Tuning

[Howard S. Rosen]

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> From: DGPEAKE@aol.com
> To: pianotech@ptg.org
> Subject: Re: Tuning
> Date: Thursday, September 25, 1997 7:00 PM
> 
> How can you get an equal temperament using perfect 5ths?

If 5ths are pure (not contracted), all of the 12 intervals within the
octave will correspondingly be expanded (even the octave itself). Since all
of the intervals are still equal, then it is equal temperament. You may not
like it but all the intervals will be the same no matter what key you are
in. 

> If it is possible to
> have perfect 5ths, your 4ths will be wild. 

They will be wider than what you are accustomed to, but not *wild*. Matter
of opinion, I guess.

> Then it is not a tempered scale.

It is, because the slightly larger octave is still divided into 12 equal
intervals. 

>  This is the 
> reason we narrow the 5ths and widen the 4ths.

The reason we narrow 5ths and widen 4ths by the amount to which you are
accustomed, is to have 12 equal semitones within a 2:1 octave. Jim Coleman
Sr. and many tuners before him suggest that a 2:1 octave is too small. If,
when you get to the 5th and 6th octave of your tuning (starting with a 2:1
octave in the temperament), you check triple octaves listening melodically,
you will then hear how flat it sounds. Stretching the octave in the
temperament helps to solve the problem. The question is BY HOW MUCH? Jim
Coleman's suggestion (answer) is ...by the amount it takes to stretch a 5th
from its normally contracted form to its pure form.
TRY IT. YOU'LL LIKE IT!
 
> 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.  

But your triple octaves will sound flat and be flat. They will be musically
unsatisfactory.
 
> I used this method in my tuning exam and scored in the 90% range.

That is because the criteria set for the tuning exam piano was established
by tuners using the same system. Tuners will always disagree about tuning.
I guess that's why exams have to be set up for the best way to STANDARDIZE.
Tuning with pure 5ths, in my opinion, yields a much more musically
satisfying result because it stretches the octaves smoothly all the way to
the top. Inharmonicity demands that stretching be done. The question of how
much will always be debateable.

Howard S. Rosen, RPT
Boynton Beach, Florida