August 24, 2009

Musica Universalis - Music of the Spheres Part 3

Good ________ (insert time of the day)!

Glad to have you all back here for today’s topic. Oh, wait, I see a few heads missing. Don’t tell me I’ve lost some of you to math?! Nooooo! Why oh why did you leave me?

*Coughs a few times*

After learning of your impending genius two weeks ago, I want to talk about harmonies beyond music. That’s right. The proportion between “perfect” frequencies cannot just be observed in music but on a much more macroscopic level as well. . .

“The Pythagoreans used music to heal the body and to elevate the soul, yet they believed that earthly music was no more than a faint echo of the universal ‘harmony of the spheres’.” (Kepler and the Music of the Spheres).

So how does that work? Well, basically, each planet = different note. The note depends on the ratio of the planet’s orbit around the sun.

This approach to our world was taken up by Copernicus (known for having confronted the fundamental belief of an Earth-centered universe). He used it to construct a first model of our solar system, using the harmonic ratios to predict the celestial bodies’ circular course around the sun.

There was just one problem: when looked at closely, it appeared the planets weren’t following those circular orbits. . .exactly.

And that’s where Kepler comes in, but that’s another story for another (next--to be more precise) time!

In the meantime, try to figure out what else in our lives follows the same harmonic proportions as musical notes :) (yep, I figured we’d end the blog entry with a fun game^^).


August 10, 2009

The Sound of Music - Music of the Spheres Part 2

Hello all! Finally, another post is ready (or rather I’m working on it, but by the time you read this, it’ll be ready . . . yeah, ok, you got it right?).

Moving on to musical notes and their sounds . . .

Pythagoras (yes, the infamous Pythagoras that devised the Pythagorean Theorem used in math) loved music too. At least, I suppose he did, for he investigated it quite a bit. And I mean, who would investigate something so profoundly unless he/she liked it? Well, actually, I just read (on Wiki) that he thought Greek music wasn’t really nice and wanted to make it sound better, using his super-mathematical-scientific-mystical-etc-power.

Anyways, he figured out that the pitch of a musical note depends on the length of the string being plucked (think about the lyre). So let’s say the musician plucks his string, and it produces a LA note. Well, if the string’s cut exactly at midpoint and the musician plucks that cord, then it’s also going to produce a LA note, but one octave higher (meaning 2 times higher). Pretty spiffy, huh?

Why does it work that way? Because the first string (the longer one), vibrates at a certain frequency which is ½ slower than the frequency of the shorter string, or, in other words, the second cord vibrates 2 times faster! This relationship is expressed mathematically as a frequency ratio of 1:2.

Of course, there are other ratios which Pythagoras thought were of the utmost importance, namely:

(1) the perfect fifth: frequency ratio of 2:3
(2) the perfect fourth: frequency ratio of 3:4

And these are the basis of musical harmony.

So, the key to this whole message, is that Music = Math.

Awesome, isn’t it? Basically, I postulate that anyone who likes music likes math! Yep, that’s right. Aren’t you amazed? You’re all innate mathematicians! Isn’t that one of the best things you could have ever found out about yourself? :)

With that, I’ll let you go!


August 8, 2009

Update on Blog

Good Morning/Afternoon/Night/Etc.

Quick news: because of time constraints (I finally realized how busy my week days, and Fridays in particular), I have decided to move the posting date to every second Monday.

Yeah, I know. I already can hear all your sighs of disappointment ('cause I just know how anxious you are to read the next episode of the Music of the Spheres series), but fear not. It's continuing, just a couple of days behind.

Also, the results for the poll are in (thank you to those who voted), and it looks like there will be some math on this blog. Yay! ^^ So for those who don't want any, well, sorry, you should have cast your vote. It's too late now to go back. But don't worry too much, I will do my best to simplify everything and explain everything AND, if you're still not satisfied with that, you can always post your questions in the comments section and I will answer them there :)

All right, my work conference is waiting for me. Hope you guys are all having loads of fun while I'm slaving away!


PS: You like the flowers? It's my way to apologize to you :3