Mathematics, applications of mathematics to life in general, and my life as a mathematician.
An orchestra of 120 players takes 70 minutes to play Beethoven’s 9th Symphony. How long would it take for 60 players to play the symphony?
If 1 woman can have 1 baby in 9 months, can’t 9 women have 1 baby in 1 month?
There didn’t seem to be enough information to solve the problem, so I looked into my personal music collection and online to find more data.
Here is what I found for Beethoven’s 9th recordings.
Berlin Philharmonic 60:10 125 musicians
Vienna Philharmonic 63:15 134 musicians
Cleveland Symphony 66:01 105 musicians
San Francisco Symphony 70:41 100 musicians
Chicago Symphony 74:52 100 musicians
Using this dataset, I calculated a least-squared linear regression and found that time = 102 minutes – 0.31 * musicians (with a mean-squared-error of only 8.64 minutes).
Therefore, a 60 member orchestra should perform Beethoven’s 9th in 83:24, give or take a few minutes.
caveat: the number of musicians is correct for each group at some recent time, not necessarily at the time of the recording in question.
I started this analysis as a joke, but the correlation seems stronger than mere chance. I submit the following theory. Prominent orchestras not only have more musicians, but more accomplished musicians and conductors, allowing them to maintain a brisker tempo through the presto sections. I intended to include the one data point from the problem statement, but it does not correlate well, so I left it out. I question the authenticity of your data! 😎
David, It could depend on the conductor.
It takes them 70 minutes, but they play Beethoven’s 4.5th.
63 minutes. That’s how long it took the London Classical Players, a period music orchestra of about 60 musicians directed by Roger Norrington, to play the 9th. I like their recording; others may have different opinions.
It can be an infinite time if some required players are missing!
Using the data of David’s Reynolds comment I found out that execution time decrease with increasing number of musicians but with a low number
of musicians as 60 the execution time will be between 70 and 75 minutes.
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