
a new quantitative, empirical analytical approach
among musicologists and music theorists.
A major issue with melodic similarity is that
assessing the likeness between two musical phrases
is an extremely difficult process, which reflects
the cognitive complexity of the task. La mayoría de
complexity associated with melodic similarity de-
tection arises from the multidisciplinary nature of
this process. Melodic similarity spans several ele-
ments of music theory, ethnomusicology, cognitivo
ciencia, and computer science, all of which have
to be considered simultaneously. Music theory
suggests how to identify syntactically relevant mu-
sical structures. Ethnomusicology accounts for the
variety and the cultural dependency of melodies
from distinct geographical regions. Music cogni-
tion describes the basic cognitive processes that
humans deploy to recognize melodies as similar.
Finalmente, computer science affords a means to create
“intelligent” computational systems able to embed
the insights provided by the other fields. A pesar de
melodic similarity has been extensively investi-
gated in all of these disciplines, there is no agreed,
clear-cut definition of the field yet. Even scholars
from the same background disagree on the ambit
and methodologies of melodic similarity.
This survey focuses on MIR systems performing
melodic similarity analysis that have been presented
desde 2004. Systems introduced before have already
been reviewed (M ¨ullensiefen and Frieler 2006;
Hofmann-Engl 2010). For the sake of completeness,
we briefly report the main strategies developed
antes 2004, which strongly affected the later re-
search environment. En 1996, McNab and coworkers
introduced an algorithm based on the edit distance
between motives (McNab et al. 1996). Emilios
Cambouropoulos (1998) devised a system based on
melodic contrast that dynamically creates motivic
categories containing similar melodic structures. En
Velardo, Vallati, and Jan
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the same year, Donncha O’Maid´ın (1998) desarrollado
a system that exploits the distance in pitch between
two melodies, weighted through correlation and dif-
ference coefficients. Más tarde, Downie (1999) presentado
a system that assesses melodic similarity based
on n-grams. Finalmente, Meek and Birmingham (2002)
developed an algorithm that exploits hidden Markov
chains.
MIREX was established in 2005 (Downie 2008).
This organization runs an important annual com-
petition that aims to compare state-of-the-art
algorithms and systems relevant for MIR. Uno de
the several tracks of the contest is SMS, and in this
respect MIREX helps to facilitate cross-fertilization
among researchers, while constantly fostering the
improvement of the techniques and strategies
adopted in melodic similarity research. MIREX
has become the main forum for researchers and
practitioners interested in evaluating and comparing
algorithms that span several tasks of MIR. As a con-
secuencia, many systems considered in this article
have been tested or trained on MIREX benchmarks.
En efecto, this competition has been providing the MIR
community with a large set of useful benchmarks
for ten years. [Editor’s note: This article was written
prior to the 2015 MIREX competition.]
Criteria
We have formulated eight criteria that are useful for
analyzing melodic similarity systems. They have
been designed to investigate the functionality of
systems from a number of different perspectives:
flexibilidad, similarity evaluation, training, y
validation. It should be noted that the proposed
criteria are not meant to be used for evaluating the
considered systems, but for characterizing them.
1. Polyphony indicates the ability of a system
to deal with musical pieces that include one
or more voices. Monophonic systems can
evaluate melodic similarity only between
pieces containing a single melodic line.
2. Scope denotes the musical genres and styles a
system is able to investigate. Some methods
have a general scope, being able to analyze a
wide range of musical styles. Others evaluate
melodic similarity only in a specific type of
música (p.ej., folk, classical, or pop).
3. Similarity function indicates the method-
ology used to calculate melodic similarity.
To calculate melodic similarity, algoritmos
rely on functions that provide a quantitative
measure. Usually, such functions are based
on well-known geometrical, matemático,
cognitivo, or musical notions.
4. Musical parameters list the parameters
that have been taken into account by
a system. Because melodic similarity is
a multidimensional problem, tools can
consider several parameters (such as pitch,
duración, etc.) to evaluate the similarity
between melodies.
5. Musical representation covers the en-
coding used to represent music, cual
can vary considerably between systems.
Each representation shows strengths and
weaknesses that affect the operation of
the algorithm. Pieces have been variously
encoded as strings, numbers, árboles, o
graphs.
6. Experiment-based denotes whether or not
the similarity function of a system has
been designed based upon the results of
some empirical, cognitive research. Melodic
similarity is deeply rooted in perception and
cognition. To develop efficient algorithms,
it is sometimes necessary to draw upon
experiments in human perception.
7. Training indicates whether or not an al-
gorithm has been trained—using some
machine-learning techniques—on some
specific data set. Trained systems are ex-
pected to have good performance on musical
pieces that are comparable to those used for
training.
8. Empirical validation investigates whether
or not the similarity function has been
validated. Algorithms exploit a similarity
function for obtaining a quantitative value
of likeness between two musical pieces.
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Taxonomy
En esta sección, we briefly describe the 15 algoritmos
for melodic similarity detection that we considered.
The systems are organized into four categories,
according to the strategies they exploit, a saber:
cognition, music theory, matemáticas, and hybrid.
Because the melodic similarity task is intrinsically
interdisciplinary, researchers have addressed it by
exploiting techniques that derive from very different
areas. This taxonomy reflects the four main areas
of investigation adopted in the field of music
information retrieval.
It is worth noting that some of these disciplines
superposición, thus it can sometimes be difficult to un-
equivocally classify techniques based on approaches
at the edge of two areas. Por ejemplo, several the-
ories of music such as pitch-class set theory (Forte
1973) and the generative theory of tonal music
(GTTM, Lerdahl and Jackendoff 1985) are strongly
founded on mathematics. Por lo tanto, any algorithm
built upon one of these theories could be safely clas-
sified both as a member of the music theory and the
mathematics categories. In such cases, and for the
sake of clarity, we have classified systems according
to the category that fits them better qualitatively.
This taxonomy aims to provide a first step in the
direction of a comprehensive ontology for melodic
similarity techniques. The proposed framework
can be extended straightforwardly by adding new
categories as well as by identifying meaningful
subcategories. En efecto, additional categories might
be needed when new approaches are developed.
Systems Based on Cognition
as pitch distance, pitch direction, and rhythmic
prominencia. Por otro lado, de Carvalho and Batista
(2012) propose a system—one based on a form of
Prediction by Partial Matching (Cleary and Witten
1984)—that simulates the operation of the human
auditory cortex in assessing the similarity between
given MIDI files.
Systems Based on Music Theory
Music theory has long provided tools for under-
standing the structure of melodies. Por lo tanto,
several melodic similarity tools are built upon the-
ories such as the GTTM (Lerdahl and Jackendoff
1985), the implication/realization (I/R) model of
Narmour (1992), and Schenkerian analysis (Forte
and Gilbert 1982).
Grachten et al. (2004) propose a melodic similarity
measure based on the I/R model. Específicamente, el
algorithm tries to implement most of the innate
processes presented by the I/R model. Melodies are
annotated by performing I/R analysis. Annotations
are then used for comparing different melodies. Para
overcoming one major problem of the I/R model—
the impossibility of unambiguously differentiating
the intervallic direction of a sequence of notes—
Yazawa et al. (2013) designed an algorithm based on
an extended I/R model that includes a number of
new symbols for improving expressivity.
In a Schenkerian vein, Orio and Rod `a (2009)
introduced an approach, based on the representation
of musical pieces as hierarchical graphs, to identify
the relative structural importance of notes. The most
relevant notes in a melody are then compared in
order to find similarities between melodic segments.
Cognitive constraints have only recently been used
for evaluating melodic similarity. Algorithms that
rely on this approach are usually based on one or
both of two methods: (1) the linear combination
of cognition-based metrics and (2) human-tailored
pattern recognition. The work of Roig and colleagues
(2013) and that of Vempala and Russo (2015) exploit
the linear combination of different metrics, based
on the evaluation of differences between pairs of
musical features extracted from the melodies, semejante
Systems Based on Mathematics
Systems in this category use a number of mathemat-
ical approaches that serve as a basis for evaluating
the degree of likeness between melodies. Many
of these algorithms represent musical data as
functions within an abstract space and exploit
notions from geometry as a means of compari-
son. Other common mathematical strategies are
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based on statistical analysis or information-retrieval
técnicas.
Aloupis and colleagues (2006) present two al-
gorithms that exploit a geometrical approach.
Melodies are represented as polygonal chains within
a pitch-time abstract plane, and their similarity is
calculated as the minimum area between polyg-
onal chains. En 2010, the S2 and W2 algorithms
were introduced (Laitinen and Lemstr ¨om 2010;
Lemstr ¨om 2010). Both are geometric algorithms
that work with point-set representations of music
and are designed to process polyphonic music. El
similarity between the query pattern and the target
melody is defined by the number of elements that
match between them, after the application of some
invariants. Finalmente, Juli ´an Urbano (2013) proposes
three different systems: ShapeH, ShapeTime, y
Time. All three rely on a geometric model that
encodes melodies as curves in a pitch/time space,
that are then compared.
Bohak and Marolt (2009) investigate how melody-
based features relate to folk-song variants. Specifi-
cally, the authors extract 94 melody-based features
from each melody that are then used for performing
comparisons.
Wolkowicz and Keˇselj (2011) propose six dif-
ferent algorithms (WK1–6) that exploit text-based
information-retrieval approaches. They extract
features from an input data set of MIDI files. String-
based methods can be directly applied to such
input files, since none of the notes is concurrent
or overlapping. Then they build n-grams (substrings
of n consecutive tokens [es decir., notas]), cuales son
used to calculate similarity between melodies. En
the framework proposed by Frieler (2006), melodies
are represented by series of arbitrary length in an
abstract space of events. n-grams are then used
for measuring the similarity of two melodies. norte-
grams have an identity that allows one to assess
their degree of similarity, thus providing further
información.
Hybrid Systems
To maximize the efficiency of algorithms, hybrid
systems combine several techniques that usually
belong to two or more of the aforementioned
categories. The SIMILE toolbox (M ¨ullensiefen and
Frieler 2004; Frieler and M ¨ullensiefen 2005) is based
on a linear combination of about 50 algoritmos
covering different aspects of the SMS task. Autores
gathered rating data by human experts, which were
considered as the ground truth for evaluating and
optimizing the linear combination of the considered
techniques’ similarity values.
Fanimae (Suyoto and Uitdenbogerd 2010) com-
bines two similarity measurements: the NGR5
acercarse, which exploits 5-grams for matching
melodies by considering only the pitch; y el
newly introduced PIOI technique, which evaluates
similarity by considering either pitch or duration.
Rizo and Inesta (2010) introduced the UA
systems—four methods designed with the objec-
tive of obtaining a good trade-off between accuracy
and processing time. Two of these methods are
based on tree representation, one is based on the
quantized point-pattern representation, and one is
the combination of the three other methods.
Comparison of Systems
By analyzing according to the criteria previously
introduced in the corresponding section, it is pos-
sible to infer general trends and exceptions in how
researchers conceived, designed, and implemented
their systems. A detailed mapping of each system
against our criteria is provided in Table 1. Cada
criterion gives an insight into one specific aspect of
a melodic-similarity algorithm. Rather than listing
decisions taken by authors with regard to each crite-
rion, we outline trends and relevant deviations from
trends that have been highlighted by the criteria.
The majority of the systems calculate melodic
similarity between monophonic sequences only.
The system developed by Laitinen and Lemstr ¨om
(Laitinen and Lemstr ¨om 2010; Lemstr ¨om 2010),
as well as the algorithm built by Suyoto and
Uitdenbogerd (2010), can additionally evaluate
melodic similarity between polyphonic pieces. Él
should also be noted, sin embargo, that some of the
systems’ authors do not provide information about
their systems’ polyphonic analysis capabilities.
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3
Most systems have a general scope, since they
can be used to calculate the likeness of any melody
belonging to any style. Por otro lado, el
algorithm developed by Vempala and Russo (2015)
focuses on melodies that are rooted in tonality, el
system by Orio and Rod `a (2009) analyzes music
in which harmony plays a functional role, y el
system built by Bohak and Marolt (2009) is designed
for folk songs only.
There is no dominant trend in similarity func-
tions exploited by algorithms. Combining several
similarity measures together, by means of a linear
combination, is a popular approach (M ¨ullensiefen
and Frieler 2004; Frieler 2006; Suyoto and Uitden-
bogerd 2010; Roig et al. 2013; Vempala and Russo
2015). In such cases, sin embargo, the specific measures
that contribute to form the linear combination
change from system to system. Other systems
(Aloupis et al. 2006; Urbano 2013) calculate the
differences of shape and area between curves that
represent melodies in abstract mathematical spaces.
There are also approaches based on statistics (Bo-
hak and Marolt 2009), the shortest path between
two nodes in a graph (Orio and Rod `a 2009), y
text-retrieval methods (Wolkowicz and Keˇselj 2011).
También, some traditional methods, such as edit dis-
tance (Grachten et al. 2004) and n-grams (Yazawa
et al. 2013), are exploited.
Musical parameters considered for calculating
similarity are almost always pitch and duration.
Information about time and frequency seem to be
expressive enough to allow a precise judgement of
likeness between musical excerpts. Some systems
also rely, sin embargo, on parameters such as harmony
(Orio and Rod `a 2009), contour (Grachten et al.
2004; M ¨ullensiefen and Frieler 2004; Vempala and
ruso 2015), and pitch direction (Yazawa et al. 2013;
Vempala and Russo 2015). It should be noted that
only the algorithm developed by Bohak and Marolt
(2009) includes a number of unusual and interesting
parámetros, such as melodic complexity, métrico
acento, and entropy.
The diversity of approaches used to calculate
melodic similarity is matched by (and perhaps even
springs from) the heterogeneity of musical repre-
sentaciones. A common method of encoding musical
information is through sequences of symbols (Frieler
2006; Rizo and Inesta 2010; Wolkowicz and Keˇselj
2011; de Carvalho and Batista 2012). Other strate-
gies explored to represent music are trees (Rizo and
Inesta 2010), graphs (Orio and Rod `a 2009), estadístico
características (Bohak and Marolt 2009), and I/R symbols
(Grachten et al. 2004; Yazawa et al. 2013). Finalmente,
two algorithms that rely on mathematics (Aloupis
et al. 2006; Urbano 2013) represent melodies as
curves in an abstract mathematical space.
Desafortunadamente, the large majority of systems
reviewed in this survey are not based on first-
hand experiments in music perception. En efecto,
only three algorithms (M ¨ullensiefen and Frieler
2004; Yazawa et al. 2013; Vempala and Russo 2015)
are guided by direct experimental enquiry. Otro
algorithms either implement theoretical hypothe-
ses, or follow well-established notions in music
percepción.
Además, solo 4 algorithms out of the 15
considered have been trained on a set of melodies
(M ¨ullensiefen and Frieler 2004; Bohak and Marolt
2009; Wolkowicz and Keˇselj 2011; Vempala and
ruso 2015). The other systems do not benefit
from the use of such machine-learning methods.
As empirically observed in many areas of computer
science and artificial intelligence, aprendizaje automático
is a promising technique that could enhance the
performance of algorithms considerably.
We observe that some of the reviewed approaches
lack empirical validation. Although most methods
have been tested on groups of melodies, the lack
of empirical validation for some of the algorithms
(Aloupis et al. 2006; Frieler 2006; Rizo and Inesta
2010; Roig et al. 2013) makes their assessment
difficult, if not impossible. In the case of the
method proposed by Frieler (2006), sin embargo, el
lack of validation process is due to the theoretical
nature of the article, which introduces innovative
mathematical notions that the author acknowledges
need future evaluation. Among the systems that do
provide empirical validation, most have been tested
on musical incipits (M ¨ullensiefen and Frieler 2004;
Orio and Rod `a 2009; Lemstr ¨om 2010; Suyoto and
Uitdenbogerd 2010; Wolkowicz and Keˇselj 2011;
de Carvalho and Batista 2012; Urbano 2013). Otro
Velardo, Vallati, and Jan
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Mesa 2. System Rankings
Sistema
2010 (13)
2011 (10)
2012 (6)
2013 (5)
2014 (4)
MIREX Edition (No. of Participants)
Laitinen and Lemstr ¨om (2010)
Rizo and I ˜nesta (2010)
Suyoto and Uitdenbogerd (2010)
Wolkowicz and Keˇselj (2011)
de Carvalho and Batista (2012)
Roig et al. (2013)
Urbano (2013)
Yazawa et al. (2013)
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Rankings in the Melodic Similarity track of different editions of MIREX.
algorithms have been tested with folk songs (Bohak
and Marolt 2009; Yazawa et al. 2013), jazz melodies
(Grachten et al. 2004), and tonal melodies (Vempala
and Russo 2015).
Although not conclusive, an analysis of the
results of the MIREX competitions in the SMS track
is informative about the strengths and weaknesses of
algoritmos. It is worth noting that the best algorithm
according to one particular MIREX competition is
not necessarily the best system in all situations.
From Table 2, it is possible to see that the systems
proposed by Urbano (2013) have been the most
successful, winning five editions of the MIREX
competition. To compare the results achieved by
the different algorithms proposed we consider their
F1-score, which is the harmonic mean of precision
and recall ranging from 0 a 1. The performance of
all the algorithms that competed in the 2010 edition
of MIREX was close. None of the systems had a
F1-score greater than 0.30: Urbano (2013) F1 = 0.30;
Laitinen and Lemstr ¨om (2010) F1 = 0.27; Suyoto and
Uitdenbogerd (2010) F1 = 0.26; and Rizo and Inesta
(2010) F1 = 0.26. En el 2011 campaign there was a
significant increment in the performance of some
of the algorithms, which doubled their accuracy.
Both the systems proposed by Urbano (2013) y
Wolkowicz and Keˇselj (2011) achieved the same
resultado, with F1 = 0.64. Después 2011, improvements
have slowed down. Hasta ahora, the best performance
has been achieved by Urbano (2013) en el 2014
MIREX competition, with F1 = 0.77. It is difficult to
compare these systems with those that did not enter
the MIREX competitions, since they have not been
assessed in accordance with the same standardized
evaluation procedure.
Although there has been a significant improve-
ment in the methods introduced in the last decade,
not all new systems are better than those developed
antes 2004. This is the case with the algorithm
developed by Yazawa et al. (2013), which perhaps
pays the price for experimenting with a new strat-
uno. Sin embargo, it is safe to assert that pre-2004
algorithms have been outperformed in all aspects by
newer methods.
Regardless of the rankings obtained by the sys-
tems in MIREX, it is possible to identify situations
in which algorithms based on different methods per-
form best. In the case of melodies that differ by only
a few pitches, intervals, and rhythms, an approach
based on the number of matching elements in the
two melodies (p.ej., Laitinen and Lemstr ¨om 2010;
de Carvalho and Batista 2012) is likely to be the
most effective. This situation is common in both
folk and classical styles, where the composer intro-
duces variety by altering a few musical elements
of a melody (see Figure 1b). In the case of melodies
that are substantially different but that occasionally
share similar musical fragments, algorithms based
on matched n-gram sequences (p.ej., Frieler 2006;
Yazawa et al. 2013) have an edge, because they are
78
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Cifra 1. Melodies with
different categories of
semejanza: el modelo (a); a
melody obtained by
changing few pitches and
durations of the model (b);
a melody that conserves
only the head and the tail
of the model (C); and an
ornamented version of the
modelo (d).
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able to detect similarities even if only tangential.
This scenario is often found in contrapuntal music
(p.ej., fugues and motets), where it is common that
only the head and the tail of a theme are maintained
throughout different repetitions (see Figure 1c).
Systems based on a linear combination of different
metrics and statistical musical differences (p.ej.,
Suyoto and Uitdenbogerd 2010; Roig et al. 2013;
Vempala and Russo 2015) are most effective when
used on melodies that are loosely similar. En esto
category are those melodies that share only a similar
contour, or in which ornamental notes are interca-
lated between the fundamental notes (see Figure 1d).
This compositional technique is used in classical
music and it is frequently encountered in pieces
built around a single melodic idea. Finalmente, cuando el
relationship between two melodies results from a
mixture of these three situations, the most effective
approach is that of Urbano (2013), which calculates
differences in the shape of geometric representations
of a melody.
Guidelines and Recommendations
The work done by researchers in the last decade
has significantly increased the number of algo-
rithms that calculate melodic similarity, and it has
improved the variety and quality of approaches.
Systems are now capable of finding melodies similar
to a target sequence of notes, and searching through
large databases of melodies in a more reliable, ef-
ficient and precise way than before. There are still
some limitations, sin embargo, and several steps can be
taken to improve the performance and functionality
of these systems.
As already mentioned in the Background sec-
ción, there is no clear-cut definition of melodic
semejanza. As Alan Marsden (2012) points out, el
notion of melodic similarity is highly dependent on
contexto. Different models are required to account
for similarity judgments carried out by people. Para
instancia, to reduce the time needed by the similarity
process carried out by human judges, in MIREX each
Velardo, Vallati, and Jan
79
person considers different sets of melodies. Estos
melodies can have very different backgrounds,
sin embargo, thus providing different evaluations. Este
strongly affects both the way in which systems are
evaluated and the development of new algorithms.
The lack of a widely approved definition of melodic
similarity is also reflected in the lack of a common
ground truth, shared by all researchers interested
in this field, against which the performance of
algorithms can be tested. The evaluation framework
provided by MIREX is a first attempt to solve this
issue. As Urbano (2013) points out, sin embargo, allá
are some problems with this musical data set.
The MIREX evaluation framework failed to give
a consistent measure of performance for the same
system over a number of years. Como consecuencia,
this framework cannot be adopted to benchmark
performances of different systems over time. El
solution for a reliable ground truth for melodic
similarity is to have an extremely large database
of melodies, in which each melody has a series
of ratings that indicate the degree of similarity
between it and all other melodies in the collection.
To develop this evaluation framework, un número
of experiments with human listeners are needed.
Because it is necessary to design a large database,
sin embargo, these experiments could be too onerous
to conduct in a traditional laboratory-based set-
ting. This issue can be overcome by conducting
experiments on the Internet, which allows exploita-
tion of the very large number of people available
en línea.
A second issue affecting current systems is that
most of them focus on monophonic music only.
We believe that next-generation algorithms should
be able to analyze polyphonic music and thus find
the degree of similarity between two polyphonic
excerpts. Polyphonic music in the Western tradi-
tion considerably outweighs monophonic music.
So the impact of polyphonic similarity systems
on musicology and music theory would be signifi-
cantly increased. Developing polyphonic similarity
analysis tools would also encourage researchers
to discover the main differences between evaluat-
ing likeness between monophonic and polyphonic
musics. This research should be informed by ex-
periments in music perception and, Sucesivamente, would
provide new insights to musicologists and music
theorists.
There is a close relationship between music cog-
nition and melodic similarity algorithms. To develop
more efficient systems, it is of paramount impor-
tance to conduct focused experiments in music
percepción. The results of these studies could even-
tually suggest innovative notions and techniques
still overlooked in the design of computational
sistemas.
Another relevant point to consider for enhancing
the performance of algorithms is their scope. Mayoría
of the methods reviewed have a general scope. En
otras palabras, these systems can be used to analyze
melodies belonging to any musical style. It is well
conocido, sin embargo, that every style has specific rules
that help create its unique sound. This is true for
melody generation as well. Por lo tanto, if we want to
obtain greater efficiency, we need to concentrate on
specific styles, rather than developing algorithms
able to parse any kind of music. While building
these style-specific tools, we might discover some
of the deepest rules that contribute to define a
style. Understanding these rules would not only
improve the efficiency of systems, but would also
help musicologists and music theorists understand
the complex phenomenon of musical style. Style-
specific rules can be extracted, por ejemplo, por
using techniques of machine learning. Only a few
systems analyzed in this survey are based on training
estrategias. This implicitly indicates that most of the
systems developed so far have a general scope or
have been manually configured following developer
intuitions. Claramente, training on specific styles will
make systems less general. To avoid this pitfall,
compound tools, made up of a series of style-specific
subsystems, can be designed. In this way, sistemas
would operate distinct subsystems, depending on
the style of melodies they are analyzing.
A weakness of using machine learning is that
there is a trade-off between performance and inter-
pretability (James et al. 2013). The more complex
the machine-learning technique used, the looser the
relationship between the predictors (es decir., musical
características) and melodic similarity. Este fenómeno
is because of the risk for overfitting in highly flex-
ible methods. Si, sin embargo, such systems aim only
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at providing a score of likeness between melodies,
and are not meant to be used as tools for studying
the general relations between musical features com-
parison and similarity, the interpretability of the
predictive model is not of interest. En este caso, el
trade-off between performance and interpretability
is not a significant concern.
Melodic similarity algorithms based on mathe-
matics have been dominating MIREX competitions
for the last five years. In our opinion, this does not
mean that algorithms based on mathematics are
intrinsically superior to those based on cognition
or on music theory. Bastante, this should encourage
the improvement of tools based upon different the-
ories, in order to close the performance gap with
mathematical systems. En efecto, the task of melodic
similarity is highly interdisciplinary and should be
tackled from diverse perspectives. Por esta razón,
it would be advisable to develop tools that merge
different approaches. By creating hybrid systems, re-
searchers can ameliorate the weaknesses of specific
técnicas, while augmenting the overall strength
del sistema.
Conclusions
Melodic similarity systems have a wide range of
applications. Por ejemplo, they can be used to
perform information retrieval on large music data
conjuntos, and they can help identify music plagiarism.
Recientemente, because of the introduction of the MIREX
competition, a large number of algorithms have
been developed. In this article, we have briefly de-
scribed existing approaches, and we have presented
a new modular taxonomy and eight criteria that are
instrumental in classifying and comparing melodic
similarity algorithms. The taxonomy classifies algo-
rithms based on their approach, es decir., whether they
are based on cognition, music theory, matemáticas,
or some hybrid of these. This article fills the gap
since the previous surveys in the area (M ¨ullensiefen
and Frieler 2006; Hofmann-Engl 2010), and provides
a clear overview of existing techniques. El analisis
del 15 systems considered has allowed us to iden-
tify the strengths and weaknesses of the algorithms
as well as wider trends in the field.
Starting from this point, we have been able to
recommend avenues of future research that one
hopes will lead to further improvement in the area.
A este respecto, we highlight the lack of a widely
approved definition of melodic similarity, cual
strongly affects both the development of algorithms
and the outcomes of competitions. We recommend
the development of a common ground truth that can
be used as a standard corpus for comparing systems.
También, we observed a worryingly small number of
systems that are able to analyze polyphonic pieces.
The capacity to analyze such music is of primary
importance in fostering the exploitation of melodic
similarity tools in real-world applications. Finalmente,
because musical works belonging to distinct styles
are often very significantly different, we have found
that it is extremely difficult to develop systems that
perform well across a range of styles. Por lo tanto,
we believe that future algorithms should have a
relatively limited scope, and that they should be
configured on a specific style of music through
machine-learning techniques.
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tu
mi
s
t
t
oh
norte
0
7
S
mi
pag
mi
metro
b
mi
r
2
0
2
3
Velardo, Vallati, and Jan