Octave Stretch in other Lands

[Richard Moody]

> 
> In the middle sections we automatically listen to the 4:2, the bass
> the 6:3 and in the treble to 2:1.
> 
> 		Newton

I thought in tuning any octave, the second partial of the bottom note was
beating with the first partial of the top note.  When the octave sounds
beatless so are the 4th and 2nd partials and the 6:3.  If we are not
hearing the first two partials, how do we know which of the others we are
hearing?

Even though I use the 3rd--10th test, I do  not tune using tenths. (I
can't reach that far for one thing) That is supposed to be a comparison of
the 4:2 partials. But if I go back and tweek the octave again,  I assume I
am only hearing (tuning to) the 2:1 partials.  Even though the 3rd--10th 
involves the 4 and second partials in the octave  I never knew these to be
out of tune with the 2:1.   
Now if you get into double and triple octaves, and these are different in
bass and treble, and from piano to piano, that is another story, but there
you are trying to get at least the 12ths (and 19ths if you have the time
and the piano) to sound musical with your octaves.This is what I call
"stretching" octaves...taking your octaves wide(slightly) of pure to make
the fifths 12ths and 19ths and the piano as a whole "sound better".  

Richard Moody