Saturday, November 30, 2013

Beethoven's Metronome Markings: Tempo choices

Beethoven and the Metronome

Musicians have long puzzled over Beethoven's metronome markings.  To our ears many of his choices seem too fast. Conductors have had to make a conscious choice whether or not to heed the markings he put in the music.

Radio Lab

In a show originally aired in February of this year (which I heard last night while driving home from my concert), the Public Radio show, Radio Lab bravely dove into the issue. Click on the link and you can listen to the show. The hosts enlist the help of Alan Pierson, conductor of the Brooklyn Philharmonic and a quartet of string players from the Philharmonic to play excerpts from the 3rd and 5th Symphonies at Beethoven's expressed markings.

The show's participants cite four of the most commonly listed reasons for why Beethoven may have chosen his speedy markings:

1. Defective metronome -- they dismiss this out of hand with a quick reference to an expert. More about this later.

2. Copyists' errors -- they find this explanation untenable and so do I.

3. Deafness/disregard acoustical considerations (hall, instrument response time, etc.). This one may have some merit, but ultimately may not explain some of the more extreme speeds he chose.

4. Vierordt's Law. Karl von Vierordt found that people tend to overestimate short durations of time and underestimate long. He found a "point of indifference" existed at around 94-96 beats per minute. I found the hosts' desire to settle upon this explanation as the answer in the last few minutes of the show to be lacking in support and a bit foggy in logic. Their explanations fail to account for such details as beat unit (quarter note, half note, etc.) or beat subdivisions used in a piece of music, both of which have a direct bearing on the pace of the beat assigned to a piece.

The ability to find a tempo that brings out the essence of a piece is one of the most important skills for a performer. Beethoven was one of the most highly trained musicians of his time and was perfectly able to replicate steady, predictable tempos when desired. Thus, I don't find the show's final explanation for the fast tempos to be wholly acceptable.

The Scientists

The issue came up again last month in an unlikely source -- the October issue of Notices of the American Mathematical Society. In the article titled, "Was Something Wrong With Beethoven's Metronome" the authors -- scientists, engineers and mathematicians -- provide a view on the subject not usually covered by musicians.  As such it is worth exploring and may provide a definitive answer to the perennial problem of whether to use Beethoven's expressed markings.

The article reopens the debate about the condition of Beethoven's metronome. As mentioned in the Radio Lab show, his original metronome has been found. However, not mentioned in the show is the fact that the weight at the bottom of the oscillating beam (the wand with the metronome markings on it) is missing! Thus, the "expert" on the show who states that the metronome "worked just fine", doesn't say what was used for the fixed weight or wherea substitue weight was placed when the device was tested.

The early metronomes were constructed using double pendula -- two weights -- a fixed weight on the bottom, usually hidden in the wooden housing and a movable one near the top end of the beam. The position of the fixed weight was set by the manufacturer and the movable weight was calibrated for adjustment by the performer.

At some point after getting his metronome, Beethoven, like countless other musicians after him, dropped his and damaged it.  He says in a letter that he is upset and is delaying the publishing of his Hammerklavier Sonata because his metronome is not working properly.

The Mathematical Society publication's authors study two scenarios.

First, Beethoven drops his metronome and it falls standing up on the floor.  The fixed weight shifts down the beam so it is now farther away from the balance point. They show that this maladjusted metronome would register a different calibration of tempos.  As an experiment, for the "correct" metronome they place the fixed weight at 5 cm from the balance point; on the broken one they place it for comparison at 7 cm from the balance point.

Their results show that for fast tempi, the "broken" metronome in this case will go slower than the factory calibrated one. In order to get the "broken" metronome to beat at the same speed as the "correct" one, a higher calibrated speed needs to be chosen.

Second, the metronome falls upside down and the fixed weight shifts towards the balance point. Here's a description of what might have happened from the article: 

Let’s envision the following hypothetical scenario. Unknown to him, the metronome Beethoven 
is working with is damaged in the sense that the heavy weight hidden by the wooden case
has been displaced. Assume Beethoven puts the movable weight on his metronome to correspond
to the marking of approximately =110. Somewhat puzzled perhaps, he finds the visibly observed
marking seems far too slow, around =70 to 80. The markings on the metronome beam 
with the light movable weight that he can clearly see do not correspond to his desired tempo.
Beethoven, dissatisfied with the slow movement of the visible metronome beam, then
moves the weight until he is satisfied with the much higher marking.

Thus, in this experiment, a marking of ♩=110 on the correct metronome would correspond in speed observed to ♩=138 on the broken one. 

While a bold hypothesis, it's hard to argue with its suppositions. 

There is a small trend in symphonic music of performing Beethoven's symphonies at his prescribed metronome markings. Perhaps these recent investigations will put this practice to rest.

Here are some clips of performances using these speeds. Also scroll down to sample noted performances at different tempos.

Metronomes also have some "off-label" uses.  Runners sometimes use a metronome to calculate or maintain a particular pace by timing foot strikes with the beat. Elite runners have a gait that is about 180 strides per minute.

In a related story, I also heard on the radio yesterday that metronomes are being used to help improve chest compression technique during the administration of CPR.  It seems that blood circulates best when the heart is compressed at around 100 times per minute.  The show's experts suggested using Walter Carlos' "Fifth of Beethoven" or Queen's "Another One Bites the Dust" as reference points.

I prefer the first movement of Beethoven's Violin Concerto!!

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