There is a trick guitar players use where they lightly tap a fret while plucking the string and making a high pitched noise. This is commonly called "playing harmonics". However even without any fancy tricks, a guitar player is playing harmonics. In order to understand this we need to know some basic physics on waves.
When someone plucks the lowest string on a guitar, you hear an E. You may think you are hearing just that one sound, but really you are hearing multiple harmonics and overtones combining to make that note and pitch. The dominating sound is the fundamental, this is the pitch we can hear.
A plucked guitar sting is a standing wave with two fixed points. The tension, density and length of the string all determine its note and pitch. waves travel slower on a more dense string and faster on a thinner string. This produces a lower pitch on the thicker strings and a higher pitch on the thinner ones. There are non-vibrating points on each string called nodes. a trick often used by guitar players is to lightly tap these nodes (found on the 5th, 7th, 12th and 19th frets), changing the length of the string and isolating one particular harmonic. This makes a high-pitched sound and raises the octave, depending on which harmonic is used.
To isolate the first harmonic pluck the sting and simultaneously tap it at the 12th fret (it takes some practice). The wave is divided in half which doubles the frequency and the note is brought up one octave. This blocks the fundamental and makes the first harmonic dominate. This has to do with modifying the length of the sting, therefor changing its frequency, the speed of the wave and its pitch. The length of the sting (L) is equal to 1/2 of the wavelenght. L=1/2(wavelength).
Blocking the string on the 7th or the 19th frets will divide the string into thirds. This time, both the fundamental and the first harmonic are blocked and the second harmonic dominates. This raises the note two octaves (L=2/2wavelength). The same thing occurs at the 5th and 24th frets but the string is divided into quarters, the fundamental, first and second nodes are blocked and the third harmonic dominates, raising the note three octaves (L=3/2wavelength).
The attachment below is me playing the fundamental, first, second and third harmonics (respectively).
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