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Perspectivas y enfoqu=
es
para determinar medidas de similitud en interpretaciones musicales mediante
algoritmos de análisis de datos
Perspectives
and approaches to determine measures of similarity for musical performa=
nces
using data analysis algorithms
Gustavo Adolfo Colmenares Pacheco=
. &=
amp;
Zenaida Natividad Castillo Marrero. =
span>
Recibido: 22-06-2020 /Aceptado: 20-07-2020 / Public=
ado:
07-08-2020
<=
span
style=3D'font-size:12.0pt;line-height:115%;font-family:"Times New Roman",se=
rif'>
Abstract. DOI: https://doi.org/10.33262/concienciadigita=
l.v3i3.1.1366
<=
span
lang=3DEN-US style=3D'font-size:12.0pt;line-height:115%;mso-bidi-font-famil=
y:Arial;
mso-ansi-language:EN-US'>
The automatic characterization of a
musical composition, and its interpretation, is a current line of research,=
due
to its importance and the technological resources available and computation=
al
tools capable for detecting voice and sound. The recognition of an interpre=
ter
when listening a composition is simple for a human, but not as simple for
machines, thus, this topic has kept a community of researchers in search of
measures to compare and accurately recognize the composition characteristics
and the interpreter. However, still a general measure has yet to be discove=
red,
although various statistical-computational techniques have been generated a=
nd
deserve to be evaluated and perhaps combined to strengthen any research on =
this
topic. This work is the product of a comprehensive literature review that c=
ollects
the main techniques and tools that have been used and proposed by researche=
rs over
the last two decades. The document will be of help to researchers who decid=
e to
undertake studies, evaluations and implementations of these tools, as well =
as
those who wish to work on automatic recognition of interpreters and
characteristics of musical compositions, or music information retrieval.
Keywords: Data analysis algorithm, Music informa=
tion
retrieval, Musical performance, Statistical Analysis, Mathematical and
Computational models.
Resumen
La caracterización automática de obras musicales, e intérprete=
s de
las mismas, es objeto de investigación en la actualidad. Debido principalme=
nte
a la importancia del tópico, pero también al auge tecnológico y la disposic=
ión
de herramientas computacionales capaces de detectar voz y sonido. El
reconocimiento automático de una composición, así como su intérprete y
características relevantes desde el punto de vista musical, ha mantenido a =
una
comunidad de investigadores en la búsqueda de medidas que permitan hacer
comparaciones e inferir con precisión sobre las características de la compo=
sición
y el intérprete; sin embargo, esta medida aún está por descubrirse, aunque =
se
han generado diversas técnicas estadístico-computacionales que merecen ser
evaluadas y quizás combinadas para fortalecer cualquier investigación en es=
te
tópico. Este trabajo, producto de una basta revisión bibliográfica, recoge =
las
principales técnicas y herramientas que han sido utilizadas y propuestas por
investigadores en las últimas dos décadas. El documento será de ayuda a los
investigadores que decidan emprender estudios, evaluaciones e implementacio=
nes
de estas herramientas, así como también aquellos que deseen trabajar en el
reconocimiento automático de obras musicales, sus características e
intérpretes, o recuperación de información musical.
Palabras claves: Algorit=
mos de
análisis de datos, Recuperación de información musical, Interpretación musi=
cal,
Análisis Estadístico y Probabilístico, Modelos Matemáticos y Computacionale=
s.
Introducción
A menudo nos preguntamos si es posible caracterizar automática=
mente
la interpretación de un pianista, considerando que cada uno tiene un lengua=
je o
una forma diferente de transmitir la obra que interpreta. La respuesta a es=
ta
pregunta ha sido objeto de estudio de muchos investigadores durante los últ=
imos
cuarenta años, luego de la aparición de los sistemas avanzados de grabación=
y el
auge de microprocesadores de alta potencia que han abierto la brecha hacia el procesamiento de grandes
volúmenes de datos y el uso de algoritmos matemáticos-computacionales compl=
ejos.
En efecto, una grabación (señal digital) de una pieza musical corta tal com=
o se
muestra en la Figura 1, puede contener varios millones de datos. En el Cuadro 1 se muestra los datos correspondientes a la pieza musi=
cal
de la Figura 1. De acuerdo a esta información puede inferirse que el
procesamiento de estos datos resulta costoso a nivel de procesamiento y
requiere de potentes algoritmos para el análisis.
Figura 1. Señal digital de una obra completa en forma=
to Wav (44.1 KHz)
Fue=
nte: Audacity Software Editor
Cuadro 1. Extracto de los valores numéric=
os
de las intensidades
Fue=
nte: Softw=
are
estadístico R (R Core Team , 2020)
La interpretación exp=
resiva
es una parte indispensable de la creación musical. Al interpretar una pieza=
, un
pianista experto da forma a diversos parámetros (tempo, ritmo, dinámica, to=
no,
articulación, etc.) de manera que no están prescritas en la partitura diseñ=
ada,
produciendo así una interpretación expresiva que pone de manifiesto las
cualidades dramáticas, afectivas, y emocionales que percibe oyente. Por ell=
o, el
estudio científico de la interpretación musical, a partir de grabaciones
sonoras, se transforma en un análisis minucioso para extraer característica=
s y
así determinar medidas que permitan establecer
diferencias y similitudes interpretativas en ejecuciones similares, ver por
ejemplo Figura 2. Capturar las propiedades estilísticas e
interpretativas de un determinado pianista, ofrece, por tanto, una amplia
variedad de caminos y enfoques dentro del área de la investigación científi=
ca.
Figura 2. Comparación de señales de una obra con vari=
os
intérpretes
Fuente: Free tool Audacity Aud=
io Software Editor
En
este artículo se presenta un panorama actualizado del estado de la técnica =
en
este contexto. Se exploran las tendencias recientes con un mayor énfasis en
aquellas que usan algoritmos basados en el anál=
isis
de datos, a fin de establecer las limita=
ciones
actuales y explorar nuevas vías que conlleven al establecimiento de métodos=
que
resulten eficaces en la caracterización de algunas obras musicales.
Metodología
Se plantea en este trabajo una revisión descriptiva sobre
algoritmos y métodos existentes para el tratamiento de datos de composicion=
es
musicales, con el fin de extraer información sobre la obra o el intérprete.=
El objetivo principal es el análisis del
estado del arte en cuanto a técnicas estadístico-computacionales que están
siendo usada por los investigadores y a su vez implementadas en software
comerciales. Está dirigido a mostrar los principales desarrollos computacio=
nales
en el tópico.
La revisión fue sistemática, y se desarrolló de acuerdo a las
siguientes etapas:
1) &n=
bsp;
Definición de los objetivos y alcance.
2) &n=
bsp;
Definición de las estrategias de búsqueda. =
p>
3) &n=
bsp;
Búsqueda bibliográfica: Bases de datos; fuentes documentadas e
información en la web.
4) &n=
bsp;
Especificación y aplicación de criterios de selección.
5) &n=
bsp;
Organización de la información. Detección de información
relevante.
6) Escritura del artíc=
ulo.
Características musicales e Interpretación =
b>
Una medida de la expresividad musica=
l es
una codificación numérica de una o varias características de la interpretac=
ión
de un músico. Según Widmer y Goebl (2004) y Kirke y Miranda (2013) los descriptores más comunes q=
ue se
pueden identificar en una onda de audio musical son intensidad, tiempo, rit=
mo, detección de picos, análisis de tonos , dinámica.
En Raphael (2009) y Ohishi et al. (2014) se agr=
egan otros
parámetros como las diferencias tímbricas y análisis
armónico. Todos estos descriptores vistos en su dimensión individual se
denominan características musicales . Hablar de interpretación mus=
ical
implica interacción multidimensional de las características mencionadas. An=
alizar
similitudes y diferencias entre diferentes ejecutantes de una misma obra
significa entonces encontrar una medida de la expresividad de cada intérpre=
te. Un
modelo computacional de la interpretación musical es por lo tanto cualquier
función matemático-computacional que asigne una medida o permita hacer una
predicción de las características de una obra musical en su ámbito
multidimensional.
Para analizar la interpretación musi=
cal
primero debe realizarse la detección y análisis de las características musi=
cales
(análisis espectral, análisis estadístico, modelos probabilísticos, redes
neuronales artificiales, etc.) para posteriormente generar modelos que prop=
ongan
medidas que caractericen la interpretación.
Análisis espectral y procesamiento digital de señales
Be=
netos et al. (2013), Dressler (2012) y Bay et al. (2009) aplican diversos algoritmo=
s y
métodos del análisis espectral como Music
Information Retrieval Evaluation eXchange (MIRE=
X) y la estimación multiple-F0 para descubrir y analizar componente=
s de
las frecuencias de audio. Estas investigaciones han producido resultados en=
la detección
y extracción de características musicales como tonos, intensidades,
acordes, duración, gradaciones de sonidos y detección de picos.
Para analizar las interpretaciones musicales y en particular la
expresión del ejecutante se plantean estudios basados en la comparación de
diferentes interpretaciones de la misma pieza por diferentes intérpretes, lo
que permite estudiar similitudes y diferencias entre cada intérprete. Un
enfoque sustentado en el procesamiento digital de señales busca codificacio=
nes
de cada intérprete a través de la comparación y análisis de parámetros
expresivos en curvas alineadas. El uso de algoritmos de Alineamiento Tempor=
al
Dinámico DTW (Dynamic Time Warping , por =
sus
siglas en inglés) ha contribuido a la detección de características music=
ales
mediante la comparación de segmentos diferentes y cortos de la onda de audio
[Adams, Bartsch , Shifrin=
span>, y
Wakefield (2004), Muda, Begam , y Elamvazuthi (2010), Holzapfel y Stylianou (2008)].
DTW es un algoritmo que ha tenido gran popularidad desde su
introducción a finales de la década de 1970 [ Sakoe , H., & Chiba, S. (1978)] <=
span
style=3D'font-size:12.0pt;line-height:115%;font-family:"Times New Roman",se=
rif;
color:black'>por ser computacionalmente eficiente y proveer una medida de
similitud de series temporales que minimiza los efectos del desplazamiento =
y la
distorsión en el tiempo, lo cual permite la transformación elástica de las
series temporales para detectar formas similares con fases diferentes, como
puede verse en la Figura 3. El algoritmo utiliza una técnica de programación
dinámica para alinear dos series temporales
de tamaño
y
de tamaño
con una plantilla determinada, de modo q=
ue se
minimice una medida de distancia total. Para alinear estas secuencias se de=
fine
una matriz de costo en la que cada celda
representa las distancias a pares entre =
el
i-ésimo componente de
y el correspondiente j-ésimo
. Generalmente se utiliza =
la
distancia euclidiana para construir la matriz de costo, la función de costo
(distancia) tiene un valor pequeño cuando las secuencias son similares y un
valor grande si son diferentes. En la práctica, se aplican restricciones pa=
ra
acelerar el algoritmo, reduciendo el número de caminos a ser considerados
durante el cómputo.
Figura 3. Alineación con DTW
Fue=
nte: Senin , P. (2008).=
Aunque DTW ha sido aplicado exitosamente para comparar palabras aisladas y diversos patrones del habla en el
reconocimiento de voz automatizado y también reconocimiento de gestos
corporales y faciales, su aplicación en el contexto del análisis de señales=
de
audio presenta un alto costo computacional, es por ello que las investigaci=
ones
que sustentan el uso de este algoritmo se limitan a extractos musicales de
pocos segundos. Cuando se buscan similitudes o diferencias interpretativas =
en
ejecuciones similares de una misma obra, los segmentos sonoros a comparar d=
eben
ser escogidos con criterio musicológico (frases, temas o ideas musicales) lo
cual se traduce en archivos de datos muy grandes (un minuto de una onda gra=
bada
con una frecuencia de muestreo de 44.1 KHz generan un vector de 2.646.000
datos).
La complejidad de DTW es orden
lo cual lo transforma en un problema de =
big data, por lo tanto, su implementación requiere má=
quinas
de alto rendimiento o HPC (High Performance Computing, por s=
us
siglas en inglés). <=
/span>
Métodos estadísticos, distribuciones de probabilidad y cadenas=
de
Markov
Los
enfoques estadísticos y probabilísticos, por otra parte, intentan describir=
las
características expresivas presentes en una señal musical mediante el análi=
sis
de parámetros estadísticos y la modelización de la distribución de probabil=
idad
de los datos. Las señales musicales reales son =
muy
variables, pero tienen una estructura intrínsecamente numérica. =
Sapp (2007) presenta un enfoque
gráfico comparativo, análisis de series temporales y medición de parámetros
estadísticos como la media y el coeficiente de correlación para establecer
diferencias interpretativas de 89 interpretaciones de una misma obra. En Te=
mperley
(2009) se propone un modelo probabilístico de la música polifónica tomando =
un
patrón de notas como entrada y combinando tres aspectos técnicos de la músi=
ca
(análisis métrico, análisis armónico y flujo). El modelo también arroja una
estimación de la probabilidad del propio patrón de notas. En Fu et al. (201=
5) se
analizan acordes musicales usando estimación de tiempo local y análisis de =
varianza.
En Yang, Lin, Su, y Chen (2008) se analiza un conjunto de dato=
s a
partir de 195 canciones populares, especialmente escogidas por sus caracter=
ísticas
expresivas.
Los segmentos son convertidos a un formato uniforme (22.050 Hz=
, 16
bits, and mono channel PCM WAV) y normalizado al
mismo nivel de volumen. Luego se usa el algoritmo DWCH (Daubechies
Wavelet Coefficient Histog=
rams )
y algoritmos estándares de contraste espectral, disponibles en paquetes de
software comercial, para extraer características musicales y construir un
espacio multidimensional. Las entradas se utilizan para entrenar tres
algoritmos de regresión: regresión lineal múltiple (MLR), regresión de sopo=
rte
vectorial (SVR) y AdaBoost (BoostR ).
En Stamatatos (2002) se presenta u=
na comparación
de características para discriminar entre los diferentes intérpretes de una
misma pieza. Basándose en el cálculo de la media simple y la media ponderad=
a,
sobre un conjunto de datos de una pieza interpretada por 22 pianistas, en d=
os
grupos, donde uno de ellos es tomado como referencia. Se encuentra un están=
dar
de interpretación o interpretación promedio entre los pianistas y la partit=
ura
de la obra, calculado a partir de las desviaciones en términos de tiempo, a=
rticulación
y dinámica. En cuanto a la dinámica, el autor aclara que es definida
considerando únicamente el nivel de sonido o intensidad de la nota tocada.<=
o:p>
Kim et al. (2011) se basan en la afirmación de que la expresió=
n en
la música de piano se puede representar sólo con tempo, volumen (intensidad=
) y duración,
para desarrollar un sistema automático de interpretación pianística denomin=
ado Polyhymnia . La entrada de este programa es un archivo
digital de una partitura de piano en formato MusicXML<=
/span>,
un tipo de archivo similar al MIDI (Musical Instrument=
Digital Interface) que es muy utilizado para archivar partituras musicales =
en
formato digital. Las marcas de dinámica son mapeadas de los valores de ataq=
ue
de las notas (MIDI velocity ). Se hace una formu=
lación
probabilística condicional y se utilizan Campos Aleatorios Condicionales (<=
span
class=3DSpellE>Conditional Random Fields por sus siglas en inglés). De acuerdo a los
autores, Polyhymnia puede aprender y predecir l=
a expresión
polifónica e interpretar los símbolos musicales automáticamente. =
Cabe hacer notar que en estas investigaciones se escogen carac=
terísticas
individualizadas de la ejecución musical, pero ninguno ha afrontado el prob=
lema
de la multidimensionalidad de la expresividad musical. =
p>
Otro enfo=
que
ampliamente propuesto en diversas investigaciones es la utilización de
variantes de los Modelos Ocultos de Markov (HMM por sus siglas en inglés) p=
ara describir
la evolución temporal de interpretaciones musicales y
reconocimiento de voz.
Grindlay y Helmbold
(2006) utilizan las HMM combinadas con Dynamic Baye=
sian
Network para modelar la relación estadística entre la estructura de la
composición musical y las variaciones interpretativas. Para producir estas =
relaciones
automáticamente, a partir de un cuerpo de datos de entrenamiento, se intenta
que el modelo pueda ser utilizado para generar actuaciones expresivas de pi=
ezas
nuevas, no incluidas en el conjunto de entrenamiento. En la investigación s=
ólo se
evalúan las variables de tiempo y velocidad de la música en dos conjuntos d=
e datos
en formato MIDI. El primero con 28 interpretaciones de la pieza Traümerei de Robert Schumann, extraídos de discos com=
pactos
comerciales de reconocidos pianistas. El segundo, extraído de grabaciones
realizadas a estudiantes de piano.
Teramura et
al. (2008); Gu y Raphael (2012); Okumura
et al. (2014) plantean modelos que supon=
en la
distribución de probabilidad subyacente de los elementos expresivos de una
interpretación musical como gaussiana Un enfoque diferente es el adoptado p=
or
Kim et al. (2013) y Moulieras y Pachet
(2016), que utilizan modelos de entropía para modelar la distribución de
probabilidad de los datos musicales.
Molina-So=
lana
et al. (2008) identificaron intérpretes de violín basados en análisis de
descriptores (energía & duración) extrayendo elementos expresivos y
construyendo modelos de tendencias. En la fase de entrenamiento se extraen
descriptores de audio por segmentos melódicos etiquetados, usando el modelo=
Implication-Realization (IR) de E. Narmour , y se procede al cálculo de distribuciones
probabilísticas para cada patrón y descriptor IR (generación de tendencias)=
. En
la fase de identificación, el sistema analiza el rendimiento de entrada y b=
usca
el modelo más similar aprendido previamente. Los resultados reportados,
muestran que el enfoque es capaz de alcanzar altas tasas de identificación.=
Fukayama et al. (2011) usaron
campos aleatorios condicionales y cadenas de Markov
en archivos MusicXML para modelar tono, duració=
n y
nota. Asumieron como
expresión melódica: tempo instantáneo, volumen y duración. Alvarado et al.
(2016) trabajaron con un enfoque de regresión bayesiana usando procesos
gaussianos para calcular la distribución posterior, sobre una función
estocástica que estima tonos y cambios de la envolvente en el tiempo. Kumar=
Ashis Pati et al. (2018) construyeron modelos de regr=
esión
basados en redes neuronales profundas capaces de predecir calificaciones da=
das
por jueces humanos expertos para interpretaciones de instrumentos de viento=
.
<=
span
lang=3DEN-US style=3D'font-size:12.0pt;line-height:115%;font-family:"Times =
New Roman",serif;
mso-ansi-language:EN-US'>Machine Learning y Principal Component Analysis
De
particular interés, en las últimas décadas, han resultado los algoritmos
basados en análisis de componentes principales y Machine Learning. En Tobudic (2002) y Widmer (2003) los autores proponen el
enfoque de aprendizaje automático basado en datos para la elaboración de
modelos de rendimiento de la interpretación musical. A través del aprendiza=
je
por instancias y la programación lógica inductiva, el sistema aprende reglas
explícitas simples y complejas de rendimiento a partir de grandes coleccion=
es
de datos reales, por ejemplo, notas, fraseo, estructuras rítmicas, etc. Una=
vez
terminada la fase de aprendizaje, el sistema puede inferir mapeos de puntua=
ción
de rendimiento. En contraste con esto, el enfoque basado en reglas fue prop=
uesto
en el modelo KTH desarrollado en el KTH Royal Institut=
e
de Estocolmo (Friberg et al., 2006), donde el s=
istema
realiza una combinación de reglas de rendimiento, las cuales han sido diseñ=
adas
manualmente a partir de juicios de expertos y pruebas de escucha.
El
éxito de las Redes Neuronales Artificiales y métodos de Deep Learning, como=
la
visión por ordenador y el procesamiento del lenguaje natural, han sido
explorados en Humphrey et al. (2012) y en Schlüter
(2017) para la recuperación de información musical. Otros enfoques, tratados
por Cancino Chacón y Grach=
ten ,
(2015) y Giraldo S. y Ramírez (2016) intentan modelar la expresión de un
intérprete musical utilizando redes neuronales de avance (FFNN por sus sigl=
as
en inglés) para predecir características expresivas en base a una puntuació=
n.
Es de hacer notar que en estos sistemas se agregan características que
describen el contexto rítmico/melódico subyacente a una nota.
Nakamura et al. (2017) aplican HMM y aprendizaje no supervisado
para la estimación de los valores de nota en la transcripción musical de una
interpretación polifónica proveniente de un archivo MIDI, mientras que Patr=
icio
y Chew (2014) exploran la cuantificación de las
diferencias de estilo interpretativo utilizando HMM en doce interpretaciones
del Preludio de la suite de J. S. Bach en Sol mayor, repartidas entre
violoncello barroco y violoncello moderno. Se consideraron en esa investiga=
ción
sólo las variables musicales de tiempo y volumen.
Las
investigaciones que aplican Análisis de Componentes Principales (PCA, por s=
us
siglas en inglés) muestran importantes resultados para reconocer determinad=
as
formas en el espectro de una onda. Lo importante de esta herramienta de
análisis es que reduce en gran medida la dimensionalidad, un factor crucial
para mejorar el costo computacional de ondas con grandes volúmenes de datos=
. Liem y Hanjalic (2015) ut=
ilizan
PCA para alinear diferentes fragmentos y detectar variaciones y similitudes=
en interpretaciones
de grabaciones orquestales. Zurek , Gamarra (201=
6)
identifican similitudes acústicas en ondas sonoras reduciendo la dimensión =
de
características extraídas con la implementación posterior de un clasificador
basado en el método de los k-vecinos más cercanos (KNN) y una red neuronal
artificial.
Resultados y Conclusiones =
span>
El resultado de estudios particulares
sobre un tópico generalmente es sesgado hacia las herramientas que se usan;=
y
el conocimiento de diferentes herramientas y estudios sobre un tópico capac=
ita
al investigador para discernir y combinar con el propósito de lograr mejores
resultados en su campo de investigación.
El presente documento presentó:=
o:p>
1)&n=
bsp;
Una
investigación bibliográfica sobre las principales metodologías, algoritmos =
y tratamiento
de datos provenientes de obras musicales.
2)&n=
bsp;
El
resultado de esta investigación permitió resumir y presentar, en forma prec=
isa,
elementos y aspectos del tópico de reconocimiento automático de característ=
icas
de obras musicales y sus interpretaciones.
3)&n=
bsp;
Se contrastan algunas técnicas
computacionales presentando fortalezas y debilidades de las mismas.
4)&n=
bsp;
De acuerdo a las características de las
composiciones musicales se orienta hacia el uso de técnicas apropiadas segú=
n el
estado del arte.
5)&n=
bsp;
Se soporta la información con bibliogr=
afía
selecta, específica y relevante, que puede ser utilizada en lo sucesivo para
abordar el tema en otras investigaciones de carácter teórico-práctico.=
Re=
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Conciencia Digital.
El artículo queda en propiedad de=
la
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Escuela Superior Politécnica de
Chimborazo, Facultad de Ciencias, Escuela de Estadística, Grupo CIDED.
Riobamba, Ecuador, zenaida.castillo@espoch.edu.ec
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