source file: m1539.txt
Date: Tue, 29 Sep 1998 11:11:40 EDT

Subject: Re: Neutral Third

From: DFinnamore@aol.com

Thanks for the explanation, Johnny R.

>the neutral third is always dead
>center, dividing the fifth into 2 identical parts.  Just as the tritone
>bisects the octave, the neutral third bisects the perfect fifth.

That's a very interesting observation.  It seems reasonable to identify some
neutral thirds as fifth-based tritones, so to speak.  But is "always" the best
term here?  Would you contend that they're not really "thirds" in the same
sense that 5/4 is, that they're really based on the fifth?  That would seem to
fly in the face of rational analyses based on higher primes, unless you mean
to say that rational intervals that fall approximately midway are something
other than neutral thirds.

>The neutral thirds of all the meantones, 12-TET,...

There are, of course, no neutral thirds in historical 12-tone meantone
tunings, least of all 12-tET.  Whatever could you mean?

>[snip] The difference of a few cents in either
>direction from 351 cents (at perfect fifth of 702 cents) is negligible for
>musical purposes.

Hmm.  So an otherwise 11-limit sonority would be just as consonant with a
16/13 as with an 11/9?  They're about 12 cents apart.  That seems equivalent
to saying that there's no musical difference between a 12-tET major 7th and a
just 15/8.

I like the concept of dividing the fifth equally like the octave has long
been.  It could be extended to any x/2^y, or maybe even to any rational
interval.  Maybe those should be called "the perfect fifth tritone,"  "the
major third tritone," etc. as distinguished from "the octave tritone."  But
should the definition of the neutral third be limited to "the perfect fifth
tritone"?  To me, its potential musical usage seems to be broader than that.

David J. Finnamore
Just tune it!