In applied statistics we have a very important and useful theorem called the Central Limit Theorem (CLT). This basically states that if you have several different random distributions at play in some process that with a large enough sample size two things will emerge no matter how different in shape the individual distributions are and even if these distributions are highly non-symmetric. These are:

1. If you add up the random values from the various and different distributions the resulting distribution will be the normal distribution (the common and symmetric Bell Curve). This will happen even if none of the underlying distribution are Bell Curves.
2. If you average all of the averages of the individual distributions, the result will be the average of the above Bell Curve.

I've always been fascinated by this; it's bigger than humans. It’s as if nature or God (or both) seek symmetry no matter what the process may be; from manufacturing ball bearings, to various processes in biology, chemistry, astronomy, etc.

The only example that comes to my mind in the music world is a large choir. Let’s say you have a 300 member moderately or poorly talented choir and everyone tries to sing the same note. Since we have 300 different random distributions, some will sing it flat and some will sing it sharp and maybe a few or none will hit it spot on. Yet, the CLT will tell you that the ensemble average (what the listeners hear) will be close to the target note and at least be recognizable if not pleasing.

I understand that the above will happen at the individual note-level and at the song-level.

My question is, has anyone seen this principle play out in music?

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For me there’s no better place in the band than to have one leg in the harmony world and the other in the percussive. Thank you Paul Tutmarc and Leo Fender.