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Traditionally, composers have used subjective Italian expressionsjo
(such as "Andante", "Allegro"...) to set the speed of their music.
Beethoven was one of the first composers to embrace the invention of
the metronome to pass on his musical legacy as objectively as
possible, with precise indications in beats per minute. However, two
centuries later, his metronomical indications are very controversial
because they are generally considered too fast, which would be
unworthy of a master such as Beethoven. In fact, many orchestral
conductors have systematically ignored these indications, which are
considered erroneous.

Many hypotheses have been proposed to explain this controversy. One of
them is that Beethoven's metronome, which unfortunately is not
preserved, could be broken or defective. If that was the case, and
attending to conductor's expert judgement selecting interpretative
tempo, a hypothetical flaw in the metronome may explain the
disagreement between Beethoven's indications and the tempo in which
his work is performed.

In a first part of this work, a mathematical model of the metronome is
built, as well as the possible flaws. An analysis of modern
metronomes, old metronomes through images and the original patent,
leads us to a precise parametrisation of Beethoven's lost metronome.
In a second part, we extract and analyse interpretative tempo data
from 36 complete recordings of Beethoven's symphonies, from 36
different conductors (more than 200 hours of music), and such data are
correlated with the initial model to shed light into this historical