Taking a break from Dave’s research we talk about Adam’s new direction into electrical engineering. This leads into a deep discussion on the properties of sound as we work our way into a neat new invention out of MIT.
Recorded September 7. Edited September 16. Published September 25, 2014.
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News
Note: Adam forgot that we already published the second episode of Dave's research. We'll do the plus1 (and final) episode of that next time. Probably.
As for a picture of the band, we couldn't find a free one. Here's something better.
Image footnote: — 1
Sound Science
Here’s a great (short) introduction to the sound theory stuff we’re getting into now.
Let’s give some better information here for what Dave was trying to say. If you have seen a traditional “sound wave” or “waveform” like what you see in traditional audio editing software, you will recognize this representation:
This is just a function, like back in math class. It just happens to be a bit more complex then the sine or cosine functions, but it’s basically the same. So the graph of this function has time on the horizontal axis and intensity (or decibels) on the vertical axis. If’s a formula like f(x) = [complex function], where x = time and the rest of it is some crazy compilation of altered sine waves that output the intensity of Adam saying “This little diversion into electronics.”
The other graph I was talking about it this:
To understand where Dave’s going with this, you have to remember that frequency is the physical movement of objects in space—the vibrations of the air molecules between your headphones and your eardrums, for example. Those are stupidly complex, but pitch is easier. That’s our perception of frequency. So a G-Sharp on a piano can be made up of many different levels of frequency, but they are all divisible by 25.96 Hz (which is short for hertz, which means cycles per second. Here’s a table of pitch frequencies if you’re curious.
(Also, the loudest frequency gives you the impression of the octave, but we’re going to ignore that.)
Now in the case of this spectral frequency visualization above, we are now talking about a more advanced mathematical process to get there. It is no longer the function that I described before. The graph still uses time for the x-axis, but the y-axis is now a distribution of frequencies that come from taking derivatives of the original sound wave. That was what Dave was trying to say: you take that “simple” function and create this multi-dimensional monstrosity that dives under your perception of pitch and reveals all of the hidden frequencies. Cool, right?
Interestingly, the color of the graph represents intensity (still decibels, but don’t worry about it). Notice how the lines look a bit like waves in a sand dune? That’s the timbre thing we were talking about earlier. These are the different harmonics of Adam’s voice. Look at this visualization of pitch:
The average pitch for the word “This,” in this example (the part between .1 and .3 seconds), is a B. So the sand dune waves that make up the first word in this phrase all rub across your ear drum, pile up in your cochlea, and then deep in your brain it gets turned back into a single dimension, about a B.
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