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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= .[1] &= amp; Zenaida Natividad Castillo Marrero.[2]

 

Recibido: 22-06-2020 /Aceptado: 20-07-2020 / Public= ado: 07-08-2020

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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.

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

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, 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.

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

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:

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.=

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PARA CITAR EL ARTÍCULO INDEXADO.

 

 

Colmenares Pacheco, G. A., & Castillo Marrero, Z. N. (2020). Perspectivas y enfoqu= es para determinar medidas de similitud en interpretaciones musicales mediante algoritmos de análisis de datos. ConcienciaDigital<= /i>, 3(3.1), 75-86. https://doi= .org/10.33262/concienciadigital.v3i3.1.1366

 


 

 

 

El artículo qu= e se publica es de exclusiva responsabilidad de los autores y no necesariamente reflejan el pensamiento de la Revi= sta Conciencia Digital.

El artículo queda en propiedad de= la revista y, por tanto, su publicación parcial y/o total en otro medio tiene = que ser autorizado por el director de la Revista Conciencia Digital.

 

 




[1] Unive= rsidad de Investigación Experimental Yachay, Escuela de Matemáticas y Ciencias Computacionales. Urcuquí, Ecuador, gcolmenares@yachaytech.edu.ec

[2] Escuela Superior Politécnica de Chimborazo, Facultad de Ciencias, Escuela de Estadística, Grupo CIDED. Riobamba, Ecuador, zenaida.castillo@espoch.edu.ec

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