Music, maths, and universal harmony
Sometimes, things just seem to pop up in my mind for no apparent reason, and today, it was this particular curiosity: 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +… (the reason I’m thinking about mathematical series may have something to do with my maths exam coming up, but that’s another matter). Now, this series is called the harmonic series, and if you keep adding the terms in this sequence forever, you’ll actually reach infinity, believe it or not.
Something I find quite interesting is that this particular mathematical construction is actually closely related to music. When you play a note on an instrument, what you hear is a mixture of several pitches called harmonics. The note you hear has a frequency called the fundamental frequency, and the other tones are not perceived as separate notes, in fact, they are what determines the sound of an instrument.
Now, what is fascinating is that the harmonics have frequencies relating to the harmonic series, they are 2, 3, 4, 5 … times the fundamental frequency. And also, the way most scales and chords are constructed revolves around the fractions in the harmonic series. Two or more notes that are sounded together whose frequencies have ratios found in the harmonic series will produce what most western people consider a pleasing sound. Now, if you double the frequency of a note, the new note will be an octave above the original, a musical interval recognized around the world. Three hundred years ago, when nobody had heard of global warming or Internet Explorer, J.S. Bach made music that still touches the hearts of people today. This music is based on principles derived from something which is presented as a curiosity in my math book.
Another one of these facts that refuse to leave my brain is that the latest findings in cosmology suggest that the universe is flat. A flat universe is a mathematical possibility that relies on the density of the universe being exactly equal to a certain critical density, and even the presence of a single extra electron is enough to destroy this. One electron, ladies and gentlemen, a fundamental particle with a mass of 9.109 3826(16) × 10–31 kg.
Yes, it is possible that this is all just a coincidence, but there seems to be many of these coincidences popping up in my brain lately. Now, the way I see it, the theory that we are at the mercy of a random universe just seems a bit off. The pieces of evidence against it may seem small, but there are many, and remember, many small drops will someday make an infinite river.
May 10th, 2007 at 2:39 am
Hmmn… I don’t believe in coincidences.
Hey, your post made me think of something - I think we discussed this in my Art Appreciation class or one of my Math classes… There’s an exact number of songs that can be created in the universe - I think you can solve it by permutation. That’s why some new songs actually sound like old songs - they can have the same melody but still be different (which when you think about it, still makes them basically the same - am I making sense to you?).
BTW, I really enjoyed reading your blog. I’ll definitely be back.
May 11th, 2007 at 1:28 am
WOW. You’re quite intelligent! That’s a very interesting thought but too intellectual for my creative, imaginative mind.
Sho
May 11th, 2007 at 4:27 pm
well, quite honestly, i understood very little of this blog, even though I did finish Calculus BC two years ago (maybe it’s because I haven’t taken math SINCE then!), but the thing about infinitely small numbers eventually adding up to infinity reminded me of a paradox from one of my math classes a few years ago: if you shoot an arrow at a tree, it goes halfway, then half-halfway, then half-half-halfway, and so on, forever, so by that logic it would never actually reach the tree! but it does.