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Originally Posted by Kirk
Thanks for that aarona ... a much better explanation than mine ... as in 'right' as opposed to 'wrong'!
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Hey Kirk
I have read your explanation it's not "wrong", you are just explaining it from a different angle.
Personally I love this sort of stuff as the history of harmonics as we know them goes back to Pythagoras (500 BC). Of course they existed before that but he was the first to observe them the way we do today. Now I don't want to confuse the subject anymore but I thought I would add the following: [Someone tell me if this makes it worse & I will go & stand in the corner, facing the wall
]
1st) Most instruments produce harmonics, but guitar's harmonics are awesome because they are easily accessible & can be controlled. Yes guitars rule!
2nd) When you listen to an open guitar string being plucked, you consciously hear the note called the 'fundamental' i.e. pluck the open 5th string you hear a nice big A.
What you may not realize is that you also hear an entire series of 'harmonic overtones' coming from the sting, guitar body, & everything else physically attached. This is one of the main reasons a guitar sounds like a guitar, piano like a piano & a violin like a cat been tortured
, each instrument may play the same fundamental note (say A above ‘middle C’ ) but they all have different timbres (sounds) based on their harmonic series of overtones as they are all built differently.
3rd) Frequency: a note on a string is named after its frequency, or the amount of times that it vibrates, i.e. the open 5th string vibrates at 110hz (or vibrates 110 times per second) now if you double that frequency to 220hz you will have an A note one octave higher (3rd string; 2nd fret) & if you double it again to 440hz you will have an A note another octave higher (1st string; 5th fret), & if you double … you get the picture.
4th) Back to the series of ‘harmonic overtones’ on a guitar string. In addition to hearing the fundamental A on the open 5th string you are also subtly (but not consciously)hearing the other ‘A’s that are octaves above it, in addition you are hearing what they call the 1st harmonic , the 2nd & so on in ever decreasing audibleness, thankfully our ear only focuses on the fundamental. Also the harmonic overtones fade out before any dissonant overtones can be heard ( the dissonant ones really annoyed Pythagoras, maybe he should’ve stood in the corner, once he’d worked out the square root of it, of course
)
So, on the open A string there are lots of ‘A’s. Then there is the next harmonic one & a half octaves above that the ‘E’ note, then the next harmonic one and a half octaves above that the ‘B’ note and so on until they become impossible to hear.
5th) Playing harmonics on the guitar. When you play a harmonic on the guitar you are
isolating the harmonic overtone & making it audible. Personally I thought the above diagram was a little misleading, as it doesn’t clearly relate to scale length.
If you play a
harmonic on the 12th fret this creates a node point as described above & the string emits 2 vibrating lengths of string either side of the node point, the note you hear is exactly one octave above the fundamental i.e. harmonic 12th fret 5th string creates an ‘A’ note one octave above the open ‘A’ note.
Why? Because you have exactly halved the scale length of the sting & doubled the frequency!
Just imagine if you played the actual note on the 12th fret(the ‘A’ one octave up from the fundamental), the only difference is that instead of one part of the string vibrating between the 12th & the bridge, you have two equal lengths either side of the 12th fret vibrating in unison.
(Go on go get your tape measure out & measure the scale length of the string from the nut to the bridge, you will find that the 12th fret is exactly half way along this scale length)
If you play a
harmonic on the 7th fret this creates two node points (7th & 19th frets) & the string emits 3 equal vibrating lengths each side of the 2 node points, the note you hear is exactly one & a half octaves above the fundamental i.e. harmonic 7th fret 5th string creates an ‘E’ note, one & a half octaves above the open ‘A’ note.
Why? Because you have divided the scale length of the sting exactly by 3 by touching the node point exactly one third along the scale length of the string. (Hence you produce the note that you would on the 19th fret if you played a normal note, except you have 3 equal lengths of string vibrating in unison making a pretty bell like sound instead of just one little bit )
Obviously you have already worked out that the
harmonic on the 19th fret is exactly the same as the harmonic on the 7th.
If you play a
harmonic on the 5th fret this creates 3 node points (5th, 12th, & 24th frets) & the string emits 4 equal vibrating lengths of string either side of the node points, the note you hear is exactly two octaves above the fundamental i.e. harmonic 5th fret 5th string creates an ‘A’ note two octaves above the open ‘A’ note.
Why? Because you have divided the scale length of the string exactly by 4. (Hence you produce the note that you would on the 24th fret if you played a normal note (two octaves above the fundamental), except you have 4 lengths of string vibrating in unison making a pretty bell like sound instead of just one little bit )
If you play an
artificial harmonic, you are creating a node point exactly 12 frets above the fretted note & this creates a note one octave above the fretted note i.e. if you fret the ‘A’ note on the 3rd string; 2nd fret you would play the harmonic on the 3rd string on the 14th fret. This creates a node point exactly half way along the fretted string creating 2 equal vibrating lengths of string.
Why does it work? If you don’t know by now, you might want to go & stand in the corner with Pythagoras.
Dan
PS. I have just typed this on the fly, if I notice any mistakes I will edit it later.
. Here it is a link.
