Short answer: because math. Longer answer: because prime numbers don’t divide into each other evenly.
To understand what follows, you need to know some facts about the physics of vibrating strings:
When you pluck a guitar string, it vibrates to and fro. You can tell how fast the string is vibrating by listening to the pitch it produces.
Shorter and higher-tension strings vibrate faster and make higher pitches. Longer and lower-tension strings vibrate slower and make lower pitches.
The scientific term for the rate of the string’s vibration is its frequency. You measure frequency in hertz (Hz), a unit that just means “vibrations per second.” The standard tuning pitch, 440 Hz, is the pitch you hear when an object (like a tuning fork or guitar string) vibrates to and fro 440 times per second.
Strings can vibrate in many different ways at once. In addition to the entire length of the string bending back and forth, the string can also vibrate in halves, in thirds, in quarters, and so on. These vibrations of string subsections are called harmonics (or overtones, or partials, they all mean the same thing.)
If you watch slow-motion video of a guitar string vibrating, you’ll see a complex, evolving blend of squiggles. These squiggles are the mathematical sum of all of the string’s different harmonics. The weird and interesting thing about harmonics is that each one produces a different pitch. So when you play a note, you’re actually hearing many different pitches at once.
It’s not difficult to isolate the harmonics of a vibrating string and hear their individual pitches. Harmonics are very useful for tuning your guitar – here’s a handy guide for doing so. They are also the basis of the whole Western tuning system generally.
The math of harmonics is really simple
As a string vibrates, its longer subsections produce lower and louder harmonics, while its shorter subsections produce higher and quieter harmonics. Click the image below to hear the first six harmonics of a string:
... continue reading