Here’s what happens: by touching the string lightly while it’s vibrating, you cause it to come to rest at that point you’re touching. This results in another node, as shown above with the second harmonic. Touching the string at the 7th or 5th fret can make the third and fourth harmonics, with higher numbers of nodes.
But if you touch the string someplace that does not result in equal segments between nodes, no harmonic is produced and the string stops. This is simply math. Guitar players can tell you all the spots where harmonics can be produced, even if they don’t care too much about the math and physics behind it. (Some of them care though!)
via: http://clearscience.tumblr.com/post/3764564296/we-talked-about-frets-on-a-guitar-and-how-when-you
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