source file: m1539.txt
Date: Tue, 29 Sep 1998 22:07:41 -0400 (EDT)

Subject: Re: Neutral Third

From: Johnny Reinhard <reinhard@IDT.NET>

On Tue, 29 Sep 1998 DFinnamore@aol.com responded to my comment below that:
> >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? 

There is no easy way to name the bisection of the perfect other than the
neutral third.  Its usage is certainly "thirdishable" compositionally.
When I speak of the neutral third of of 12 ET, I am basically plotting its
location -- as the bisection of the perfect fifth.  As a melodic interval
it easily suffers up to 5 cents tempering.  As such it even includes just
plottings, to a point.  Perhaps harmonically someone might object.  Not I,
apparently.  

> 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.

They seem to function for me as "thirds" regardless of their derivation.
Perhaps there is a special quality available to this particular interval
that is located midway within nature's dominant interval.

> 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'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'm note sure there is much of a difference harmonically, at least in
terms of function.  
 
The "neutral" quality is sort of like limbo, a DMZ zone, Switzerland (as
we once believed it to be).

Johnny Reinhard
AFMM

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End of TUNING Digest 1539
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