partial answers

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Allen writes:

<< ) His question is, “Why does the string divide into all of the

different available fractional segments and not just even multiples of two?”

I was hoping for a much better answer than just, “Because it does” but

Benade, Helmholtz and Rayleigh, the best I can tell, all assume this to be a

fact and I don’t really find the “why.”  Any thoughts >>

Greetings, 
        This gets back to "why God?" real quick.  Pythagoras thought it all 
mystical, super-rationalists just say "This is what is", old hippies just say 
it is proof of how far-out the world actually is, crystal-gazers just smile, 
like it is a fact that proves the unseen world exists. 
         I take the string behaviour I have observed as evidence that 
everything is happening at once, and when that string vibrates, every available 
multiple of the lowest frequency is not only a "natural" but also, a logical 
consequence.  I would find it odder if a string somehow vibrated at unrelated 
partials, or vibrated with only a few multiples.  
           It is possible, if one listened hard enough, frequencies could be 
found that corresspond to fractional multiples of the fundamental, but their 
amplitude is so low that we would consider them absent.  However, they are not. 
 Chaos theory would find a transitional point where the lesser frequencies 
are masked by those resulting from the simple ratios, but not obliterated.  So 
then it becomes more a question of why the ear evolved to hear only those 
frequencies that align with an organizing principle( partials corresponding to even 
multiples).   I believe that our hearing apparatus was pretty well evolved by 
the time strings were being used as musical instruments, so this is learned 
behaviour.  Gamelan music uses a totally different harmonic spectra, and is 
very musical, yet alien, to me.   

Most of us hear what we want to hear,anyway, it seems, so I suppose that is a 
partial answer...
         

Ed Foote RPT 
http://www.uk-piano.org/edfoote/index.html
www.uk-piano.org/edfoote/well_tempered_piano.html
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