Another question regarding Well Temperament

[Richard Moody]

>     I have just finished a Broadwood 7' grand restringing and action
set-up,
> and last night put Paul Bailey's '92 well temperament on it.  This is a
very
> clean sounding tuning, and while it hasn't the contrast of say a
Kirnberger,
> there are numerous places in the temperament in which the M3 and m3 share
a
> proportional rate, (at least, the way I have it does).  These triads have
a
> clarity, yet at the same time, a lot of "activity", as Margo says.
> Regards,
> Ed Foote RPT

I have often wondered about the triads in ET as far as the beat rates go
between the M3, m3 and P5.  Here three rates interact.  If you take the
G(3)-B-D  triad, the G-B (M3) rate is 7.778 while the B-D (m3) is  13.327.
The ratio of these is 1.713 which doesn't seem too proportional (if at all)
and the numerical difference, or beat of the beat frequencies would be
5.549.   Further there is the .664 of the G--D 5th.  Now if this cancels
then the rate of the triad should be 4.885.
     The only notible coincidence arithmeticaly I could find is that
13.327/5.549=  2.401693998919  while 7.778/5.549= 1.401693998919  an EXACT
difference of 1 !.   Such an exactness to the 13th place is too signifigant
to be ignored, yet what does it mean??---other than a numerical
significance between between G--B--D  in ET, possibly some kind of
proportional.  I suppose if this is an aesthetic proportion depends on the
polls. All those who like ET raise their hands.
    Besides the musical dexterity of ET, perhaps this proportion has  some
kind of harmonic appeal just as the simple harmonic proportions of Just Int.
or Pythagorean or Meantone.  ---ric