Building bridges (was: JAWARI)

Hi,

There was a little discussion on the (um, slightly inactive)
new-musical-instruments list in August, led by a question whether this
could be used to tailor harmonicity and which I'd wondered, too.

Raman points out that when a plucking or striking point is on a string
node the corresponding partial should be missing from the resultant
sound. So-called (Thomas, I guess) Young's Law, he found this doesn't
apply to these instruments. There's some literature about a similar
effect in pianos, if not so pronounced, and which suggests reasons of
soundboard or bridge assembly admittance. Since the elasticity of this
less than stationary termination usually isn't uniform in every plane
the vibrations may not be either (more specifically these are the
vertical and horizontal planes, neglecting that drawn by the length of
the string at rest); much exaggerated, the same can be said for the
jawari, the way the string works.

Ed Foote posted recently that this is given for the cause of "false
beats" in pianos; however, I think non-uniform bridge elasticity is the
norm rather than exception and false beats, while common, aren't always
present. Well, Benade reported slight intentional mistuning of unison
strings; instead of beating, Weinreich observed within a range they
appear to lock phase despite their differing frequencies. Based on this
premise, Legge and Fletcher were able to build a simple model showing
the same for single strings with anisotropic admittance at a
termination, complete with the otherwise missing partials. Meanwhile,
Sankey (or rather, his son) explored the design of harpsichord bridges
and their effects to partial content and strength.

A start at least.

Clark

Raman, C.V. "On some Indian string Instruments". Proceedings of the
Indian Association for the Cultivation of Science 7 29-33 (1921)
<http://www.geocities.com/ResearchTriangle/Facility/4118/raman/>

Sankey, John. "Bridge Pins of Harpsichords".
<http://www.geocities.com/Vienna/Studio/1714/string.html>

Hall, Donald and Peter Clark. "Piano string excitation: The question of
missing modes". Journal of the Acoustical Society of America v.82 no.6
(Dec. 1987), p.1913-1918.

Legge, K.A. and N.H. Fletcher. "Nonlinear generation of missing modes on
a vibrating string". JASA v.76 no.1 (July 1984). p.5-12.

Weinreich, Gabriel. "Coupled piano strings". JASA v.62 no.6 (Dec. 1977).
p.1474-1484.

Benade, Arthur. "Tuning the piano", in "Horns, Strings and Harmony".
Anchor Books, Doubleday & Co. Garden City, NY. 1960. p.124-132. (Here,
or somewhere else he writes a little about non-uniformly loaded strings,
I think to explain conically bored woodwinds)

Hi, Clark. thanks for the information -- very useful.
Haresh.

--- In tuning@egroups.com, Clark <CACCOLA@N...> wrote:
> Hi,
>
> There was a little discussion on the (um, slightly inactive)
> new-musical-instruments list in August, led by a question whether
this
> could be used to tailor harmonicity and which I'd wondered, too.
>
> Raman points out that when a plucking or striking point is on a
string
> node the corresponding partial should be missing from the resultant
> sound. So-called (Thomas, I guess) Young's Law, he found this
doesn't
> apply to these instruments. There's some literature about a similar
> effect in pianos, if not so pronounced, and which suggests reasons
of
> soundboard or bridge assembly admittance. Since the elasticity of
this
> less than stationary termination usually isn't uniform in every
plane
> the vibrations may not be either (more specifically these are the
> vertical and horizontal planes, neglecting that drawn by the length
of
> the string at rest); much exaggerated, the same can be said for the
> jawari, the way the string works.
>
> Ed Foote posted recently that this is given for the cause of "false
> beats" in pianos; however, I think non-uniform bridge elasticity is
the
> norm rather than exception and false beats, while common, aren't
always
> present. Well, Benade reported slight intentional mistuning of
unison
> strings; instead of beating, Weinreich observed within a range they
> appear to lock phase despite their differing frequencies. Based on
this
> premise, Legge and Fletcher were able to build a simple model
showing
> the same for single strings with anisotropic admittance at a
> termination, complete with the otherwise missing partials.
Meanwhile,
> Sankey (or rather, his son) explored the design of harpsichord
bridges
> and their effects to partial content and strength.
>
> A start at least.
>
>
> Clark
>
>
> Raman, C.V. "On some Indian string Instruments". Proceedings of the
> Indian Association for the Cultivation of Science 7 29-33 (1921)
> <http://www.geocities.com/ResearchTriangle/Facility/4118/raman/>
>
> Sankey, John. "Bridge Pins of Harpsichords".
> <http://www.geocities.com/Vienna/Studio/1714/string.html>
>
> Hall, Donald and Peter Clark. "Piano string excitation: The
question of
> missing modes". Journal of the Acoustical Society of America v.82
no.6
> (Dec. 1987), p.1913-1918.
>
> Legge, K.A. and N.H. Fletcher. "Nonlinear generation of missing
modes on
> a vibrating string". JASA v.76 no.1 (July 1984). p.5-12.
>
> Weinreich, Gabriel. "Coupled piano strings". JASA v.62 no.6 (Dec.
1977).
> p.1474-1484.
>
> Benade, Arthur. "Tuning the piano", in "Horns, Strings and Harmony".
> Anchor Books, Doubleday & Co. Garden City, NY. 1960. p.124-132.
(Here,
> or somewhere else he writes a little about non-uniformly loaded
strings,
> I think to explain conically bored woodwinds)