source file: m1540.txt
Date: Wed, 30 Sep 1998 14:57:20 EDT

Subject: Re: Neutral Third

From: DFinnamore@aol.com

Johnny:

The fifth-bisected neutral third may well be the most common kind; it would
obviously be the kind used whenever the third equally bisects a 
very impure fifth.  I simply recoil at calling it the only kind.  But 
it does seem like an interesting coincidence that both of the simplest 
13-limit rational neutrals fall within a few cents of dead center of 
3/2.

I wrote
>> 16/13 ... 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.

You responded
>I'm not quite sure what you're getting at here.  11/9 (347.4 cents) and
>16/13 (359.5 cents) are certainly distinctive intervals and each has a
>special relationship within its own number constellation (e.g. 11-limit
>and 13-limit).  Melodically, they would seem acceptable neutral thirds.

I'd agree that in most melodic situations 11/9 and 16/13 are virtually 
the same thing.  Further, it's probably sufficient simply to refer to 
the whole melodic zone in the middle as "neutral," and call it a 
bisected fifth.

>I'm note sure there is much of a difference harmonically, at least in
>terms of function.

That's easy; in octave-reduced terms, one functions as the 13th subharmonic of
1/1 and the other as the 11th harmonic of 16/9.  
(Like you didn't already know that :-)  Theoretically distinct but practically
the same?  It would be possible to construct situations 
in which the "wrong" one would produce unwanted beating - 12 cents 
is plenty for that; that's all I was getting at.  Perhaps in practice those
situations have been very rare.

David J. Finnamore
Just tune it!