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Thesis . 2017
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Thesis . 2017
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El metrónomo de Beethoven. Modelado físico de un misterio histórico

Authors: Martín Castro, Almudena;

El metrónomo de Beethoven. Modelado físico de un misterio histórico

Abstract

Beethoven fue uno de los primeros compositores en acoger la invención del metrónomo para transmitir con mayor precisión su legado musical. Sin embargo, dos siglos después, el carácter de sus anotaciones metronómicas resulta controvertido. Consideradas, en general, más rápidas de lo que musicalmente podría considerarse adecuado, algunos autores han apuntado a un posible defecto en el metrónomo como origen del problema. Esta es la hipótesis que se analiza en el presente trabajo. En primer lugar, y tras una breve introducción a las aportaciones realizadas desde la musicología que resultan imprescindibles para comprender el alcance de la polémica, se analizan los principales trabajos científicos que han abordado el problema desde la perspectiva física de la mecánica del metrónomo y sus resultados. A continuación, se argumenta que los modelos matemáticos utilizados en dichos trabajos previos no reflejan con precisión el comportamiento de un metrónomo real y, por tanto, sus conclusiones quedan en entredicho. En su lugar, se propone un modelo de doble péndulo más completo que considera (i) una corrección para ángulos grandes, (ii) una corrección debida a la masa del mecanismo y (iii) rozamiento y fuerza impulsora, y se plantean distintos posibles fallos en el mecanismo que podrían haber dado lugar a una descalibración del metrónomo. La validez de este modelo queda demostrada mediante un estudio experimental de un metrónomo moderno, lo que a la postre aporta una metodología para hallar los parámetros del metrónomo original de Beethoven a partir de planos y fotografías antiguas. Finalmente, se extraen y analizan los tempi de 36 integrales sinfónicas dirigidas por 36 directores distintos y se contrastan con las anotaciones originales de Beethoven a través de la lente del modelo teórico y las posibles distorsiones propuestas para tratar de arrojar luz sobre un misterio histórico. ------------------------------------- Beethoven was one of the first composers to adopt the use of the metronome to transmit his musical ideas more accurately. Ironically, two centuries after his death his metronome markings are still under dispute as they are considered, in general, too quick to be played. As a result, some performers and academics have suggested that Beethoven's "sick metronome" is to be blamed for the controversy. The present work analyses this hypothesis and explores the relation between slow performance tempi and those produced by a broken metronome. First, a short introduction contextualises Beethoven's metronome markings within the field of Musicology, a discipline that will be fundamental to understand their controversial nature. Next, we analyse other scientific papers that focus on the mechanical characteristics of the metronome. Some of the proposed mathematical models fail to describe the metronome accurately and, therefore, their conclusions are questioned. A more complete double-pendulum model is proposed, which takes into account the necessary corrections due to the amplitude of the pendulum movement, its complete mass and the effect of friction and impulse forces. Additionally, different distortions to the model that could have affected the metronome's frequency are analysed. This new model is validated empirically through the study of a contemporary metronome. As a result, we develop a methodology for approximating Beethoven's metronome parameters (its masses and dimensions) through the analysis of ancient metronome photographs. Finally, we analyse 36 complete symphonic recordings (all the symphonies directed by 36 different conductors) and compare their tempi with Beethoven's metronome markings with the aid of the proposed metronome theoretical model, casting new light over this historical mystery.

Keywords

metronome, tempo, music information retrieval, Beethoven, musical performance, metrónomo, double pendulum

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