The Chronicles of Tau

I was wondering if I’d have a topic suitable for hailing in July and it turns out I do. Thursday being piano day, I thought it was particularly appropriate that I stumbled onto this fascinating video on YouTube, a video that proves you can marry art and science. There is so much math in music that I thought it would be of interest to all of you to see a music video that was produced entirely with a mathematical algorithm based on tau.

So you’re probably asking, "What the heck is tau? Never heard of it." Join the club. I too had never heard of it before tonight. We are witnessing history. According to Wikipedia, tau did not exist prior to January of this year when Cal Tech physicist Michael Hartl published a paper proposing that this new constant would make for more precise measurements than pi.

You all remember pi from high school algebra, right? Pi is the constant 22/7 that has been used by architects, engineers, and - you guessed it - mathematicians (among others), since antiquity to define the circumference of a circle and thus accurately measure it. It is probably the most commonly used and frequently used mathematical equation in history. The video credits the ancient Greek mathematician Pythagorus with having come up with pi but a quick glance at the encylopedia confirms that, though Pythagorus refined it, pi has been with us since the dawn of civilization. It can in fact even be found in the bible (though under a different name, of course.)

Pi is a curious little thing. I can’t remember from my high school math whether it’s unique among mathematical equations but, if not, it’s as close as you get. It is what is called a transcendental number because it cannot be solved. Mathematicians have been fascinated by this equation for millenia and have attempted to solve it for as long. Go ahead and try. Get out pad and paper and divide 22 by 7. You will find it cannot be done. It has an infinite number of decimal places and no pattern to the digits. Pi is typically referred to as simply the value 3.1419 but most mathematicians settle for a truncation of 50 decimal places. (For you math buffs 22/7, which actually calculates to 3.1428, is not the exact constant but very close and was used throughout history until Pythagorus refined it to 3.1419.) Throughout history, they’ve made a game out of solving the constant, trying to see how many digits they could calculate. In 1948, one of the first mechanical calculators was used to extend it to a record 1,120 decimal places. Personal computers can now be programmed to calculate it to billions of digits. A supercomputer can now do so to a trillion decimal places. And still no solution.

So why is pi so important? Because civilization is constructed on circles and pi allows us to accurately build a circle. So accurate is it that pi to just eleven decimal places will construct any circle used on this planet. In fact, pi to eleven decimal places can construct a circle the size of Earth to an accuracy of just one millimeter. Pi to 39 decimal places is sufficient to draw a circle the size of the entire observable universe to an accuracy the size of a hydrogen atom. Such is the power and the value of pi.

Why do I mention all this? Because pi as one of the great mysteries of the universe has been supplanted by tau, courtesy of our friend from Cal Tech per his paper published this year. Thousands of years of mathematical wisdom gone. Pi out, tau in. Put simply, tau is simply pi times 2, which Professor Hartl claims is far more accurate than pi, though I do not know whether his peers agree with this and, frankly, as a business professional who uses a lot of math but is hardly an expert, I find it unfathomable that something more accurate than a hydrogen atom would be at all meaningful.

Such as that is, we may be in a brave new world if Hartl has his way. But this essay is really about the marriage of mathematics and music and that is where tau has suddenly reared its beautiful head. In 2006, a big splash was made on YouTube with the so-called Pi Song. The musician who made the video simply took the value of pi, extended it to over 100 decimal places, and put every one of the digits to a musical note, thus creating what may be the first song ever generated entirely by a mathematical equation, even if it is only one minute long.

The cool thing is that it’s actually a pretty decent little tune - which is why it’s been a YouTube hit for five years. But then history was made again this week when, on June 23, another musician took tau and set that to music. Only this time, instead of merely setting each digit to a musical note, he used tau to create chords, cadences, and inversions – and even extrapolated a scale and tempo from it, all explained in the video. And then he actually created a symphony with it. And it’s pretty impressive.

Even if the Pi Song is not the first mathematically generated piece of music, this Tau sound certainly must be the first mathematically generated symphony and, at four minutes, it’s well worth listening to. This is tau extended to 126 decimal places. Just think what it would sound like extended to a thousand. If tau is making history, then the Tau Symphony certainly deserves a page in the books.

So, to usher out June and hail in July, and in honor of piano day, I present to you the Pi Song from 2006 followed by the Tau Symphony of 6-23-11.

Enjoy.

The Pi Song

Never mind the Pi music, here's what Tau sounds like (video)