Harmonic Series Guitar

I was reading some stuff about the derivation of musical scales - the math behind why things sound the way they do - and came upon the harmonic series.

The harmonic series mathematically is the series (a sum) like this:   1+1/2 + 1/3 + 1/4+1/5 +.... +1/n up to infinity.  In nature there are natural resonances in vibrating objects (like a guitar string, or organ pipe) that are these ratios of the string or pipe's length, so there's thinking these resonances may be related to why musical scales sound good to us.

From the "A Mind For Madness" Blog, this blogger (that ties the harmonic series to musical overtones and discusses the idea that perhaps the musical scales used have their "musical-ness" due to their relationship to this natural resonant properties that's expressed in the harmonic series. I first read about this idea on his blog, so I'll give credit there, although it's entirely possible this idea may be out there elsewhere.

 Vocalist showing the harmonic overtone capabilities in his voice - kindof freaky right?

Now obviously, from the above video you can tell that the resonances don't tie directly the current dominant equal tempered musical scale that we have, but there are many resonances that happen right on the musical scale where we have musical notes.  The 7 note in this video (click link) really stands out as being foreign to our current musical scale, but most of other note positions are familiar.

Hear the harmonic scale in action. Here's guitarist Dante Rosati who's composed a piece of music using the harmonic scale.  It's definitely different, but something foreign it's still quite cohesive and even a bit hypnotic if you ask me.  Pretty cool stuff.