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Dan Levitan`s Mathematical Finding - Beethoven is most regular in regard to rhythm


Prof maps math of music, with Mozart least predictable

February 21, 2012 - 4:31am By BOB WEBER The Canadian Press

Elvis Presley once said that when you have rhythm, you have it all over. Now, a McGill University professor has used advanced mathematics to prove that The King was more right than he knew.

Daniel Levitin has found, hidden within nearly 2,000 pieces of classical music, a mathematical pattern that not only holds constant over 400 years of musical history, but also corresponds to fluctuations in everything from the human heartbeat to traffic flow on busy highways.

"I think it’s mind-blowing," said Levitin, whose paper was published Monday in the Proceeding of the National Academy of Sciences.

"Nobody’s claiming that the composers know the equation or were trying to fit their work to the equation (but) they’re writing music that conforms to it, perhaps because the brain responds preferentially to it."

Physicists call the equation in question a one-over-f power distribution.

In its simplest form, it’s a way of mathematically describing the relative frequency of events. In a one-over-f distribution, the second most common event happens half as often as the most common, the third most common event happens one-third as often, and so on.

One-over-f patterns are everywhere.

The formula describes annual flooding levels of the Nile River, voltage fluctuations in electronic components and traffic flow on U.S. interstates. It can be found in the signals across nerve endings, the minute variations of a human heartbeat, even in DNA patterns.

In the 1970s, one researcher found one-over-f in the pattern of pitches used in a small sample of classical music. Levitin said he’d always wondered if the same held true for rhythm.

"Rhythm is what gets you out of your seat, so I’ve been wanting to do this study for 20 years."

He and his colleagues took 1,788 different pieces of music by composers from J.S. Bach to Scott Joplin and broke each line of music down according to the length of its individual notes. Entering the data took 500 hours, but the result was worth it.

"What we found is that, like pitch, rhythm conforms to this one-over-f law," Levitin said.

There’s more.

The version of the equation Levitin used also contained a variable called beta, which refers to predictability. Levitin found the value of beta was unique to and consistent for each com-poser.

Beethoven was the most rhythmically predictable composer; Mozart the least.

"There’s a kind of mathematical signature that ties together all the works of an individual composer," Levitin said. "That was just astonishing to us."

Nobody knows why all this should be, but Levitin has a theory.

"Our brains have evolved over hundreds of thousands of years. Part of the evolution of brains is that they have to incorporate certain regularities and principles of the physical world, even ones we’re not aware of. There are these things that are built into the structure of the brain that follow regularities in the physical world. I think this one-over-f is something (like that).

"The brain knows about this one-over-f distribution even if we don’t. . . . It’s evidence that music may be tapping into structures of our brain."

About the Author
By BOB WEBER The Canadian Press


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