Klarinet Archive - Posting 000319.txt from 1999/11

From: "Roger Kronqvist" <omega@-----.au>
Subj: Re: [kl] KEYS
Date: Tue, 9 Nov 1999 14:11:15 -0500

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----- Original Message -----
From: David Renaud <studiorenaud@-----.com>
Subject: Re: [kl] KEYS

> 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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