Klarinet Archive - Posting 000298.txt from 1999/11

From: David Renaud <studiorenaud@-----.com>
Subj: Re: [kl] KEYS
Date: Tue, 9 Nov 1999 07:16:15 -0500

Edwin V. Lacy wrote:

> I'm having some trouble understanding this. The perfect 5th is one of the
> two intervals in the tempered scale (the other being the perfect octave)
> which can be tuned on the piano without any beats between the two notes.
>

Fifths must be slightly contracted, and fourths slightly expanded, or equal
temperament
becomes nearly impossible. All existing piano tuning method books teach this.
This has been accepted as fact since equal temperament has been practiced.
But your right that the quoted speeds are too fast.The accepted beat rate is
less
then one per second on the progressing 5ths. More like an average two beats
every
five seconds in the temperament but varying up and down the piano.

There are a few proponents of pure fifth tuning. This is a radical stretch.
If you write me I will refer you to articles on it.A "pure fifth" tuning
results in very fast thirds, and very stretched octaves on a piano.Dr
Sanderson(inventor the the accutuner used as a reference by many concert
technicians)
,and Jim Colemen,RPT, have written extensive articles on this for the Piano
Technicians Guild.
Furthermore a pure fifth at the 3:2 partial level(correct tuning) still beats
at the expanded
6:4 coincidental partial level. Beatless at the 6:4 level (incorrect 5th)
beats at the 3:2 level.
You can never have both. All the partials will never in reality line up at
all levels.

Even the humble octave can not be pure at all coincidental partial levels.
Matching between 4:2 and 6:3 coincidental partials is accepted in the
midrange,
6:3 or more in the bass, and there is a great deal of diverse opinion about
the top end,
but most tuners go for about pure 3:2 fifths as they work up a piano.

Furthermore pianos tends to lie. We had a guild technical seminar tonight with
several
prominent technicians from a 150 mile radius attending including our National
Arts Center
technician. We tuned the three strings of a unison within one tenth of one
cent accuracy
with a very very expensive machine and yet it was noisy. Upon correcting it by
ear we
found that the strings at to be offset by 0, -.8, and -1.7 to get a pure pure
sustained unison.
This is allot, but that is how big the inharmonisity variations were just
between a unison in a
Yamaha U1 in practice against theoretical. The point being the stiffness of
the
string makes higher harmonics increasingly sharp relative to theoretical, this
varying greatly
string to string. Getting nearly "pure", slightly contracted fifths in
reality takes a great deal
of cheating, and something in the harmonic structure is always, always left
beating. The
human ear will tend to focus on the lower harmonics, and be fooled into
thinking everything
is pure when it is not. With training to focus on higher harmonics it can
sound like a real mess.

This is why low bass on very small pianos suffer. The shorter strings are
thicker to compensate,
thus stiffer. The stiff string has sharper harmonic content, and can become
almost impossible to
tune, without gross compromises as one must choose some partial level to line
up, and the
other coincidental partials will still sound poor.

Tuning is always a compromise at all levels.

Sincerely
Dave
Renaud

Registered Piano Technician

> I wonder if what you are describing is the frequency of the "difference
> tone," a pitch or apparent pitch which is generated by the frequency
> differential of two notes? The difference tone between the two notes of
> any interval will be higher if the interval is transposed to a higher
> pitch, so perhaps this is what you were mentioning.
>
> It is true that there is a difference between the perfect 5th in the
> tempered scale as compared to the Pythagorean scale (as well as others),
> but the difference is relatively small in this case. The 5th in the
> equally tempered scale will equal 700 cents, or 100ths of a semitone,
> while in the Pythagorean, the 5th consists of 702 cents. However, even in
> this case, the perfect 5th will produce beats at a frequency nowhere the
> magnitude you described.
>
> Having taken a course in acoustics many years ago, my memory could
> certainly be faulty. But, your thesis as stated above is precisely
> contrary to what I have taught and have read concerning the topic.
>
> Ed Lacy
> el2@-----.edu
>
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