We all know how to change notes on a guitar string. We place our fingers at specific and various places along the finger board known as “frets”. What fretting actually does is change the length of the string-no surprises here. But what are the mechanics behind using string length to change musical pitch?
Changing String Length
If you pluck an open guitar string, it will vibrate at a certain rate or frequency. So, for instance, if you pluck the open A string, it will vibrate back and forth at a rate of 110 Hz (Hertz). What does this mean?
Go down to the playground and push an empty swing, it will swing back and forth at a specific speed-let’s say 35 times per minute. Once you get it started, it will find the speed that it wants to swing back and forth on its own. Scientists and engineers call this speed (or frequency) the resonant frequency. A resonant frequency is simply the natural rate at which something wants to vibrate or oscillate. So the resonant frequency for a properly tuned A string is 110 Hz.
This means that after we pluck a string (just like we gave the swing a push), the string will swing back and forth (or vibrate/resonate) 110 times every second.
And as the string swings back and forth 110 times each second, it disturbs the air around it 110 times each second. And these disturbances travel through the air 110 times per second until they reach our head. Then they push our ear drums in and out 110 times per second and we “hear” an A note.
Now, let’s go back down to the playground. If we take our same swing and shorten the chains, what happens? Right, you’ve all seen it. The swing swings back and forth faster (perhaps 65 times per minute). Because the chains are shorter, the swing can’t swing as far. It makes a smaller arc. Since it doesn’t have as far to go on each “trip” or cycle, it makes more “trips” in each minute. So it has a higher resonant frequency.
A similar thing happens when we fret our guitar. If you measure the length of your strings from bridge to nut and from the twelfth fret to the bridge or nut, you will find that the twelfth fret is exactly half way between the nut and the bridge. What this means is, when you fret your guitar at the twelfth fret, you are cutting the length of your string exactly in half.
When you cut the string exactly in half, it is (caution, deep concept coming up!) only half as long. Since it is only half as long, like the swing, it doesn’t travel as far on each vibration so it makes more excursions per second. To be exact, it vibrates twice as fast. And this is what defines an octave. A note that is twice the frequency of another is said to be an octave above it. So when we play a note at the twelfth fret on our D string, we get another D note-this one an octave higher. Isn’t it cool how things work out like that?
Fretting different notes on the guitar is a convenient way of changing string length. Shorter strings vibrate faster (just as shorter swings swing faster). And faster vibrations are interpreted by our auditory systems as higher pitched notes. And notes that have frequencies that are half or twice as much as each other are heard as being an octave apart. Isn’t physics cool?