Duplex

[Clark]

> > Did I post already about that Taskin fp at Cité de la musique?
>
> I don't think so.

Yes, in June but only in passing, my observations were quite accidental
and unsystematic. It's from the 1790s, has secondary
bridges behind primary, with secondary string lengths open. Unusual
bridges, the duplexes mounted on second sound board.

This looks like the one, check the second photo.

<http://servsim.cite-musique.fr/museedelamusique/detail_notice.asp?ExtIDLink=OEUVRE567>


> How do you take the square root of a negative number?

That's easy! But doy, I dropped something. This should work

[r1c1={l}]
[r1c2={tdl}]
[r1c3=int((-1+sqrt[1+4*(r1c1^2)/(r1c2^2))))/2)]
[r1c4=r1c1*sqrt(1/((r1c3)*(r1c3+1)))]


> > I wonder, what would be the results of making front duplexes
> > proportional to strike lengths?
>
> Interesting thought. Should be easy enough to check against what 
> you've posted here (If I can figure out what you posted here). What 
> can you tell us? 

Less to do with Ron's scheme, my curiosity about strike lengths predates
this a little.

Young's law apparently isn't fully effective, what predicts the absence
of partials with nodes at striking or plucking points.  Transverse
string stiffness, for approximations of small displacement, shouldn't
affect but the position of nodes, partials still should be absent. These
partials are found to develop somewhat delayed of others and with
smaller amplitudes.

I have copies of three papers investigating the phenomenon, one of which
concerns causes not strongly present in pianos, rather an idiosyncratic
bridge design (Raman, C.V. "On some Indian stringed instruments", Proc.
Indian Assoc. Cultiv. Sci, v.7, 1921. p.29-33). Hall & Clark focus upon
irregular distribution of striking forces and soundboard compliance
("The question of missing modes", JASA v.82 nr.6, 12/87. p1913-1918);
Legge & Fletcher concentrate on bridge impedance (where square roots of
negative numbers come in) along with board compliance ("Nonlinear
generation of missing modes on a vibrating string", JASA v.76 nr.1
07/84. p.5-12).

It would seem, however, that fron````plexes are much simpler to handle,
coupling is much more direct and can be modelled without so much
reference to the entire system. An argument exists, I think that these
partials are supposed to be undesirable, but which doesn't explain about
modern strike points.

Anyhow, see if the stuff works now.


Clark