Piano Strings

Hi,

Slowly I'm catching up with messages!

> There's a lot more to the design of the piano than
> you might have thought!

Yep. A most informative online article about gearing and friction, which
translates to piano actions, is on the NASA site. So I guess it's
official - it _is_, or at least it can be rocket science. ;)

Modern pianos more or less have plain wire inharmonicity double each
progressively higher octave; speaking lengths are reduced by about 47%
and wire by 2 sizes or so. Albert Sanderson's widely used IH formulas
were averaged from measurements of instruments (as with Robert Young's
<http://www.afn.org/~afn49304/young.html>, and others), and common
scaling factors are percent of tensile breaking strength, impedance and
'power'; yet other factors in the behavior of a wire include material
and temper, terminations, waste lengths, bridge mass, soundboard
stiffness, loading and mass, hammer mass, even other vibrating unison
strings and duplexes.

Many calculated bass string inharmonicity curves do no intersect that of
the tenor and treble strings, and which results in an audible break
corresponding with the physical one. Our rescaling attempts to correct
this and other problems in original scales, often yielding curves (since
IH influences tuning and stretch) to an extent that resemble the Rhodes
stretch tuning posted by Joe Monzo.

C.V. Raman's article "On some Indian stringed instruments"
(<http://www.geocities.com/ResearchTriangle/Facility/4118/raman/strings.html>)
describes vina and tanpura not obeying the Young-Helmholtz Law due their
special bridges; two articles discuss the presence - if reduced in
amplitude - of partials corresponding to piano hammer striking points at
string nodes (Young's cited in one for pointing out they aren't
missing): Donald Hall and Peter Clark's "The Question of Missing Modes"
(JASA 82, p1913-1918), and K.A. Legge and N.H. Fletcher's "Nonlinear
Generation of Missing Modes on a Vibrating String" (JASA 76, p.5-13).

Gabriel Weinreich's "Coupled Piano Strings" describes more in depth the
effects of deliberate mistuning of unison strings that Benade reports,
findings which John Sankey concludes affect single strings besides
(<http://www.geocities.com/Vienna/Studio/1714/string.html>). In quite an
interesting parallel of the influence mentioned here of pickups on
guitar strings, more intentionally, John Stuart (Stuart & Sons, AU) is
using magnets to change the vibratory patterns of piano strings.

Fourier transforms for three concert pianos are at
<http://wapin.com/howitworks.htm>, showing how variable are the number
of partials at least for one instrument family.

The amplitudes and even number of these partials can degenerate with
time, especially with wound bass strings and there have been a few novel
products intended to prevent build-up of dirt and corrosion with various
barriers, from plating to sprayed-on synthetics. (I never changed
strings when I played guitar - yuck!).

Clark

Clark wrote...

>Hi,
>
>Slowly I'm catching up with messages!

Hey, dude! Informative post, as always. Thanks.

-=Carl