## An Orchestra Puzzle

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?

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1. #### Jessica:

If 1 woman can have 1 baby in 9 months, can’t 9 women have 1 baby in 1 month?

2. #### David Reynolds:

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! ðŸ˜Ž

3. #### tanyakh:

David, It could depend on the conductor.

4. #### Austin:

It takes them 70 minutes, but they play Beethoven’s 4.5th.

5. #### Felipe Pait:

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.

https://www.gramophone.co.uk/review/beethoven-symphony-9-4

6. #### Ary Tebeka:

It can be an infinite time if some required players are missing!

7. #### Angelo Scordo:

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.