standards

[Richard Moody]

> >>>  Richard West:
> >>>
> >>>  > I had two reasons for starting this thread:  1)  The PTG
exam is
> >>>  > based on clean 2:1 octaves, which is fine, but I don't
like the
> >>>  > results, and I don't tune that way.  I'm wondering if
others agree
> >>>  > or not,

I learned to tune aurally and was taught the 3rd--10th test and
the
"double 10th tenth" test.   I was never taught 2:1  6 :3 or any of
the other relations.  That came later from books.
To test if an octave is  "in tune you compare the 3rd to the
10th."  If they agree the octave is "in tune" which is according
to traditional aural methods and given in every book.
    Now if 2:1 is to be achieved that means the second partial of
the bottom note matches the frequency of the first partial of the
upper note in an octave.  However if you use the 3rd--10th test
you are comparing a 5 :4 ratio to a 5:2 ratio.  or comparing the
4th partial of the bottom note to the 2nd partial of the top note,
which of course can be called a  4:2 octave.
    Consider the "double 10th"  (or 17th) test.  Here the a 5:4
ratio is  compared to a 5:1 ratio; thus we hear the fundamental
(1st partial) of the top note beating (NOT or very slowly if you
are stretching) with the 4 partial of the lower note which is two
octaves below.
     I always assumed that these 3rd and 10th and 17th tests
"proved" the octave.  I do think they give "clean sounding
octaves"  Whether these are "clean  2:1 octaves I don't know or
really care.  I was never concerned about 2:1 until I took time to
study
the exact relation of which partials were actually causing the
beats I was hearing.
    I like the treble octaves and double octaves proved by the
3rd--10th--17th tests.   I can't tune without these test.  I think
we are assuming that if the 4  and 2 partials agree so will the 2
and 1.  If we want to consider the 2;1 nature of the octave we
must remember there are also the 4:2, 6:3 and 8:4 coincidents.
    These other ratios come into play in the bass.  While I follow
the 3rd
--10 tests going down, I also consider the octave +  5 (12th) AND
double octave + 5 (19th).   The 12th involves the 3:1 partials.
On many smaller uprights and grands it is impossible to get a
beatless octave of say  F2--F3, with a decent 12th of F2--C4.
Unless considered, you risk a "moaning 12th" (my term) which
sounds
like an slow echo bad reverb or actual mistuning.
    With a good scale I sometimes fine tune the temperament (OK,
read "fix mistakes") with the 12th and 19ths of the bass notes,
often down to F2.
    The bass is fraught with pitfalls for the aural tuner.  The
10ths below C2 can be heard according to the 5:2 partials or the
10:4 partials.  which is my excuse for when they get uneven, or
suddenly hard to hear.
    Richard Moody