source file: mills2.txt
Date: Wed, 15 Nov 1995 22:27:36 -0800

Subject: Re: TUNING digest 559

From: Gary Morrison <71670.2576@compuserve.com>

> The 12 tone equal temperament scale is derived from the overtone
> series of a vibrating string. 

   Of course most of us tuning listers will be prompt to point out that 12TET
doesn't provide a *really great* harmonic series approximation.  The 5th
harmonic is way sharp and it misses some really neat harmonics - 7, 11, and 13
for example.  It does, however, provide a fairly EFFICIENT mapping to the
harmonics it does match - matching the first 5 harmonics reasonably well on as a
coarse resolution as 100 cents, is in my view an impressive feat.  

   Buuuut, that's not the central focus of your question.  In response to your
question, I suppose it's worth pointing out that Brian is speaking about a
classification of tunings that ... well, I was starting to say "intentionally
avoid" harmonic relationships, but I suspect it would be more appropriate to
say, "make no effort to match" harmonic relationships.  

   I'm still catching up on Brian's NJNET posts, so I'm not certain of the
context behind his allusion to different vibrational modes.  Buuuut, everything
I've read of those posts so far suggest that they are based upon abstract
mathematical formulations (other than those of JI and ET), and not upon "found"
pitch relationships, by which I mean pitch relationships found in natural
vibrational systems.  

   That is unless of course he's found a NJNET mathematical formulation for the
vibrational modes of spheres or whatever.  I kind of doubt if those vibrational
modes are predictable by formulations like the inharmonic series formulations
he's mentioned (such logs of factorials).  

   So I kinda doubt if vibrational modes of physical structures other than
strings is his main point really.  Unfortunately, since I haven't gotten that
far yet, I'm not much good for commenting on what he was speaking of there.  


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