Ludwig van Beethoven was the first great composer in history with a metronome.
Johann N. Maelzel, the creator of this device, gave him one of the first he made.
The composer was enthusiastic to the point of obsession.
He revised a good part of his works to include his
tempo
: the number that marks how fast to play.
Until then, composers gave rough indications (such as
allegro
or
andante
).
Thanks to Maelzel's invention, Beethoven was able to fix forever how he wanted his works to sound.
Neither faster nor slower.
Unfortunately, it is possible that I did it wrong.
For almost 200 years, many conductors and musicians have ignored
Beethoven's
tempo
cues
because they are too fast.
Many go against musical common sense.
In some pieces, like his
Hammerklavier
sonata
, following them is almost impossible even for virtuosos.
This discrepancy between
Beethoven's
tempos
and those that most consider reasonable is one of the great mysteries about his work, and for which many solutions have been proposed: perhaps his deafness altered his perception of the
tempo
, or there was a transcription error;
there has even been speculation about his cognitive decline.
A popular explanation is that the metronome was broken, which is difficult to verify because the device is missing.
"There is controversy with this issue," explains Theodore Albretch, professor of Musicology at Kent State University (USA) specializing in the biography and music of Beethoven.
"For his symphonies, Beethoven wrote some metronomic marks between 1817 and 1818. Years later, people have tried to follow them, they have found them too fast and have concluded that the metronome probably had some problem."
“Beethoven, although he has become an accommodating, classical composer, was a more brutal and radical guy.
He did not compose to accommodate the interpreter.
It was extreme "
Convinced of this hypothesis, Peter and Hedi Stadlen, musicologists, searched for the lost metronome for years.
They thought that they would find a problem in the mechanism that would allow them to deduce the
tempos
that Beethoven had wanted to write.
They only found the carcass and died without an answer.
Some directors defend these annotations.
This is the case of Pablo Heras-Casado, one of the most internationally recognized Spanish conductors: "Cases like this occur in many more scores, already from the 20th century: by Stravinsky, Bartók, many more people have scores like this," he adds .
These experts defend a different vision of the composer.
“Beethoven, although he has become an accommodating, classical composer, was a more brutal and radical guy.
He did not compose to accommodate the interpreter.
He was extreme, there are
tempos
that are almost untouchable, but he knew very well what he wanted.
Anyway, he was not interested in sharpness, a note-by-note clarity, but rather in creating a tumult, ”explains Heras-Casado.
An investigation published this Wednesday by two Spanish scientists, which addresses the question from classical mechanics and
big data
, breathes new life into the Beethoven metronome hypothesis.
His results offer an unprecedented explanation to the mystery: the metronome was not broken, Beethoven used it badly.
His work also makes it possible to recalibrate anomalous scores and assign them the
tempo
that the German genius probably wanted to give them.
Almudena Martín Castro, pianist, physicist and graduate in Fine Arts, and her husband, Iñaki Úcar Marqués, clarinetist and doctor in Telematics Engineering, addressed the mystery
of Beethoven's
tempos
inspired by a phenomenon known as the wisdom of crowds.
If you calculate the average of many intuitive solutions to a problem, the answer is usually very close to the true figure.
They applied this idea to Beethoven's music.
They extracted by computer the
tempos
of the composer's nine symphonies, performed by 36 different conductors between 1940 and 2010. Over 170 hours of music.
And they calculated the averages.
The result, they hoped, would give a clue as to what had gone wrong on the metronome.
“It is not easy to extract, by computer, the
tempo
of a piece of music.
Something that humans do naturally to a computer costs a lot, "says Martín Castro.
"In classical music it's even more difficult because they don't have the percussion base of other musical genres."
This forced the researchers to spend months testing algorithms and cleaning up data.
But they found a pattern.
“The deviation that we saw in the analyzes was systematic.
If people play at 40 bpm [beats per minute, in English], Beethoven had scored 52 bpm.
If the directors play 50, Beethoven had written 62 ”, indicates Úcar Marqués.
The deviation between the marks of the German composer and the average of the
intuitive
tempos
they analyzed is always the same: around 12 bpm.
They needed to explain this anomaly in a metronome that they could not see or touch, because it is lost.
It turns out that, with enough ingenuity, you don't have to have it in front of you.
They decided to create a mathematical model of how this device works.
That way they could break it, even if it was virtually.
They bought two metronomes: one to take it apart and precisely measure each part of its mechanism, and another to analyze its movements.
After several weeks they created a system of equations that describes how any metronome behaves.
It was only necessary to determine the lengths and weights of the pieces of the original Beethoven metronome, which is not known where it is.
"We did it from photos and the patent for Maelzel's metronome," says Úcar Marqués.
“Once we had the model, the first thing we did was test all the hypotheses that have been raised historically: either that the masses have broken or that they have moved, that the metronome was poorly lubricated or that it was incorrectly positioned, tilted over the piano.
But none of them slows down the metronome in a homogeneous way, ”says Martín Castro.
“Breaks, inclinations, friction… it doesn't matter, they don't coincide or they give crazy results.
They affect unevenly, the
fast
tempos
become a little slower and the slow ones, much slower and make it stop, which would not make any sense ”, says Úcar Marqués.
After more than a year of work and without a solution, they decided to look for less conventional alternatives.
They went through their data, their models, their calculations and something unexpected appeared.
On the Maelzel metronome scale, 12 bpm is about a centimeter and a half apart.
And there is an element that measures exactly that: the top weight.
The piece of metal that is raised or lowered to set the rate at which it swings.
"The value you take is the one that is read above the weight, that is the convention," explains Martín Castro.
“But in Beethoven's metronome the weight was shaped like a trapezoid, with the long side up and the short side down, and it formed an arrow pointing downwards.
Depending on whether you read above or below, the difference of 12 beats per minute appears there.
It was a usability problem ”.
There is an annotation in the manuscript of the ninth symphony that could confirm this possibility, since Beethoven makes an annotation in a margin: "108 or 120, Maelzel."
Did Beethoven consider two possible readings of the same measure?
"Many people, when they buy a toy or an appliance, do not read the instructions before using it," suggests Albretch about this solution.
“The instructions that accompanied the metronome are lost.
It would be interesting to see them.
What we do know is that Maelzel, around 1817, sent Beethoven a table with the numbers to put for an
Allegro
, a
Moderato
, an
Adagio,
or an
Andante
.
Whether Beethoven looked at her, or not, we don't know.
But it is possible that he did not pay much attention to it. "
Big data
and algorithms so that a computer could understand the
tempo
.
Complex physics to solve the mathematical model.
But, in the end, two hundred years of mystery could be explained by a usability problem.
Now, perhaps several purist directors and musicians will be able to sleep more peacefully.
Or not.
Because starting today, the 250th anniversary of the musician's birth, can Beethoven be played exactly the way Beethoven wanted?
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