Tuning

[Jim Coleman, Sr.]

Hi Dave:

My comments are interspersed below.

On Thu, 25 Sep 1997 DGPEAKE@aol.com wrote:

> How can you get an equal temperament using perfect 5ths? If it is possible to
> have perfect 5ths, your 4ths will be wild.  Then it is not a tempered scale.

That is just the point of the Pure 5ths temperament, the 4ths will be
faster, but they will progress evenly, just as the M3rd, m3rds, 
M6ths and the m6ths will do.

Besides the 4ths being faster, the octave will be spread more. If 
you have a SAT available, try adding about 1.5 cents to the measured
stretch value of the A4 and tune the temperament. You will find that
almost all of the 5ths will be pure, but the 4ths will be wider and you
may at first hate the wide octave A3-A4.

At the Olympia one day seminar held on Saturday the 13th the pure 5ths
tuning was overwhelmingly favored inspite of the wide octaves and busy
4ths. The vote was 197 to 149

I think I can help you to see by using this example.

We are so used to tuning almost pure octaves, that the idea of 
stretching them as much a 1 bps is just revolting to us. But, we have
tolerated 1 bps 4ths for years and thought nothing of it. The 1 bps
4th does not bother us at all when we are listening to music. Neither
will the 1 bps octave bother us at all when we are listening to music.
Perhaps one might suggest that the 1.5 bps 4ths would bother us. Well,
I hardly think so when I consider that we are accustomed to hearing
7 bps M3rds and more in m3rds.

I guess you'll just have to try it for yourself and see if you like the
music. I will tell you this from many experiences, the overall sound
of the piano takes on a new dimension of solidity where double, triple
and sometimes quad octaves sound better than they ever have before.

>  This is the 
> reason we narrow the 5ths and widen the 4ths. When I tune aurally, I stack
> the 3rds and check the 4ths and 5ths (up a 3rd, down a 5th) and if I have a
> gradual progression of beats in the 3rds and 6ths, and no wild 4ths and 5ths,
> you will have a tempered scale.  

Your system of tuning by 3rds and 5ths will really lend itself to tuning
by pure 5ths. The only thing you will have to do to make sure you 
end up with equal temperament is to make sure that your octave is 
expanded first (about 1 to 1.5 bps), then you must divide that octave
up evenly with your 3 M3rds (they will be a tiny bit faster, and to 
insure that you have not skewed the progression rate, extend an extra
contiguous M3rd outside the octave and make sure that octave is also
expanded), then when you drop down a 5th from the second M3rd, tune it
pure. I think in your case, I would suggest that you tune up 3 M3rds to
get the octave for purposes of checking the octave stretch, then drop
down a 5th from the second M3rd again as you usually do. In all this,
I am assuming that you use the Faust temperament or the John Travis
temperament.
> 
> I used this method in my tuning exam and scored in the 90% range.
> 
It's a good thing that you used your regular temperament, because the
Pure 5ths temperament was not designed for passing the PTG tuning test.
It was designed to make the whole piano sound better.

> Dave Peake, RPT
> Portland, OR
> 
Thanks for your comments and please write again if you still have some
questions. This may help others who were too bashful to understand it
better.

BTW, I remember how kind you were to me to pick me up at the airport
in Portland and you hosted me at your home. Give my best regards to 
your family.

Jim Coleman, Sr.