Tuesday, December 30, 2008

Taking the fun out of Music

I'd imagine everybody who reads this blog knows I play music. If you didn't... well there you have it. I play music.

I stumbled upon something that fascinated me about two years ago, and in discussions I found myself unable to clearly articulate or explain it. Therefore, I will write a bloggings on it to get that group of neurons in order.

We all know there is an underlying physics to music: sound/pressure waves, vibrations, acoustics. Most people have a concept of how plucking one guitar string turns into a Bb in the ear. Fewer people understand that the Bb plucked by a guitar is actually made up of several harmonics (vibrations with different frequencies) happening all at once (the loudest just happening to be a Bb)

The next step is making different pitches/notes. Some of us have noticed that one octave on a guitar means you put a finger right in the middle of the string (cut the length in half). Cut it half again to go up another octave. [if a 12 inch string play a C, a 6 inch string will play a C one octave higher, a 3 inch is yet another octave higher...). But what if you tire of C's? In western music, there are 12 notes in a chromatic scale. And for piano (and guitar) today, what is called an equal temperament is used to decide the length of strings (position of frets). This means the ratio of adjacent strings (or frets) is the same no matter which string you choose. Basically what it comes down to is that if an A is 100 inches long, an Ab is 5.9% longer, 105.9 inches long. If you make this step 12 times... you should come back to an A that is one octave lower and find it to be 200 inches long. So, the difference between each step is 2(1/12), the twelfth root of two (1.05946309...).

Sorry, that last paragraph was a little number heavy, but here's the catch. although pianos are tuned to this fixed interval, the natural order of pitches is based in simple ratios (not 2(1/12)) from the root. The intervals are:
1 9/8 5/4 4/3 3/2 5/3 15/8 2
You may note I did not include the full 12 note chromatic... this is because the 12 not chromatic CANNOT be tuned perfectly. an Ab will be tuned from a C by the relative difference of a major third (5/4)... This is going to be really freaking close... but slightly off. A major 3rd is four steps up the chromatic scale, you'll need three of that interval for an octave... therefore (5/4) * (5/4) *(5/4) should equal 2? Right... You can see it's actually 125/64... or just slightly more than 2. So if you start with a C, then tune an Ab from the C, an E from the Ab, then a lower C from the E... the ratio between Cs won't be two, as it should be... it'll be 125/64 = 1.95.

If you look at the chart above with an analytical eye, you'll find that none of the simple roots work perfectly. But with equal temperament, they all come out to 2 when expected. The downside to equal temperament is that the shape of the sounds waves is such that they interfere with each other. Using "just tuning" music will sound great in some keys (because the physical waves do not interfere and create beats)... but this can cause major problems in other keys.

Here's the skinny. Our modern tuning is extremely versatile, but doesn't exactly fit the nature of the sound waves being emitted. Other systems (which exist) can produce a purer sound, at the expense of versatility. I still think this is fascinating, but it's late. If you still care, start here, where you can hear a lot of what I'm talking about.

Wednesday, December 24, 2008

Hollywood Philosophy

Whew, long time no blog, here's a quick update on the center of the universe:
-I turned 25
-I had ankle surgery last Tuesday to get rid of some bone spurs and scar tissue. The surgery was far more intensive than anyone expected. Consequently, I've been in a lot of pain, but I am glad I did the surgery. It's clear my ankle would never have returned to any sort of normalcy without it.
-I still work
-My house is starting to look like a house. I have an $8 Christmas tree with one ornament and a star my girlfriend made from pipe cleaners.
-For Thanskgiving, the gf and I went to visit my parents. We had three busy days; Sonoma and Napa, San Francisco, and Yosemite. Good times.

I just finished hooking up a new DVD player that I bought my gf for Christmas. As all geeks are wont to do, I wanted to try it out. I put in my copy of House of Flying Daggers (beautiful cinematography and choreography) and watched the last few minutes.

It seems Eastern films and books portray hereos, not as super natural freaks, but more as humans that are maximizing their every potential. Superman was an alien, Spiderman was bitten by a radioactive spider, the X-Men are mutants...Batman and Ironman were both normal, however, both were born filty rich. But the heroes in eastern films like HoFD, Crouching Tiger..., and a lot of old kung fu are just human. They may have trained for years, or edured incredible hardships. For those watching Western movies the theme becomes: I cannot do incredible things without lucky difference. The Eastern heroes suggest: Work hard and anyone can take down the Leader of the evil Jaguar clan.

Asian heroes that do have super powers also seem to have a higher chance of living in a fantasy world. I suppose the western genre that proves me wrong are the Schwarzennegers, the Stallones, rarely possesing super powers, but still saving the day.

Anyway, this is the view from my seat... I'm curious to hear comment, especially from those with more exposure to Asian culture than I.