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Ever wonder why the fret dots are located where they are on a guitar? Typically they are located at the third, fifth, seventh, ninth and twelfth fret (and again at the 15th, 17th 19th etc…). Yes, they are visual markers for where you are, but they also coincide with something that is musically more basic.
A string will vibrate at its fundamental frequency. For example, the open A on the fifth string, properly tuned, vibrates at 110 hertz. If you cut the length of the string in half, keeping the tension constant, you will double its frequency. That’s what happens at the twelfth fret. On an A string, played at the twelfth fret, the pitch is 220 hertz, and an A one octave above the open string. That’s what it means for something to be an octave.
This brings us to harmonics. You can play a harmonic by putting your finger on the guitar at certain points, and removing your finger just as you pluck the string. People first learn this at the twelfth fret. There, it produces a tone that is an octave above the open string, and “purer” in sound. This harmonic is also called the second partial.
You can play harmonics at other places along the fretboard, and guess where they are? Yes, at each point where you typically see an inlaid dot.
The second harmonic, or third partial, is at the seventh fret. It divides the string into thirds. The pitch that it creates is a perfect fifth above the first.
The third harmonic, or fourth partial, is at the fifth fret, it divides the string into quarters, and it’s pitch is two octaves above the fundamental tone.
The fourth harmonic, or fifth partial, is at the ninth fret. The ninth fret is 2/5 of the way up the fretboard, and so there the harmonic divides the string into fifths. This produces a note that is a two octaves plus a major third above the fundamental note.
Notice that with these harmonics, we have now produced a major chord, including two octave notes, a fifth and a major third.
The fifth harmonic, or sixth partial is at the third fret. Here, the fretboard is divided into sixths, and as you might expect, the pitch from this harmonic is an octave higher than what you would get at the seventh fret.
What about the sixth harmonic, or seventh partial. This pitch is closest to a minor seventh, but is far enough away from what we use as a minor seventh that we do not actually use it. You could find it by dividing your scale length by seven, and (with really fresh strings) playing a harmonic at that spot. Compare that pitch to what you hear at the tenth fret, and you will find that they are significantly off.
By the way, in the olden days before electronic tuners, one of the best ways to tune a guitar to itself was to match harmonics. The Sixth string at the fifth fret harmonic is the same as the fifth string at the seventh fret. That applies also to the fifth and fourth strings, fourth and third, and second and first. For the second and third, you match the ninth fret harmonic on the third string to the fifth fret harmonic on the second string. Because of the purer tone of a harmonic, this is a surer way to tune, especially with slightly dead strings.
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