Mike Macgirvin
Diary and Other Rantings
Beyond Silicon Valley
   
Monday, Jul 07 2008, 12:55 pm
Feb 24, 2006
Musical theory in a nutshell

There are a few musical notes that always go well with each other. They call it 1-4-5. In the key of A, the notes are A-D-E. This is the fundamental progression of 90% of western music. But why? Why are there 12 notes in an octave? Why can't there be 17? We'll ignore sharps and flats. Sharps and flats are an exercise in chaos theory dreamed up by an ergotine-crazed madman. Why do some notes have half steps and some whole steps between notes? Whoa! One thing at a time. We'll cover that another day. 

So what is it about these three notes that makes them sound good together? 

Simple. Convert to frequency. Let's use A=440hz. The 'D' below it is 293.66 hz. What's magic about this? The ratio 0.667470909. It's the closest note in the European scale to (2/3f) where f = 440. What about E? 329.63hz. Or a ratio of 0.74915909. It's the closest note in the European scale to (3/4f).  So the entire reason why notes sound good together is because they have simple frequency ratios. What about (1/4f, 1/2f, and 2f)? Those my friend are octaves.  They always sound good together.

Now let's ask the next logical question - so then why are there 12 notes in the European scale instead of 17 or 22 or something else? Go back to 7th grade math. What's the lowest common denominator of our magic good sounding ratios 2/3 and 3/4?

Bingo! 12 (2/3 -> 8/12 and 3/4 -> 9/12). Therefore, if you want to have a musical system which includes both 2/3f and 3/4f (our good sounding frequencies), the minimum number of unique steps it needs to have (if the steps are assumed to be equal) is 12. In fact, you need to have twelve steps between 1/2f and 1f (or 1f and 2f).

[...An interesting side note is that if you have a digital frequency source, 293.33333 makes a better sound with A than concert 'D'. Likewise 330hz is a more perfect E than E itself. That's because these are perfect ratios, unlike the European scale which is based on centuries of compromise and rounding errors.] 

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Feb 22, 2006
Speaking of drugs...

The 'Love Parade' is being revived in Berlin. The European rave festival was shut down a few years back because there was no way to pay for cleanup costs. Looks like they've found a corporate sponsor (McFit - an exercise chain) to pay for the garbage trucks.

Love Parade, indeed. It should probably be called "A week of X". Hope the pharmaceutical companies have pumped up their inventories. One and a half million people doing Ecstasy, speed, whatever -  and dancing 24/7 for a week or so to content-free techno-pop. You do the math. Actually, I wonder if anybody approached the pharmaceutical community for sponsorships... 

Comments:

Cindy
February 22, 2006 16:26
Cindy
I had no idea the 'Love Parade' had been shut down. I'll have to consult my Berlin friends about that!

meanwhile, I encountered this error when accessing this page via Firefox:

Warning: Invalid argument supplied for foreach() in data.php on line 99

thought you might like to know :-)


mike (Mike Macgirvin)
February 22, 2006 18:35
[*TOP MEMBER*] mike
Yeah, I've been fighting that function... it's a spider checker. it hasn't been working well and it's darn rudimentary, it loops through a static array with two hardcoded entries (currently) and returns a yes/no result - beginning to think it's a php bug. I'll write it another way until I can trace it through.

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