Conservative Octaves?

[Jim]

Dear Robert:

In your last post you mentioned: "my intent is to discuss what motivates
us to stretch our octaves".

I have been in long pursuit of this very thing.  There was a time when in
1948 I believed that an octave should be tuned with the fundamental
of the upper note exactly in tune with the 2nd partial of the lower note.
Man, have we come a long way.

While preparing for the TuneOff with Virgil Smith, I began to prove to
myself that what he was really doing was making the best match possible for
the single, double, triple and sometimes quad octaves.  In order to do
this, one must stretch the first single octave to the very limit and
do the same for the double octave in order for the triple octave to sound
like an even match.  This means that there must be at least 1/2 beat
increase of the 10th over the 3rd test just as long as the single octave
still "sounds" good.  The day before the test, I selected the next highest
stretch mode which Dean's program allows on the RCT.  This caused the A3 to
A4 stretch to be over a 1/2 bps (actually .6).  This is the most I have
ever stretched an octave using the 3rd-10th test.  The octave was
right on the edge of acceptability.  The double octave was a little
bit faster.  Many of the better Tuners have been following the idea of this
progression:  3rd < 10th < 17th.  If the 17th is not greater than the 10th,
then you will have a pure single (2-1 type) octave in the upper half
of the double octave.  This does nothing toward helping the triple octave
match.  I remembered that George Defebaugh always made the 17th faster
than the 10th.  In the early days of the tuning exam, we discovered the use
of the 10th-17th to prove clean single octaves in the C7 to C8 range.  But
we don't want clean single octaves coming up out of the temperament area
because it will be too difficult to have good triple octaves later.

If we do not strive for fairly close triple octaves, the top end of the
piano will usually sound flat to the musician.  One can prove this to
himself by doing a melodic/harmonic test which I have written about a few
months ago.  I'll repeat it if anyone wants it.

I thought Virgil Smith was being rather bold when he announced that he
could obtain good triple and sometimes quadruple octaves.  I now see how
he approaches that.  He has converted me. I think that this is also what the
musician wants to hear. So, you can now see who was the real winner in
the great TuneOff in Chicago.

Bob, since you were there, I would be interested in your reaction to
both of our tunings in regard to our octaves (try to disregard our few
less-than-perfect unisons).

Jim Coleman, Sr.