Dirty, Filthy Sound

I finally got around to reading through This is Your Brain On Music by Daniel Levitin. It's an excellent read even for non-musicians. Now, inspired by micro-scale analyses, I'm taking a look at what makes current popular music "tik" (you'll get that joke in a minute). It's deeper than just composing a catchy tune. You can engineer the next hit single down to literally a hair's width of sound. To appreciate that though, we need to know a bit about acoustics. If you never made it that far in your physics courses (don't worry, I didn't either), here's the illustrated, non-math version.

A pure sound is plotted over time as a sine wave, which looks like this.
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Keep in mind that this is just a single oscillation, so the sound it represents takes place over a tiny fraction of a second. The amount of oscillations that happen per second is the frequency in Hertz (Hz) and determines the pitch we hear. The height of the wave at any point (the amplitude) determines the loudness of the sound.

Sound is somewhat analogous to light though. The "white" light we see from the sun is not actually white, but rather a blend of many wavelengths of light that we don't perceive unless something external separates them for us, like a prism or an object that reflects only a certain color. Sound is similar in that a note produced by a musical instrument is not what we think of as a single pitch. The sound is composed of several different wavelengths stacked on one another (called harmonics), and are usually in multiples of the lowest frequency being played. So if a saxophone plays the middle "A" note, which is an oscillation of 440 cycles per second, what we really hear is a collection of layered frequencies:

440Hz (1st harmonic),

880Hz (2nd harmonic),

1320Hz (3rd harmonic),

1760Hz (4th harmonic)...

... etcetera, usually at decreasing levels of volume. Our brain then collapses the layers and tells us we're hearing only the first harmonic, the "A" at 440Hz.

When you add those higher harmonic pitches to the original sine wave at varying loudness levels, the shape of the wave starts to change. There's some intense math involved in the transformation process, but if your study habits are anything like mine, math homework is easily avoided with YouTube videos:

That animation shows us that by adding just the odd-numbered harmonics to a sound, the wave gradually becomes square-like. There are an endless number of final shapes depending on which harmonics compose a sound and what loudness each harmonic is at. And even though we only hear the 1st harmonic, our brain tells us what type of sound we're hearing based on that summative shape. Each musical instrument has its own, unique set of harmonics which is why we can tell a piano apart from a saxophone, for example, even when they're playing the same note.

Oh my, Saxophone! What sharp spikes you have!

The sum of the saxophone's unique set of harmonics creates sharp and rapid ups and downs which is part of what makes the sound much more cutting and abrasive than that of the piano. With computers, we can synthesize even sharper changes -- some too sharp to occur naturally.

These two staple synthesizer shapes are particularly strange because of the instantaneous amplitude changes in each oscillation. This will never occur in nature since it's impossible for an object to go from one position in its vibration to another position in zero time. Imagine a ball bouncing. No matter how hard you throw it at the ground, some amount of time will always have to pass for it to go from the ground to the height of its bounce. Synthesizers do a pretty good job of approximating these impossible jumps though, giving us the opportunity to hear unique and interesting sounds we wouldn't otherwise be able to experience. For fun, here's a range of frequencies for each wave form. Pay close attention to the lower frequencies and see if you can hear the shape. They sound about how they look.

Even if your ears are musically untrained, you can probably hear the sharp edges in the sound. You may not be able to count them at such high frequencies, but you can feel them -- a sort of rapid popping at the lower frequencies moving toward an artificial, electronic buzz at the higher frequencies. There's a sweet spot in these shapes from about 30Hz-200Hz where you can distinguish both the note being played and the shapes' characteristic popping. Make a melody with these frequencies and you'll have a tune where every note sounds like it's coming from something being violently ripped apart. The result therefore sounds destructive, cutting, and dirty.

And that's the hot thing right now. American popular music at the moment leans toward dance music (the extreme in visceral stimulation) so think of the potential these wave forms have! Imagine if you put a square or saw wave melody to a drum track that vibrates the room and then set the whole thing to a tempo of about 120-130 beats per minute to emulate the heartbeat of a dancing nightclub patron. You'd have one of the most physically energizing sounds possible! Oh, wait...

This general formula for success is already all over Top 40 lists. As much as I hate to subject you to Ke$ha, Tik Tok is pretty easy to parse: Square waves during the verses; low-frequency saw wave during the chorus; unrelenting drums; and a tempo of exactly 120 BPM. And did you catch the two saw wave bits in the first few seconds of the video, thrown in for good measure? If you want a more recent chart-topper and a bit more of a listening challenge, check out Britney Spears' Till The World Ends, which has squares and saws running at the same time.

The key to being a pop artist is to understand what's trending, then pack as much of it in your songs as possible. And that might mean exploiting even subtle cognitive processes like the way the saw wave's ripping sound evokes aggressive energy. Certainly Ke$ha's song wouldn't be as popular or dance-able if the synthesizer were replaced with, say, a piano (though our friend, Saxophone might be a contender). If Ke$a's producers can just tap into a formula of trends to create a hit track, shouldn't anyone with that formula be able to mechanically do the same? Consider this the intro to an inevitable future blog post entitled, "How To Write A Hit Single."