Difficult to design a piano that large.

[Delwin D Fandrich]

----- Original Message -----
From: <toto@fovea.pndr.upenn.edu>
To: <pianotech@ptg.org>
Cc: <toto@fovea.pndr.upenn.edu>
Sent: November 09, 2000 10:36 AM
Subject: Difficult to design a piano that large.


>
> > In air at sea level and at freezing the speed of sound is approximately
331
> > m/sec or approx. 1090 ft/sec.  It increases as temperature increases.
Using
> > this figure, the wavelength at 27.5 cps is 12 m or 39.6 ft.
>
> I would like to add that it is not necessary for the piano string to
> generate the fundamental frequency for the listener to perceive the
> fundamental frequency.  Our brains have evolved the ability to extrapolate
> the specific harmonics back to a fundamental without actually hearing that
> fundamental.  I once brought the topic up in my Physics of Acoustic
> class in college.  My question was in regard to a 2 inch speaker cone
> with a limited frequency response (eg: 300-10000 Hz).  How is it possible
> to hear a note significantly below the lower cutoff frequency?
>
> Remarkably, we extrapolate.
>
> Larry Toto
> ---------------------------------------------------------------

Larry, et al.,

(I know this showed up a few days ago, but I was headed out of town and just
now have gotten around to a reply.  It is an important issue, especially
with very small pianos.)

Yes, we do.  But only up to a certain point.  While I'm hardly qualified as
an Acoustical Physicist, I have read and studied a bit on this topic.  My
findings are hardly conclusive, but...

While our ears and brain do have a remarkable facility to extrapolate the
fundamental from the audible clues given by the harmonics, it does take some
finite amount of time.  When the bass notes of the piano are being played
rapidly, or when multiple bass notes are being played simultaneously, the
brain can easily be overloaded.  Or, possibly, they are simply not be given
enough time to process the information and come up with the correct answer.
At this point, unless there is at least some information (signal) at the
fundamental frequency, the sound simply becomes percussive.  These abilities
and perceptions vary among different individuals.

It appears that at least some energy at the fundamental frequency is
desirable, even necessary, for the ear/brain to lock on and identify pitch
during passages of quickly repeating bass notes or when multiple notes
(chords) are being played.  Exactly how much is very much open to question.

With the two examples I was testing some years ago one had virtually no
energy at the fundamental through the lowest octave and a half -- about half
an octave up, some very small amount of fundamental started showing up,
pretty much just a blip on the screen.  The other piano had between 5% and
10% of the energy in the fundamental (increasing from a minimum at A-1),
still not very much.  Played and compared note by note the differences were
obvious, but not dramatic.  Played in performance -- i.e., actually making
music --  the differences appeared to be much greater than the measurements
indicated.  The second piano drew comments (about the bass) such as 'more
articulate,' 'has much better clarity,' 'you can hear the notes,' etc.

We tend to think of the concert grand as being much louder than its smaller
counterparts, when in fact there is not all that much difference in the
acoustical output power that is directly related to the size of the piano.
Some, to be sure.  But, remember, we have to double the volume of a piano
for it to be apparent to our ears.  What we do hear is the much greater
clarity in the bass section resulting from the longer bass strings and the
design of the soundboard that puts much more acoustical energy in the
fundamental and lower harmonics.

Del